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

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1 BioE Exam 1 2/20/2018 Answer Sheet - Correct answer is A for all questions 1. A particular voltage divider with 10 V across it consists of two resistors in series. One resistor is 7 KΩ and the other is 3 KΩ. What is the voltage across the 3 KΩ resistor? A. 3 V B. 10 V C. 0 V D. 7 V E. Cannot be determined. Explanation: 10 V = 3 V. [ circuits0358.mcq ] 2. 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 static electric field to another. [ circuits0255.mcq ] 3. How many joules does a 100 W soldering iron expend in 5 seconds? A. 500 J B J C. 20 J D. 50 mj E. Cannot be determined. Explanation: 1 J = 1 W x 1 sec [ circuits0204.mcq ] 1

2 4. What is the voltage across R 1 if R 1 = 30Ω and I = 2mA? A. 60 mv B. 60 V C. 15 KV D. 15 mv E. Insufficient information is given to answer. Explanation: Kirchhoff s Current Law says the same current, I, must pass through both resistors, so the value of R 2 is irrelevant and the voltage across R 1 is simply I R 1. [ circuits0320.mcq ] 5. The following is not true about the electric field E: A. It only exists on the line between a single charge and a test charge. B. For a single charge, it falls off as the square the distance from the charge. C. For a single charge, it is a vector oriented radially outward or inward depending on whether the charge is positive or negative. D. It represents the electrostatic force on a unit test charge anywhere in space. E. It is the negative gradient of the voltage between some reference point and anywhere in space. Explanation: The field exists everywhere, being what the force would be on a single positive test charge at each location, and it can be generated by any number of charges. [ circuits0434.mcq ] 6. Multiplying volts amperes seconds yields units of A. energy B. voltage C. current D. charge E. power Explanation: 1 watt = 1 ampere 1 volt 1 joule = 1 watt 1 second [ circuits0196.mcq ] 2

3 7. 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 whose resistances can be varied from 0 to. C. The ideal voltage source in the circuit maintains a fixed voltage (V s ) 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 (V s ). Explanation: All are true. [ circuits0319.mcq ] 8. 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 lead disconnected as a floating reference. Explanation: The resistance setting should only be used for measuring passive resistance of a resistor or network of resistors. Our meter does not have an automatic shut-off, so the battery will drain if you don t leave it in the off position. Unless both leads are connected to the circuit, voltage between them is meaningless. You should NEVER plug anything into the wall socket, and are advised never to use the current setting on the meter unless you really know what the current is, because it can damage the meter. [ circuits0251.mcq ] 3

4 9. Which statement about the following diagram of current in a wire is false? A. The current I is flowing from left to right. B. It demonstrates Kirchhoff s Current Law, stating that (to a first approximation) charge is not allowed to build up on the wire as a whole. C. The electron on the right leaves the wire because the electron on the left enters the wire, but not instantly (limited by the speed of light). D. All real wire, except superconducting wire, has some finite, though relatively small, resistance. E. Electrons in a conductor are in a valence band such that they can move easily from one atom (represented by stationary positive charges) to the next. Explanation: I is defined as positive current, and flows in the opposite direction of the electrons. [ circuits0359.mcq ] 10. What is the voltage between points A and B, if R 1 = 10Ω, R 2 = 20Ω, R 3 = 30Ω, and V = 12V? A. 4 V B. 3 V C. 2 V D. 6 V E. None of the other answers is correct. V Explanation: The current is I = R 1+R 2+R 3 and the voltage between A and B is I R 2. [ circuits0200.mcq ] 4

5 11. What is the resistance between points A and B, if R 1 = 20 MΩ, R 2 = 20 MΩ, and R 3 = 10 Ω? Calculate only to two significant digits. A. 20 MΩ B. 10 Ω C. 10 MΩ D. 30 MΩ E. 40 Ω Explanation: The total resistance is R 1 + R2R3 R 2+R 3. [ circuits0206.mcq ] 12. What are the Thevenin equivalent voltage T V and Thevenin equivalent resistance T R for the circuit between points A and B, if R = 10Ω and I = 5A? A. T V = 50V; T R = 10Ω B. T V = 0.5V; T R = 10Ω C. T V = 2V; T R = 50Ω D. T V = 5V; T R = 2Ω E. None of the other answers is correct. Explanation: T V is the open circuit voltage, which is I R. Since the circuit is, itself, the Norton equivalent, the resistance is simply R (the same resistance for both the Thevenin and Norton equivalents. Alternatively, the short circuit current is I, since all of the current will run through the short circuit and none through R, and the Thevenin resistance is T V /I = R. [ circuits0199.mcq ] 5

