Deck 23: Alternating Current Circuits

Question 1

The graph shows the voltage across and the current through a single circuit element connected to an ac generator.
Determine the frequency of the generator.

A)0.14 Hz
B)7.14 Hz
C)12.5 Hz
D)25.0 Hz
E)50.0 Hz

Answer 1

12.5 Hz

Question 2

The graph shows the voltage across and the current through a single circuit element connected to an ac generator.

-Identify the circuit element.

A)The element is a 25- $\varOmega$ resistor.
B)The element is a 35- $\varOmega$ resistor.
C)The element is a 0.45-H inductor.
D)The element is a 360-µF capacitor.
E)The element is a 510-µF capacitor.

Answer 2

The element is a 360-µF capacitor.

Question 3

Three 4.0-µF capacitors are connected in parallel across the terminals of a 60.0-Hz generator. What is the capacitive reactance of the circuit?

A)39 $\varOmega$
B)110 $\varOmega$
C)330 $\varOmega$
D)660 $\varOmega$
E)1.0 × 10³ $\varOmega$

Answer 3

660 $\varOmega$

Question 4

What is the capacitive reactance of a circuit comprised of a 65.0-µF capacitor and a 50.0-Hz generator?

A)49.0 $\varOmega$
B)72.5 $\varOmega$
C)97.6 $\varOmega$
D)145 $\varOmega$
E)308 $\varOmega$

Question 5

The graph shows the voltage across and the current through a single circuit element connected to an ac generator.
Determine the rms current through this element.

A)1.4 A
B)2.0 A
C)3.4 A
D)3.9 A
E)5.6 A

Question 6

A variable capacitor is connected to an ac source. What effect does decreasing the capacitance have on the reactance and current in this circuit?

A)
B)
C)
D)
E)

Question 7

The reactance of a capacitor in a circuit at 110 Hz is 35 $\varOmega$ . Determine the capacitance.

A)41 µF
B)260 µF
C)51 mF
D)0.10 F
E)0.31 F

Question 8

The graph shows the voltage across and the current through a single circuit element connected to an ac generator.

-What is the reactance of this element?

A)20 $\varOmega$
B)25 $\varOmega$
C)30 $\varOmega$
D)35 $\varOmega$
E)40 $\varOmega$

Question 9

An ac voltage source that has a frequency f is connected across the ends of an inductor. Which one of the following statements correctly indicates the effect on the inductive reactance when the frequency is increased to 2f?

A)The inductive reactance increases by a factor of two.
B)The inductive reactance increases by a factor of four.
C)The inductive reactance is unchanged.
D)The inductive reactance decreases by a factor of four.
E)The inductive reactance decreases by a factor of two.

Question 10

Which one of the following graphs shows how the inductive reactance varies with frequency?

A)a
B)b
C)c
D)d
E)e

Question 11

A battery is used to drive a circuit. After a certain amount of time, the current is zero amperes. When the same circuit is driven by an ac generator, the current is non-zero and alternates. Which combination of elements is most likely to comprise the circuit?

A)resistors only
B)inductors only
C)capacitors only
D)a combination of inductors and resistors
E)a combination of inductors and capacitors

Question 12

The graph shows the voltage across and the current through a single circuit element connected to an ac generator.
Determine the rms voltage across this element.

A)49.5 V
B)70.0 V
C)112 V
D)140 V
E)170 V

Question 13

An ac generator is connected across the terminals of a 3.25-µF capacitor. Determine the frequency at which the capacitive reactance is 375 $\varOmega$ .

A)60.0 Hz
B)72.4 Hz
C)85.7 Hz
D)98.9 Hz
E)131 Hz

Question 14

A variable inductor is connected to an ac source. What effect does increasing the inductance have on the reactance and current in this circuit?

A)
B)
C)
D)
E)

Question 15

When the frequency of an ac circuit is decreased, the current in the circuit increases. Which combination of elements is most likely to comprise the circuit?

A)resistors only
B)inductors only
C)capacitors only
D)capacitors and resistors
E)inductors and capacitors

Question 16

Two 3.25-µF capacitors are connected in series across the terminals of a 50.0-Hz ac generator that has a peak voltage of 244 V. Determine the rms current in the circuit.

