BioE 1310 - Exam 1 2/18/2020Answer Sheet - Correct answer is A for all questions

1. Multiplying amperes × seconds yields units of

A. charge

B. voltage

C. current

D. energy

E. power

Explanation: 1 coulomb = 1 ampere × 1 second[ circuits0377.mcq ]

2. Energy is related to power as follows:

A. Power is the derivative of energy with respect to time.

B. Energy is the derivative of power with respect to time.

C. Average energy over time is the change in power.

D. None of the others is correct.

E. Energy is power divided by time.

Explanation: Power (brightness of the lightbulb) is the derivative of energy (gas in the tank for the generator).[ circuits0083.mcq ]

3. How many joules does a 12 V car battery expend attempting to start a car during 5 seconds if the electric motorin the starter draws 10 amperes?

A. 600 J

B. 24 J

C. 4.17 J

D. 6.0 J

E. Cannot be determined.

Explanation: 1 J = 1 W x 1 sec = 1 V x 1 A x 1 sec.[ circuits0133.mcq ]

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4. Which of the following statements is false about resistors?

A. When connected in series, the conductance of two resistors adds.

B. The same amount of current that enters one end must leave the other.

C. The voltage across a resistor (positive or negative) is proportional to the current (positive or negative) flowingthrough the resistor.

D. If a constant current is flowing through a given resistor, the power dissipated as heat is proportional to thatcurrent squared.

E. If a constant voltage is across a resistor, the power dissipated as heat is proportional to that voltage squared.

Explanation: When connected in series, the resistance of two resistors adds.[ circuits0134.mcq ]

5. Which of the following is false about the following circuit, whose output is at the terminals to the circuit’s right(or all are true)?

A. All are true.

B. A potentiometer in the circuit creates what is, in effect, a voltage divider with two resistors the ratio of whoseresistances can be varied from 0 to ∞.

C. The ideal voltage source in the circuit maintains a fixed voltage (Vs) across itself.

D. The output voltage is shown relative to ground.

E. The output voltage increases with clockwise rotation of the potentiometer from 0 to (Vs).

Explanation: All are true.[ circuits0319.mcq ]

6. American Wire Gauge (AWG) describes the diameter of single-conductor wire in inches used in electrical wiring.For copper wire, 20 AWG wire has a diameter of 0.0320 inches and a resistance of 10 Ω per 1000 ft. The diameterof 14 AWG wire is 0.0640 inches. What voltage drop would one expect along a 2000 ft piece of single-conductor 14AWG copper wire with 2 A of DC current through it?

A. 10 V.

B. 20 V.

C. 40 V.

D. 2.5 V.

E. 5 V.

Explanation: 14 AWG copper wire has twice the diameter and thus 14 the resistance per foot of 20 AWG copper

wire, or 2.5 Ω per 1000 ft. 2000 ft thus has a resistance of 5 Ω. 2 A × 5 Ω = 10 V.[ circuits0486.mcq ]

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7. What is the resistance between points A and B, if R1 = 20 Ω, R2 = 40 Ω, and R3 = 40 Ω? Calculate only to twosignificant digits.

A. 40 Ω

B. 10 Ω

C. 20 Ω

D. 100 Ω

E. 30 Ω

Explanation: The total resistance is R1 + R2R3R2+R3

.[ circuits0318.mcq ]

8. The property of inductance in a coil may best be described as follows:

A. The magnetic field surrounding a current contains energy, and it requires a voltage applied over time to changethat energy.

B. The mass of the electrons provides inertia, which makes them want to keep moving in a given direction.

C. The current in a coil is proportional to the voltage across the coil over the resistance of the coil.

D. The buildup of charge on one section of the coil is offset by the depletion of charge on a neighboring section ofthe coil.

E. The magnetic field within the coil is non-linear with respect to the magnetic field of the earth.

Explanation: Answer B is the actual inertia of the electrons, an insignificant factor. Answer C is simply Ohm’s law,accounting for the coil’s resistance, not its inductance. Answers D describes capacitance. Answer E is not related toinductance.[ circuits0178.mcq ]

9. The power dissipated by a 1K Ω resistor with 20 mA through it is

A. 400 mW

B. 200 mW

C. 20 µW

D. 20 W

E. 400 W

Explanation: Power equals voltage times current, which, in a resistor, equals current squared times resistance.[ circuits0317.mcq ]

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10. Regarding this graph showing the output voltage and current between the two terminals of a circuit containingonly resistors and perfect DC voltage and current sources, with varying load resistances placed between the terminals,the following are true, except

