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Experiment 1 – Basic Resistive Circuit Parameters Report Due In-class on Wed., Mar. 14, 2018

Note: (1) The Prelab section must be completed prior to the lab period. (2) All submitted lab reports should have a TA signatures for both

(a) completed Prelab and (b) recorded lab data.

1.0 PURPOSE To (i) investigate the relationship between voltage and current in a simple resistive circuit and to (ii) examine the condition for maximum power transfer to a load in such a circuit.

2.0 INTRODUCTION 2.1. The Digital Multimeter  

The digital multimeter (DMM) is one of the most versatile, general-purpose laboratory instruments capable of measuring dc and ac voltages and currents, as well as resistance. The quantity being measured is indicated by a numerical display. A typical DMM has three terminals of which one is a COMMON ungrounded terminal (usually black). One of the two terminals (usually red), is the positive reference terminal for current (mA), and voltage/resistance (V/kΩ/s) measurements. Several switches are provided to select the measurement mode (i.e., DC mA, DCV, ACV, etc.) and the meter range. For this course the DMM which will be used is the Fluke 8010A. For this reason, the Fluke DMM is discussed in more detail here. Figure 1 shows the front panel features of the Fluke 8010A.

 

Figure 1: The display for the Fluke 8010A (taken from [1]). Label 9 does not apply here.

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The main elements of the meter are as follows: (1) LCD Digital display. (2) AC/DC Function Switch (should be OUT for dc and IN for ac measurements). (3) V/mA/kΩ/S Function Switches for measuring voltage (V), current (mA), resistance (kΩ)

and conductance (S). These are used in combination with (2) depending on whether the circuit is ac or dc. The conductance measurements require pushing the kΩ switch along with a pair of conductance range switches.

(4) Range Switches for selecting the measurement ranges – switch IN means that the range is selected.

(5) mA Input Connector – this is protected with a 2A fuse. Use the red lead in this input. (6) COMMON Input Connector. This is the test lead connector used as the ‘low’ or ‘common’

input for all measurements. To avoid confusion, use the black lead in this input. (7) V/mA/kΩ/S Input Connector. This is the test lead connector used for all voltage, resistance,

continuity and conductance measurements. Use the red lead in this connector. (8) 10A Input Connector. This is used for the 10A Range current function. (It won’t be used in

this course.) (9) Not available on the 8010A meter.

(10) Power Switch. IN is ON. Before connecting the meter, the appropriate measurement mode must be selected and the meter range set to its highest value. In this experiment, the measurement of current, voltage and resistance using the DMM is examined. 2.2. Voltage Measurements - The DMM as a Voltmeter  

Voltage is measured ACROSS a given element by placing the meter across (in PARALLEL with) the element. The positive (red) lead is connected to the assumed positive reference and the negative (black) lead to the assumed negative reference. With this connection the meter will read positive if the assumed polarities (i.e. the +/– polarities ) are correct. See Figure 2. All measurements of voltage or potential difference in a circuit require that a reference point, assigned a voltage of zero, be established. Such a point is known as the REFERENCE NODE and is indicated on a circuit by the "ground" symbol. In our simple circuits, it will be assumed to be the same as the node to which the negative terminal of the voltage supply is connected.

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Figure 2: Voltage measurement with the Fluke 8010A (taken from [1]).

 

2.3. Current Measurements - The DMM as an Ammeter  

Current THROUGH an element is measured by placing the meter in SERIES with the element. This may require the circuit connection to be broken (open-circuited) and the meter placed in the circuit. Power should be OFF when disconnecting any element. The meter will read positive when conventional current is flowing into the positive (red) lead. See Figure 3.

 

Figure 3: Current measurement with the Fluke 8010A (taken from [1]).

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2.4. Resistance Measurements - The DMM as an Ohmmeter  

The resistance of a resistor can be measured using the DMM. The resistor is connected between the positive voltage lead and the common lead. When the kΩ mode is selected the resulting display is a measure of the resistance. See Figure 4. Although resistive elements come in many shapes and sizes, a large class of resistors fall into the category which is used for circuit components. The most common type of resistor is the carbon composition or carbon film resistor. Multicolored bands are painted on the resistor body to indicate the standard value of the resistance. Figure A1 in the appendix gives the colour codes for carbon composition resistors.

Figure 4: Resistance measurement with the Fluke 8010A (taken from [1]).

 

2.5. Accuracy of the Measurements The accuracy with which the DMM measures each quantity and the frequency range of the input quantity being measured are specified by the manufacturer (usually underneath the meter). These specifications should be examined to determine the accuracy of the reading.