6 13. Which of the following is (are) true about superposition in solving DC circuits I - Each current source and voltage source is considered separately, setting all the others to zero, and the resulting currents are added. II - Setting a source to zero means making a voltage source a short circuit and making a current source an open circuit. III - Superposition relies on the fact that Ohm s law is linear, i.e., that currents add linearly with voltage, and cannot be relied upon to hold when non-linear components such as diodes are involved. A. I, II, and III B. I and II C. II and III D. I and III E. Only I Explanation: All three are true, Superposition relies on the linearity of the contributions from each of the sources with the others assuming their inherent resistance. A voltage source of 0 volts is a piece of wire; current flows without any voltage drop. A current source of 0 amps is an open connection, no current flows no matter what the voltage. III is true because the currents and voltages from the different sources cannot ignore each other if non-linear components are involved. [ circuits0175.mcq ] 14. An electric heater is powered by a 12 V battery. The heater draws 3 A. (Assume the battery is a perfect voltage source). The following are true except (or all are true): A. All are true. B. The resistance of the heater is 4 Ω. C. The power dissipated by the heater is 36 W. D. The power dissipated by the battery is 36 W. E. The current flowing inside the battery from its negative terminal to its positive terminal is 3A. Explanation: All are true. [ circuits0438.mcq ] 6

7 15. Given that I 1 = 3A, I 2 = 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 = (I 1 + I 2 ) R. If they were voltage sources instead of current sources, they would indeed conflict. [ circuits0139.mcq ] 16. Given that V = 20V, R 1 is unknown, R 2 = 10KΩ, and R 3 = 10KΩ, what is the current through R 2? A. 1 ma B. 500 µa C. 2 ma D. Cannot be determined. E. 4 ma Explanation: R 1 can be ignored since the same V will be across it and R 2 and R 3 in series. So the current through R 2 is simply I = V/(R 2 andr 3 ) [ circuits0375.mcq ] 7

8 17. What is the power P v for the voltage source and the power P i for the current source? A. P v =4W, P i = 4W B. P v = 4W, P i = 4W C. P v = 4W, P i =4W D. P v =4W, P i =4W E. none of the others is correct. Explanation: The current sources is charging the voltage source (battery). Thus the battery is dissipating power (positive) since current and voltage are the same direction. The current source, however, has current running through it the opposite direction from the voltage across it, and rather than dissipating power, it is delivery power elsewhere in the circuit. Note that the total power in the circuit must be 0. [ circuits0287.mcq ] 18. Which of the following is (are) true about Kirchoff s current law? I - The sum of currents flowing into a node is equal to the sum of currents flowing out of that node. II - It states that charge behaves like a non-compressible fluid. III - It depends on the fact that current charge = time. A. I and II B. I and III C. II and III D. I, II, and III E. II Explanation: current time = charge. [ circuits0262.mcq ] 19. The following are true about complex conjugates (Z and Z ) except (or all are true) A. Multiplying by Z is the same as dividing by Z. B. ZZ is always a real number. C. Expressed as phasors, Z and Z have opposite angles with respect to the real axis. D. All are true. E. Z + Z is always a real number. Explanation: Multiplying by Z is the same as dividing by Z in terms of phase shift, but not in terms of gain. [ circuits0267.mcq ] 8

9 20. A system is said to have a gain of 60dB. What is the ratio of the output voltage to the input voltage of the system. A. 1,000 B C. 1,000,000 D E. None of the other answers is correct. Explanation: For voltage, 60 = 20log 10 (1, 000). [ circuits0386.mcq ] 21. Which of these statements is false about phase? (or all are true) A. Phase is the imaginary component in a complex number. B. Phase can be expressed in units of degrees, radians, or cycles. C. All are true. D. Frequency, which is the derivative of phase with regard to time, if often expressed as either radians per second or cycles per second. E. Phase is whatever is in the parenthesis in the following equation showing Euler s identity, e j() = cos() + jsin(). Explanation: Phase is the imaginary exponent in the phasor representation of a complex number. [ circuits0381.mcq ] 22. Evaluate the complex number expressed in polar notation by A. 2 2 (1 i) B. 2(1 + i) C D E. none of the other answers Explanation: = [ circuits0379.mcq ] 9

10 23. Which of the following is (are) true about the circuit below? I - The circuit is a low pass filter. II - The magnitude of the two impedances is equal at frequency ω = 1 RC. III - The impedance of each of the two components varies with frequency. A. I and II B. I, II, and III C. II and III D. I and III E. II Explanation: At ω = 1 RC the magnitudes of the two impedances are equal. The circuit is a low pass filter. The resistor s impedance does not vary with frequency. [ circuits0266.mcq ] 24. 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 ] 25. Evaluate the complex exponential e j 3π 4 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 ] 10