A. The slopes will differ for the Thevenin and Norton equivalent circuits.

B. Point A represents a short circuit between the terminals.

C. Point B represents an open circuit between the terminals.

D. At Point A, no current will pass through RNorton.

E. At Point B, no current will pass through RThevenin.

Explanation: Since RNorton = RThevenin, the slopes will be the same. More fundamentally, the circuits areequivalent, meaning they behave identically.[ circuits0487.mcq ]

11. A battery is measured as having a voltage of 9 V without any load attached. Then a 5 Ω resistor is attachedacross the battery’s leads and 5 V is measured across that resistor. What is the internal resistance of the battery?

A. 4 Ω

B. 1 Ω

C. 9 Ω

D. 5 Ω

E. cannot be determined

Explanation: With the 5 Ω resistor attached the current is 1 A (because there is 5 V across the resistor). Thereforethe remaining 4 volts must be across an internal resistance in the battery of 4 Ω.[ circuits0090.mcq ]

12. What is the total capacitance of this branch if C1 = C2 = 0.001µF?

A. 500 pF

B. .002 µF

C. ∞ µF

D. 200 pF

E. .005 µF

Explanation: Total capacitance in series is 11C1

+ 1C2

[ circuits0256.mcq ]

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13. What is the voltage between points A and B, if R1 = 10Ω, R2 = 30Ω, R3 = 20Ω, and V = 12V?

A. 6 V

B. 3 V

C. 2 V

D. 4 V

E. None of the other answers is correct.

Explanation: The current is I = VR1+R2+R3

and the voltage between A and B is I×R2, or more simply, V R2R1+R2+R3

.[ circuits0261.mcq ]

14. All the following are true about the complex exponential ejωt, except

A. Imejωt = jsin(ωt)

B. ejωt is the complex conjugate of e−jωt

C. |ejωt| = 1

D. ejωt = cos(ωt) + jsin(ωt)

E. 6 ejωt = ωt

Explanation: Imejωt = sin(ωt) is, itself, a real number.[ circuits0488.mcq ]

15. The following diagram illustrates that voltage represents what physical dimension?

A. change in energy per unit charge between locations A and B

B. force on a unit charge × the time it takes to get from A to B.

C. force along the direction vector from A to B.

D. charge × velocity between A and B

E. None of the others.

Explanation: Voltage is a measure of how much energy it takes to move a unit charge from one location in a staticelectric field to another.[ circuits0255.mcq ]

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16. The following is an appropriate thing to do the digital voltmeter in your PittKit.

A. Measure the voltage directly across a battery using the ‘voltage’ setting.

B. Measure the internal resistance of a battery using the ‘resistance’ setting.

C. Measure the current in a wall socket.

D. None of the others is appropriate.

E. Measure the voltage at one point in a circuit with the red lead, using the ‘voltage’ setting, leaving the black leaddisconnected as a “floating” reference.

Explanation: The ”resistance” setting should only be used for measuring passive resistance of a resistor or networkof resistors. Unless both leads are connected to the circuit, voltage between them is meaningless. You should NEVERplug anything into the wall socket, and are advised never to use the current setting on the meter unless you reallyknow what the current is, because it can damage the meter.[ circuits0251.mcq ]

17. The original question here has been removed and credit given for any answer or no answer.

A. B. C. D. E.

Explanation:

Alternate acceptable answer: ABCDEF[ circuits0000.mcq ]

18. Which are the correct values for the Norton Equivalent of the following circuit, given that V = 4 V and R = 2KΩ?

A. INorton = 2 mA; RNorton = 2 KΩ;

B. INorton = 2 A; RNorton = 2 KΩ;

C. INorton = 4 mA; RNorton = 1 KΩ;

D. INorton = 4 A; RNorton = 1 Ω;

E. Cannot be determined from the information given..

Explanation: This circuit is already the Thevenin Equivalent. Shorting its terminals gives INorton = VThevenin/RThevenin,since for the Norton Equivalent, all of INorton will pass through the short rather than through RNorton; Leaving theterminals open yields VThevenin, which is what results from passing INorton through RNorton, so RNorton can thusbe found, or simply recall that RNorton is always equal to RThevenin.[ circuits0489.mcq ]

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19. Given that I1 = 3A, I2 = 5A, and R = 16Ω, what is the voltage across the resistor?