A)0.917 A
B)0.802 A
C)0.308 A
D)0.621 A
E)0.125 A

Question 17

Which one of the following graphs illustrates how capacitive reactance varies with frequency?

A)a
B)b
C)c
D)d
E)e

Question 18

An ac voltage source that has a frequency f is connected across the terminals of a capacitor. Which one of the following statements correctly indicates the effect on the capacitive reactance when the frequency is increased to 4f?

A)The capacitive reactance increases by a factor of four.
B)The capacitive reactance increases by a factor of eight.
C)The capacitive reactance is unchanged.
D)The capacitive reactance decreases by a factor of eight.
E)The capacitive reactance decreases by a factor of four.

Question 19

The current in a certain ac circuit is independent of the frequency at a given voltage. Which combination of elements is most likely to comprise the circuit?

A)resistors only
B)inductors only
C)capacitors only
D)a combination of inductors and resistors
E)a combination of inductors and capacitors

Question 20

Which circuit elements act to oppose changes in the current in an ac circuit?

A)resistors only
B)capacitors only
C)inductors only
D)both resistors and inductors
E)both capacitors and resistors

Question 21

Which one of the following statements concerning an ac circuit is true?

A)The current and voltage are in phase for a capacitor in an ac circuit.
B)On average, the power dissipated by a resistor in an ac circuit is zero.
C)For a resistor in an ac circuit, the current and voltage are 90° out of phase.
D)Inductors in an ac circuit offer little opposition to current at high frequencies.
E)When only resistance is present in an ac circuit, voltage and current are in phase.

Question 22

The table below shows the values of the resistance, capacitive reactance, and inductive reactance for five RCL circuits. Which circuit will have a negative phase angle?

A)
B)
C)
D)
E)

Question 23

An ac circuit consists of a series combination of an inductor and a capacitor. What is the phase angle between the voltages across these two circuit elements?

A)0°
B)90°
C)180°
D)270°
E)360°

Question 24

Use the information given in the figure for the series RCL circuit to determine its total impedance.

A)300 $\varOmega$
B)500 $\varOmega$
C)1500 $\varOmega$
D)1700 $\varOmega$
E)1900 $\varOmega$

Question 25

When the frequency of an ac circuit is increased at constant voltage, the current increases and then decreases. Which combination of elements is most likely to comprise this circuit?

A)resistors only
B)inductors only
C)capacitors only
D)a combination of inductors and resistors
E)a combination of inductors and capacitors

Question 26

Which one of the following statements concerning the impedance of an RCL circuit is true?

A)The impedance is dominated by the capacitance at low frequencies.
B)The impedance is dominated by the resistance at high frequencies.
C)The impedance depends only on the values of C and L.
D)The impedance depends only on the resistance.
E)The impedance is independent of frequency.

Question 27

The voltage across and the current through a single circuit element connected to an ac generator are shown in the graph.
At what frequency do charges oscillate in this circuit?

A)0.01 Hz
B)0.04 Hz
C)0.09 Hz
D)11 Hz
E)25 Hz

Question 28

Two 0.20-H inductors and one 0.44-H inductor are connected in series across the terminals of a 60.0-Hz ac generator. What is the total inductive reactance of this circuit?

A)230 $\varOmega$
B)320 $\varOmega$
C)158 $\varOmega$
D)56 $\varOmega$
E)27 $\varOmega$

Question 29

For which one of the following circuit arrangements will the power factor be non-zero?

A)a capacitor in series with an ac generator
B)an inductor in series with an ac generator
C)two capacitors in series with an ac generator
D)a capacitor and resistor in series with an ac generator
E)a capacitor and inductor in series with an ac generator

Question 30

The voltage across and the current through a single circuit element connected to an ac generator are shown in the graph.
Which one of the following statements concerning this circuit element is true?

A)The element is a resistor.
B)The element is a capacitor.
C)The element is an inductor.
D)The element could be a resistor or an inductor.
E)The element could be an inductor or a capacitor.

Question 31

In an ac circuit, a 0.055-H inductor is connected to a generator that has an rms voltage of 18 V and operates at 50.0 Hz. What is the rms current through the inductor?