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2.6. Ohm's Law and Power  

Ohm's Law is based on a linear relationship between voltage and current. Ohm's Law states that the voltage across many types of conducting materials is directly proportional to the current flowing through the material. It is expressed mathematically as 𝑣 = 𝑖𝑅 (1) where the constant of proportionality, R is called the RESISTANCE. A resistance for which the voltage versus current relationship is a straight line is a LINEAR RESISTANCE. A linear resistance obeys Ohm's Law because the resistance is always constant. However, a resistance whose ohmic value does not remain constant is defined as a NONLINEAR RESISTANCE. The power, P, through a linear resistor (or indeed any circuit component) may be easily calculated by multiplying the voltage across the resistor by the current flowing through the resistor, as in

𝑃 = 𝑣𝑖. (2) 2.7. References  

[1] 8010A/8012A Digital Multimeters Instruction Manual, John Fluke MFG. CO., INC., 1993. [2] J.W. Nilsson and S.A. Riedel, Engineering 1040, Pearson Custom Library, Pearson, 2015. [3] S. Wolf and R. Smith, Electronic Instrumentation Laboratories, Prentice-Hall, NJ. 1990. [4] E. Gill, H. Heys, J. E. Quaicoe, and V. Ramachandran, Lab manuals from previous offering of courses ENGI 1040 and ENG 1333.

3.0 PRELAB

This section must be completed prior to the lab period. At the start of the lab, ensure that a TA has reviewed and signed your Prelab. The signed Prelab must be submitted with the lab report. Only one Prelab per group needs to be submitted.

3.1 Read the Introduction (Section 2 of the instructions for this lab) and, from the course textbook, Section 2.2, pg. 32 - Electrical Resistance (Ohm's Law).

3.2 Using the information in Appendix A of this lab, determine the colour coding for each of the following resistors: (a) 100 Ω (b) 330 Ω (c) 1 kΩ (d) 2.2 kΩ (e) 10 kΩ

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3.3 If the resistor in part 3.2 (d) has a ‘gold’ band tolerance, determine the range of values which

the resistance may take. 3.4 For 𝑅 < 200  𝑘Ω, the 8010A DMM has a maximum error given by ±(0.2% of the reading +

1 digit). Consider the following example: A resistor with colour bands indicating a resistance of 1 kΩ and a tolerance of ±5%  is measured with the DMM and found to have a value of .981 kΩ. The maximum error is found as follows:

.981 kΩ ± (0.2% of .981 kΩ + 1 digit) where one digit now corresponds to 0.001 kΩ.

Therefore, the measurement becomes

.981 kΩ ± (0.002 × .981 kΩ + 0.001 kΩ) = .981 kΩ ± (0.002 kΩ + 0.001 kΩ) = .981 kΩ ± 0.003 kΩ

Note that (0.002 × .981 kΩ) was rounded to 0.002 kΩ since it is not meaningful to say that the precision of the error is greater than that indicated by the last digit measurable by the device. From the point of view of the error, the resistance value lies in the range extending from .978 kΩ to .984 kΩ. Notice that this value is well within the tolerance specified (the manufacturer’s tolerance of ±5% guarantees that the resistance is somewhere between .95 kΩ and 1.05 kΩ). Thus, using the multimeter and the specified accuracy we have determined a much smaller error on the value of the actual resistance.

Using the above example, determine the error and range of values for a standard value 330 Ω resistor which is measured with the DMM as having a resistance of .325 kΩ. Does this fall within the gold-band tolerance?

4.0 APPARATUS AND MATERIALS

(1) Fluke 8010A Digital Multimeters (DMM) (2) 1 Sun Equipment Powered Breadboard: Model PBB-4060B (3) Standard Resistors: 100 Ω, 470 Ω, 680 Ω, 2x1 kΩ, 1.5 kΩ, 3x2 kΩ, 2.2 kΩ, 3.3 kΩ, 4.7 kΩ,

and 10 kΩ (4) Various connecting wires

     

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5.0 EXPERIMENT 5.0. Prelab Signature 5.0.1. Have your prelab reviewed and signed by a TA.

5.1. Ohm's Law Consider the simple circuit shown in Figure 5:

 

Figure 5: A simple single-resistor dc circuit

5.1.1. Construct the circuit of Figure 5 on the breadboard using R = 470 Ω. The DMM used as an ammeter is represented by A and the DMM used as a voltmeter is represented by V. The latter DMM will be used to measure the resistance before being actually used as a voltmeter. DO NOT CONNECT OR TURN ON the voltage source at this stage. Measure the value of 𝑅 using the DMM specified by setting that device on the 2 kΩ range (also see Section "2. Introduction"). In the “Observation and Comment” section, record the value in the title of Table 1.

5.1.2. Connect the voltmeter (DMM) across 𝑅 in accordance with the directions given for voltage measurements specified in Section 2 (Introduction). That is, connect the red lead from the voltmeter to the positive (+) side of 𝑅 as shown in the diagram and the black lead to the negative (-) side of 𝑅. Set the voltmeter range to 20 V dc. Connect the ammeter (DMM) with the red lead on the same node as the black lead for the voltmeter and the black lead on the same node as COM terminal of the powered breadboard. Set the ammeter range to 20 mA. Connect the red lead from the 0 to 16 V terminal of the breadboard power to the same node as the + side of 𝑅. NOW turn on the voltage source (powered breadboard) and adjust the supply until the voltmeter (DMM) reads approximately 2 volts.