A. 128 V.

B. 0.5 V.

C. 2 V.

D. 32 V.

E. This circuit cannot exist because the currents conflict.

Explanation: The currents sum, since they are in parallel, and both go through the resistor, so V = (I1 + I2)×R.If they were voltage sources instead of current sources, they would indeed conflict.[ circuits0139.mcq ]

20. Given ideal capacitors and inductors, the following are true except

A. Power is dissipated as heat by both capacitors and inductors as a function of the voltage squared or currentsquared, respectively.

B. A current is required to change the voltage between the plates of a capacitor.

C. A voltage is required to change the curent through an inductor.

D. The impedance of either a capacitor or an inductor is purely imaginary.

E. The impedance of either a capacitor or an inductor varies with frequency.

Explanation: Power is not dissipated as heat by either capacitors and inductors. Energy, stored as voltage in acapacitor and as current in an inductor, is completely returned to the circuit. Another way of looking at it is thatsinusoidal voltage and current are 90 degrees out of phase, so their product integrates to zero, resulting in zero power.[ circuits0490.mcq ]

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21. Given a non-zero current I through this inductor with the switch closed, what voltage would theoretically begenerated between A and B if the switch were opened instantly (in zero time)?

A. ∞B. 0

C. I

D. +V

E. None of the other answers is correct.

Explanation: ∞ because the voltage across the coil is LdIdt . The current goes from I to 0 instantly, so point A goes

to infinity above +V, and therefore point A is also infinity above ground (point B).[ circuits0201.mcq ]

22. What is the transfer function H(ω) of the circuit at ω = 1√LC

, given point a is the input and point b is theoutput?

A. H(ω) = 1

B. H(ω) = 0

C. H(ω) =∞D. H(ω) = R

L+C+R

E. None of the other answers is correct.

Explanation: The impedance between points a and b at ω = 1√LC

is zero, so given the general rule for a voltagedivider, H(ω) = R

0+R = 1.[ circuits0459.mcq ]

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23. Conductance is the reciprocal of

A. Resistance.

B. Capacitance.

C. Impedance.

D. Inductance.

E. Admittance.

Explanation: Conductance, like its reciprocal, resistance, is purely real, as opposed to any of the other answers.[ circuits0491.mcq ]

24. A transformer with 1000 turns of wire in the primary and 50 turns of wire in the secondary is assumed to be100% efficient. Given a sinusoidal voltage at the primary with peak voltage = 100 V, what is the RMS voltage atthe secondary:

A. 5√2

VRMS.

B. 50√2

VRMS.

C. 5√

2 VRMS.

D. 5 VRMS.

E. 50 VRMS.

Explanation: VRMS = VRMS√2

. Voltage is proportional to number of turns of wire in a transformer.[ circuits0439.mcq ]

25. Based on the diagram below, the following statements are true, except (or all the others are true).

A. It expresses the concept that total current into any node equals total current out, but this is only true if thecircuit consists of a single closed loop of components.

B. It illustrates Kirchoff’s current law.

C. It shows four components (A, B, C, and D) with nodes between each, where conductors from adjacent componentsconnect.

D. It expresses the assumption that charge can be considered to be non-compressible, not building up within acomponent, and thus current around an isolated loop is equal everywhere.

E. All the others are true.

Explanation: At any node in any circuit, total current in equals total current out.[ circuits0492.mcq ]

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26. All of the following are true about the following system except (or all are true)?

A. All of the answers are true.

B. The system has a transfer function H(ω) = Y (ω)X(ω) .

C. The system is a voltage divider.

D. If Z1 and Z2 are real, this is simply a voltage divider consisting of two resistors.

E. The transfer function H(ω) = Z1Z1+Z2

.

Explanation: All are true.[ circuits0436.mcq ]

27. The following statements are true about the circuit below, except

A. VA and VB are independent of VS , the supply voltage.

B. The circuit is known as a Wheatstone bridge.

C. The circuit consists of two voltage dividers

D. When R1R2

= R3R4

, VA = VB .

E. The circuit is analogous to a beam balance, a device for determining that two weights are the same, and as suchcan be used to accurately detect small differences between large values.

Explanation: VA and VB each depend on the ratio of the resistances in their respective voltage dividers, and bothchange proportionally with VS , i.e., VA = VS

R2R1+R2

.[ circuits0493.mcq ]

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28. Which of these statements is false about the Bode plot, or all are true?

A. All are true.

B. It consists of two plots describing a system: the gain (change in amplitude) in dB and the phase shift, both asfunctions of frequency (also displayed logarithmically).

