bridge
DESCRIPTION
WeuhgtTRANSCRIPT
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Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by
![Page 2: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/2.jpg)
, (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
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4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.0 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is
![Page 4: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/4.jpg)
balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010
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511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
![Page 6: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/6.jpg)
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
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3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
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4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resist Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is
![Page 9: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/9.jpg)
connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *)
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RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?
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For example: if the indication o Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by
![Page 12: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/12.jpg)
, (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
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4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.0 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is
![Page 14: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/14.jpg)
balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010
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511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the une Wheatstone bridgeGoal
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Learn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)
![Page 17: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/17.jpg)
where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
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4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.0 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is
![Page 19: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/19.jpg)
balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010
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511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+30 Wheatstone bridge
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GoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)
![Page 22: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/22.jpg)
where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
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4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.0 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship:
![Page 24: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/24.jpg)
. (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W201051
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1/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a re Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
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IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridge
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In procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
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4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse
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adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
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3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For exa Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these
![Page 31: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/31.jpg)
meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move
![Page 32: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/32.jpg)
for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.
![Page 33: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/33.jpg)
According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
![Page 34: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/34.jpg)
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)
![Page 35: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/35.jpg)
Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For exa Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an
![Page 36: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/36.jpg)
ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move
![Page 37: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/37.jpg)
for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.
![Page 38: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/38.jpg)
According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
![Page 39: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/39.jpg)
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)
![Page 40: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/40.jpg)
Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitan Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an
![Page 41: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/41.jpg)
ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move
![Page 42: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/42.jpg)
for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.
![Page 43: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/43.jpg)
According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.0 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
![Page 44: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/44.jpg)
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)
![Page 45: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/45.jpg)
Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=3000 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these
![Page 46: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/46.jpg)
meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move
![Page 47: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/47.jpg)
for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.
![Page 48: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/48.jpg)
According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.0 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
![Page 49: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/49.jpg)
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)
![Page 50: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/50.jpg)
Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=3000 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these
![Page 51: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/51.jpg)
meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move
![Page 52: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/52.jpg)
for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.
![Page 53: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/53.jpg)
According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.0 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
![Page 54: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/54.jpg)
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)
![Page 55: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/55.jpg)
Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142.
![Page 56: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/56.jpg)
2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
![Page 57: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/57.jpg)
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)
![Page 58: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/58.jpg)
Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142.
![Page 59: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/59.jpg)
2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
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2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)
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Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142.
![Page 62: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/62.jpg)
2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
3.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an
![Page 63: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/63.jpg)
ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move
![Page 64: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/64.jpg)
for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.
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According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
0*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142.
![Page 66: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/66.jpg)
2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
3.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an
![Page 67: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/67.jpg)
ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move
![Page 68: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/68.jpg)
for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.
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According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
0*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142.
![Page 70: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/70.jpg)
2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
5.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
ce is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142.
![Page 71: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/71.jpg)
2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
mple: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in
![Page 72: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/72.jpg)
different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
mple: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References
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1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
sistance box?Wheatstone Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related Topics
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Electrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridge
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In procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
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4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
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IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process.
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Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
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4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
Introduction
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We have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one
![Page 81: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/81.jpg)
tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.
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According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these
![Page 83: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/83.jpg)
meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move
![Page 84: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/84.jpg)
for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.
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According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142.
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2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
3.0 Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
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2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)
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Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142.
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2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
5.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
0*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327.
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3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
7.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
rtainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
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5.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
f the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
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ance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be
![Page 93: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/93.jpg)
identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.
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According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resista Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge.
![Page 95: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/95.jpg)
The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W20
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10511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.
![Page 97: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/97.jpg)
In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)
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Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.
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Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistanc Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1)
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Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/5
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1/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
![Page 102: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/102.jpg)
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure
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1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.0
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5.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discus Wheatstone bridgeGoalLearn the operation of the Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1)
![Page 105: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/105.jpg)
Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/5
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1/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
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References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such mea Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current
![Page 108: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/108.jpg)
flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W
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2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?
![Page 110: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/110.jpg)
For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
surements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse
![Page 111: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/111.jpg)
adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
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3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in
![Page 113: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/113.jpg)
different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
s how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
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1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e.
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the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions
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1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142.
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2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
e box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875).
![Page 118: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/118.jpg)
Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)
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Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.0
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9.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in
![Page 121: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/121.jpg)
different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse
![Page 122: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/122.jpg)
adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
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3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in
![Page 124: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/124.jpg)
different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
nce box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
1.03.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References
![Page 125: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/125.jpg)
1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
Wheatstone bridgeGoalLearn the operation of the Wheatstone bridge.
Related TopicsElectrics, electrical circuit
IntroductionWe have learned before how to measure the resistance using a voltmeter and a current meter. The accuracy of such measurements is limited by the internal resistances of these meters. Ideally, we need the internal resistance of a voltmeter to be infinity, and that of an ammeter to be zero. But that is not possible and all the measurements with these meters will have unavoidable instrumental errors.In this experiment we will learn a way to measure the resistance precisely by using an equipment called Wheatstone Bridge, which is invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843[1,2].