5.1.3. Record the voltmeter reading and the ammeter reading for the situation in 5.1.2 in Table 1. Adjust the power supply to give voltmeter readings of approximately 4, 6, 8, 10 and 12 volts making sure to read the corresponding ammeter readings. Record all voltmeter and corresponding ammeter readings in Table 1.

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5.2 Power Transfer to a Load Resistor  In this experiment, we wish to determine the power dissipated by the load RL in Figure 6 below for various values, while keeping 𝑅!,𝑅!, and 𝑅! fixed.

Figure 6: A linear circuit containing multiple resistors

5.2.1. On the breadboard, set up the circuit of Figure 6, but do not yet connect the voltage source. Resistors 𝑅! and 𝑅! are the standard 2 kΩ and resistor 𝑅! is the standard 1 kΩ resistor. Using the DMM as an ohmmeter, measure the following standard resistors and record them as R1, R2 and R3 in Section 6.2.1.

5.2.2. Using the DMM as an ohmmeter, measure the following standard resistors and record the values in Table 2: 100 Ω, 680 Ω, 1 kΩ, 1.5 kΩ, 2 kΩ, 3.3 kΩ, 4.7 kΩ, and 10 kΩ. (For convenience, you can do this step in combination with step 5.2.3.)

5.2.3. Construct the circuit, with 𝑣! adjusted to + 10V. With 𝑅! taking the successive measured values of the 100 Ω, 680 Ω, 1 kΩ, 1.5 kΩ, 2 kΩ, 3.3 kΩ, 4.7 kΩ, and 10 kΩ resistors, use the DMM as a voltmeter to determine the load voltage 𝑣! across 𝑅!. Record all voltage readings in Table 2.

5.2.4. Turn the power supply off and remove it from the circuit. Place a short circuit between nodes 𝑐 and 𝑏 and remove 𝑅! from the circuit. Using the DMM as an ohmmeter, measure the resistance (𝑅!") between nodes  𝑎 and 𝑏. Record the value in Section 6.2.1.  

NOTE:

1. Before leaving the laboratory, have your experimental results examined and signed by a TA. Also, the Prelab should have been signed.

2. The lab report should include the Prelab and the fully completed Section 6 showing the signatures of a TA for both the Prelab and the experimental results.

3. Late submissions (after 9:00 am on Wednesday, Mar. 14) will be penalized and may not be accepted.

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Faculty of Engineering and Applied Science Memorial University of Newfoundland

 

 

 

 

 

 

 

 

 

 

 

ENGINEERING 1040: Electric Circuits Experiment 1 – Basic Resistive Circuit Parameters

 

Report Due In-class on Wed., Mar. 14, 2018

All parts of the lab must be a collaborative effort of both students.

 

Name Student ID

Student # 1 Student # 2

 

 

Section  #:  ______________________       Day  of  Lab:  ________________________  

                  (Mon,  Tue,  Wed,  or  Thu)  

Date  of  Submission:  _______________________________________  

 

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6.0 Observations and Comments  

6.1 Ohm’s Law  

6.1.1. Measurements  

Table 1: Voltage and current measurements for a ____________Ω resister

Voltage (V) ± (0.1% +1digit)* Current (mA)±(0.3%+1digit)*

* These accuracies are found on the bottom of the 9010A.

6.1.2. Analysis and Comments

a) From the data of Table 1, plot a graph of voltage versus current.

Graph 1: Voltage versus current of a linear resistor

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b) From the graph, determine the value of 𝑅.

c) Compare this calculated value with the value of 𝑅 measured using the DMM in 5.1.1, and suggest possible reasons for any discrepancy.

d) State your conclusion for this experiment.

6.2 Power Transfer to a Load Resistor  

6.2.1 Measurements  

Resistor values for the circuit given in Figure 6:  

𝑅! = ___________________________

𝑅! =  ___________________________

𝑅! = ___________________________

𝑅!" =  _____________________________    

   

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Table 2: Load Power Measurements and Calculations

Standard Value of 𝑅!  (Ω)

Measured value of 𝑅! (Ω)

Measured Load Voltage, 𝑣!  (V)

Load Power 𝑃! (W)

100

680

1k

1.5k

2k

3.3k

4.7k

10k

6.2.2 Analysis and Comments  

a) Using the measured values for 𝑣! and 𝑅! calculate, and record in Table 2, the power dissipated by each load resistor. Provide one sample calculation in the space given below.  

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b) From the data of Table 2, plot a graph of Load Power versus Load Resistance on the semi-log graph below. Sketch a smooth curve through the points. Note that the vertical axis is linear, while the horizontal axis is logarithmic.

Power

↑ ↑ ↑

100 1000 10000 Resistance (Ω)

c) From the above graph, determine and record the value of 𝑅! at which maximum power is dissipated by the load. How does this resistance compare with the resistance  𝑅!"?

d) State your conclusion for this experiment.

Graph 2: Power versus load resistance

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6.3 Discussion  

a) Discuss any technical difficulties encountered during the lab.

b) State and comment on five major learning outcomes of the experiment.                                                          

Hand-in pages 9-14 of lab instructions and attach Prelab.