C. It fully describes the behavior of the transfer function H(ω).

D. It represents a complex number in polar coordinates as a function frequency.

E. It is commonly used the describe the frequency response of a filter.

Explanation: All are true.[ circuits0387.mcq ]

29. Evaluate the complex exponential√

2e−j π4

A. (1− j)B.√

2(j − 1)

C. (j − 1)

D. −√

2(j)

E. none of the other answers is correct.

Explanation:√

2e−j π4 =√

2( 1√2

+ −j√2) = (1− j).

[ circuits0182.mcq ]

30. Which of the following is false about permittivity (or all are true)?

A. It permits a constant current to leak between the plates of the capacitor.

B. Even free space has a non-zero permittivity.

C. It can be increased by the alignment of charges in the material between the plates of a capacitor.

D. All are true.

E. In a given capacitor, it determines the capacitance for a given area of plates and distance between them.

Explanation: A capacitor may leak, but not because of permittivity. Permittivity relates to the storage capacityfor charge between the plates due to the material between them.[ circuits0152.mcq ]

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31. The following statements are true about the circuit below, except

A. The voltage across R2 equals I R2R1+R2

.

B. The current through both resistors is the same.

C. The voltage across each resistor is proportional to its resistance.

D. The power dissipated by the current source is −I2(R1 +R2)

E. The power dissipated by R1 is I2R1

Explanation: The voltage across R2 equals IR2, and is independent of R1.[ circuits0494.mcq ]

32. A system is said to have a gain of 60dB. What is the ratio of the output voltage to the input voltage of thesystem.

A. 1,000

B. 10−6

C. 1,000,000

D. 0.001

E. None of the other answers is correct.

Explanation: For voltage, 60 = 20log10(1, 000).[ circuits0386.mcq ]

33. All of the following are true about the following system, except (or all are true)?

A. The system is a high pass filter.

B. The transfer function H(ω) = 1, at ω = 0.

C. This is a linear system, describable by a linear differential equation.

D. At ω = 1RC the system response |H(ω)| = 1√

2.

E. All of the answers are true.

Explanation: The system is a low pass filter.[ circuits0495.mcq ]

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34. The following are true about the circuit below except (or all are true)

A. At very low frequencies it approaches zero impedance.

B. The circuit resonates at a particular frequency.

C. At frequency ω = 1√LC

the impedance is 0.

D. All are true.

E. At very high frequencies it approaches infinite impedance.

Explanation: At very high frequencies the coil approaches infinite impedance and at very low frequencies thecapacitor does likewise. This is a bandpass filter (letting a certain frequency through at ω = 1√

LC, not a high-pass

filter.[ circuits0263.mcq ]

35. Evaluate the complex exponential ej 3π4

A. (−1+j)√2

B.√

2(1− j)C. (1− j)D.√

2(−1 + j)

E. none of the other answers is correct.

Explanation: The magnitude is 1 and the angle is 135.[ circuits0265.mcq ]

36. Which of the following is false about the impedance of the following branch?

A. At ω = 0 it is ∞.

B. At ω =∞ it is R.

C. It can be found by taking the reciprocal of the sum of the reciprocals of R and jωL

D. It completely describes the relationship between the voltage across the branch and the current through it.

E. It represents a solution that can also be found using linear differential equations.

Explanation: At ω = 0, the impedance of the inductor, jωL, goes to zero, and thus so does the impedance of thebranch.[ circuits0353.mcq ]

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37. The figure below shows the inner workings of an old-fashioned ammeter, in terms of its components: a galvi-nometer and a parallel resistor, RP . The following are true except (or all are true).

A. All are true.

B. A galvinometer is an electromechanical device capable of measuring a small current by its effect of moving aneedle with a magnetic force against a delicate spring.

C. The purpose of the resistor RP is to shunt most of the current, leaving only a small fraction to pass through thegalvinometer.

D. The resistance of the ammeter is intentionally very low, so that the current can be measured without introducinga significant voltage to push back against it.

E. The ammeter circuit is an example of a current divider.

Explanation: All are true[ circuits0496.mcq ]

38. The following are true about sinusoids except (or all are true)

A. All are true.

B. Adding two sinusoids with the same frequency always produces a sinusoid at that same frequency.

C. Taking the derivative of a sinusoid shifts its phase 90 to the left.

D. They may be represented as the sum of a complex exponential and its complex conjugate.

E. The second derivative of a sinusoid is some negative constant times the original sinusoid.

Explanation:[ circuits0268.mcq ]

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