11 26. The following is not true about a linear system whose transfer function is H(ω) = 1 jω : A. Its output signal is purely imaginary at all points in time. B. Putting e jωt at the input yields 1 jω ejωt at the output. C. It is a lowpass filter D. It performs integration. E. It goes to infinity at DC. Explanation: Although H(ω) is itself imaginary, its output signal can be real, imaginary, or complex at particular points in time, depending on the input signal. [ circuits0435.mcq ] 27. Which of the following is false about permeability in electromagnetism (or all are true)? A. The permiability of free space is zero. B. Permeability is to inductance as permittivity is to capacitance. C. The inductance of a coil can be increased by including certain materials within the coil that support the formation of a magnetic field. D. All are true. E. Greater permeability permits an inductor to store proportionally greater energy for a given current. Explanation: The permeability of free space µ 0 is not zero. It, and the permittivity of free space ε 0 determine the speed of light in a vacuum. [ circuits0384.mcq ] 28. 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 the branch. [ circuits0353.mcq ] 11

12 29. 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), which is a complex number at any given frequency ω. C. Given a particular signal V in (t) = Asin(ωt), the output signal V out (t) will always be a sinusoid of frequency ω. D. Given an input signal V in (t) = e jωt the output signal V out (t) will never have a magnitude greater than 1. E. This is a linear system and thus can change magnitude and phase, but never frequency. Explanation: This is a passive linear system, and thus the magnitude of the output phasor will always be equal to or less than the input phasor. The transfer function H(ω) has a magnitude and a phase at any given frequency ω, which determines the change in magnitude and phase between the input signal and the output signal. [ circuits0372.mcq ] 30. 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 Z 1 and Z 2 are real, this is simply a voltage divider consisting of two resistors. E. The transfer function H(ω) = Z1 Z 1+Z 2. Explanation: All are true. [ circuits0436.mcq ] 12

13 31. Which of the following is false about the following diagram of a capacitor (or all are true). A. Direct Current (DC) may pass through the capacitor forever, provided there is no significant inductance to build up a magnetic field. B. The material between the plates represents the dialectric, which increases capacitance by the alignment of dipoles in the electrostatic field. C. The capacitor is shown in a charged state. D. The capacitance is proportional to the area of the plates and inversely proportional to the distance between them. E. All are true. Explanation: Answer A is nonsense. [ circuits0323.mcq ] 32. Admittance is the reciprocal of A. Impedance. B. Capacitance. C. Resistance. D. Inductance. E. None of the other answers is true. Explanation: Whereas conductance (the reciprocal of resistance) can be viewed as a type of admittance, it is not always equal to the total admittance of a circuit that also may contain capacitance and inductance. So A is the right answer. [ circuits0380.mcq ] 33. 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 as functions 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 ] 13

14 34. Which of the following statements is false about the following system? A. At ω =, the system introduces a 90 phase shift. B. The system response H(ω) = jωl R+jωL C. This is a high pass filter. D. This system is called linear because it can be modeled by a linear differential equation. E. If V in (t) is a sinusoid of frequency ω, V out (t) is also sinusoid of frequency ω. Explanation: At ω =, the system introduces a 0 phase shift, since H(ω) = jωl R+jωL = 1 [ circuits0355.mcq ] 35. What is the impedance across the branch shown below, at frequency ω = 1 LC? A. R B. 0 Ω C. Ω D. 1 jωc E. jωl Explanation: L and C in parallel have infinite impedance at ω = 1 LC, and so are inconsequential, leaving R as the only impedance. [ circuits0370.mcq ] 14

15 36. The following is not true about a perfect 1 µf capacitor with 1 V across it at t = 0 seconds: A. The energy dissipated as heat within the capacitor discharging completely would be 1 µj. B. A current of 1 µa coming out of the positively charged plate and returning to the negatively charged plate would drain the capacitor completely in 1 second. C. The energy on the capacitor at t = 0 seconds is 0.5 µj. D. If a 1 KΩ resistor is attached across the capacitor, the initial power in the resistor would be 1 mw. E. If a 1K resistor is attached across the capacitor, the magnitude of the initial current in the resistor would be 1 ma. Explanation: Capacitors and coils store energy in such a manner that it is completely recoverable. They do not dissipate energy in the form of heat. [ circuits0437.mcq ] 37. A transformer with 1000 turns of wire in the primary and 50 turns of wire in the secondary is assumed to be 100% efficient. Given a sinusoidal voltage at the primary with peak voltage = 100 V, what is the RMS voltage at the secondary: A. 5 2 V RMS. B V RMS. C. 5 2 V RMS. D. 5 V RMS. E. 50 V RMS. Explanation: V RMS = VRMS 2. Voltage is proportional to number of turns of wire in a transformer. [ circuits0439.mcq ] 38. Which of the following is false, as regards this diagram in lecture in the section about AC power (or all are true)? A. All are true B. Since the capacitor integrates current to produce voltage, the current and voltage are 90 out of phase. C. The average product of the sin and cos over one cycle is zero. D. The energy stored in an ideal capacitor, 1 2 CV 2, is returned to the circuit with 100 percent efficiency. E. The average power resulting from non-zero voltages and currents in a given component can be zero. Explanation: The average power resulting when the AC voltage and current are 90 out of phase, as in a capacitor or inductor, is zero. [ circuits0383.mcq ] 15

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