![Page 126: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/126.jpg)
Fig. 1 Wheatstone Charles (1802-1875). Fig. 2 The circuit diagram of a Wheatsone bridge
1. A Wheatstone bridge circuit As shown in Fig. 2, the unknown resistor RX and the other three adjustable resistors RA, RB and RS form a circuit called a "bridge". A galvanometer G (a sensitive current meter) is connected to two points, 2 and 4. In operation, we adjust the resistance of RS till the current flowing through the galvanometer IG is zero. This process is called "balancing" of the bridge. The galvanometer G is connected there exactly for balancing the bridge. When the bridge is balanced, the current passing through the resistors RA, and RB is the same, and that passing through RS and RX is the same. We then have the relationship: . (1) Since the accuracy of the measurement crucially depends on the smallness of the current through the ammeter, a galvanometer with high sensitivity is used. The galvanometer is therefore very delicate and can be easily damaged if excessive current is let to pass it. To prevent this, the galvanometer is first bypassed with a shunt resistor for a coarse adjustment so that the bridge is roughly balanced. When the bridge is balanced at the low sensitivity, the finer adjustment can be achieved by reducing the shunt resistor gradually.
2. Sensitivity of a Wheatstone bridgeIn the measurement, the galvanometer would monitor the currents passing along 2 and 4. When the balance of the two arms of the bridge circuit is reached, a tiny change of the resistor RS, described as δRS, will cause a deflection of the galvanometer δIG. The Wheatstone bridge’s sensitivity M is defined by M =δIG•RS /δRS. Obviously, the larger the M is, more accurately the RS for the balance of the bridge circuit could be measured. Hence, M can be used to describe the sensitivity of a Wheatstone bridge. M is also deduced by , (2)where, RG is the resistor of the galvanometer, SG is the sensitivity of the galvanometer, is the voltage provide by the DC power supply[3].
3. Uncertainty of a Wheatstone bridgeIn procedure, the resistor RS is adjusted until the current flow through the galvanometer equals to zero. Hence the uncertainty of the bridge circuit depends directly on this process. Usually the resolution limit of a measurement instrument with a pointer is defined by one tenth of the smallest division on the instrument scale (The minimum change that could be identified by eyes). If a change of δRS will cause the pointer of the galvanometer to move for a smallest division from its balance position, the measurement uncertainty uB1(RS ) introduced by the bridge can be written as . (3)Experiment deviceThree ZX21A resistors, an unknown resistor (about 2kΩ), an 85C1 galvanometer, a DC power supply, some connecting wires and two tapping keys.
Procedure1. Set up the circuit as shown in Fig. 2.
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2. Measure RX at different values of RA /RB. (Set the voltage of power supply to 3V.)Set RA and RB according to RA /RB values given in Table 1. Adjust RS until IG equals to zero. Determine RX at different RA/RB values. R'S is the measured resistance when IG is 2μA, i.e. the smallest division the galvanometer scale. Fill out the table and find for which value of RA /RB, the sensitivity of Wheatstone bridge is largest.Table 1 Data table when RB=2000WRA/RB RA/W RS/W R'S /W *) RX/W2010511/51/101/20*) Here, please note the unit of dIG is Div.
3. Measure RX at different values of RA /RX., when RA =RB.(Set the voltage of power supply to 3V.)Carry out the measurement with RA/RX similar to RA /RB given in Table 1(Note: RX should be the value determined at the largest sensitivity M in table 1). Fill out the table and find for which value of RA /RX, the sensitivity of Wheatstone bridge is largest.Table 2 Data table when RA=RBRA/Rx RA/W RS/W R'S /W RX/W
4. The measurement of RX at different power supply voltages.According to Table 2, set RA, RB and RA/RX when the sensitivity M is the largest. Carry out the measurement at different power supply voltages and fill out the Table 3. How is M dependent on the power supply voltage? =___________, =___________, =___________。Table 3 Data table at different power supply voltage.Voltage/V RS/W R'S /W
1.03.05.0
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7.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.
3.05.07.09.0 Questions1. Derive the equation (1).2. Determine the measurement uncertainty of RX when the sensitivity M is the largest in the table 3.Supplementary information about the resistance box: how to caculate the unertainty limits of a resistance box?For example: if the indication of the ZX-21 type resistance box is 30362.5Ω, and the zero resitance is 0.02Ω, then the unertainty limits a is:a=30000*0.1%+0*0.1%+300*0.1%+60*0.1%+2*0.5%+0.5*2%+0.023. Discuss how is measurement uncertainty of RX on different values of RA/RB, RA/RX and the power supply voltages.
References1. S. Hunter Christie, The Bakerian Lecture: Experimental Determination of the Laws of Magneto-electric Induction in different masses of the same metal, and its intensity in
![Page 129: Bridge](https://reader036.vdocuments.us/reader036/viewer/2022062315/5695d3061a28ab9b029c91dc/html5/thumbnails/129.jpg)
different metals, Philosophical Transactions of the Royal Society of London, vol. 123, 1833, pp. 95-142. 2. Charles Wheatstone, The Bakerian Lecture: An Account of Several New Instruments and Processes for Determining the Constants of a Voltaic Circuit, Philosophical Transactions of the Royal Society of London, vol. 133, 1843, pp. 303--327. 3. 沈元华,陆申龙 基础物理实验 (Fundamental Physics Laboratory) 高等教育出版社 北京 2004 pp. 165-168.