A)0.62 A
B)2.0 A
C)3.2 A
D)1.0 A
E)14 A

Question 32

Which one of the following phasor models correctly represents a circuit comprised of only an inductor and an ac generator?

A)a
B)b
C)c
D)d
E)e

Question 33

Complete the following statement: When the current in an oscillating LC circuit is zero,

A)the charge on the capacitor is zero.
B)the energy in the electric field is maximum.
C)the energy in the magnetic field is a maximum.
D)the charge is moving through the inductor.
E)the energy is equally shared between the electric and magnetic fields.

Question 34

Use the information given in the figure for the series RCL circuit to determine the phase angle between the current and the voltage.

A)zero degrees
B)+5.3°
C)-9.6°
D)-84°
E)+90°

Question 35

The table below shows the values of the resistance, capacitive reactance and inductive reactance for five RCL circuits. In which circuit will the voltage lead the current?

A)
B)
C)
D)
E)

Question 36

A series RCL circuit operating at 60.0 Hz contains a 49- $\varOmega$ resistor and an 5.0-µF capacitor. If the power factor of the circuit is +1.00, what is the inductance of the inductor in this circuit?

A)0.86 H
B)1.4 H
C)2.3 H
D)57 H
E)320 H

Question 37

The graph shows the impedance as a function of frequency for a series RCL circuit. At what frequency does the capacitor make the largest contribution?

A)f₁
B)f₂
C)f₃
D)f₁ or f₃
E)f₁ or f₂ or f₃

Question 38

The voltage across and the current through a single circuit element connected to an ac generator are shown in the graph.

-Determine the reactance of this circuit element.

A)20 $\varOmega$
B)25 $\varOmega$
C)40 $\varOmega$
D)57 $\varOmega$
E)80 $\varOmega$

Question 39

The voltage across and the current through a single circuit element connected to an ac generator are shown in the graph.
Determine the rms current through this circuit element.

A)1.0 A
B)1.4 A
C)2.0 A
D)2.8 A
E)4.0 A

Question 40

Note the following circuit elements: (1) resistors, (2) capacitors, and (3) inductors. Which of these elements uses no energy, on average, in an ac circuit?

A)1 only
B)2 only
C)3 only
D)both 2 and 3
E)both 1 and 3

Question 41

An ac generator supplies an rms (not peak) voltage of 180 V at 60.0 Hz. The generator is connected in series with a 0.50-H inductor, a 6.0-µF capacitor and a 300- $\varOmega$ resistor.

-Determine the peak voltage of the generator.

A)180 V
B)255 V
C)300 V
D)360 V
E)480 V

Question 42

An ac generator supplies an rms (not peak) voltage of 180 V at 60.0 Hz. The generator is connected in series with a 0.50-H inductor, a 6.0-µF capacitor and a 300- $\varOmega$ resistor.

-What is the peak (not rms) current through the resistor?

A)0.46 A
B)0.52 A
C)0.65 A
D)0.78 A
E)0.85 A

Question 43

An ac generator supplies a peak (not rms) voltage of 150 V at 60.0 Hz. The generator is connected in series with a 35-mH inductor, a 45-µF capacitor and an 85- $\varOmega$ resistor.

-Which one of the following statements concerning this circuit is true?

A)The voltage leads the current.
B)The circuit is more capacitive than inductive.
C)The voltage and current are exactly out of phase.
D)The voltage and current are in phase.
E)The phase angle for this circuit is positive.

Question 44

The following table gives the reactance and rms voltage across the elements of a series RCL circuit:
Determine the peak (not rms) voltage of the ac generator.

A)150 V
B)212 V
C)300 V
D)414 V
E)533 V

Question 45

An ac generator supplies a peak (not rms) voltage of 150 V at 60.0 Hz. The generator is connected in series with a 35-mH inductor, a 45-µF capacitor and an 85- $\varOmega$ resistor.

-Determine the rms current in the circuit.

A)0.28 A
B)0.40 A
C)0.75 A
D)1.1 A
E)1.6 A

Question 46

An ac generator supplies a peak (not rms) voltage of 150 V at 60.0 Hz. The generator is connected in series with a 35-mH inductor, a 45-µF capacitor and an 85- $\varOmega$ resistor.

-What is the capacitive reactance for this circuit?

A)59 $\varOmega$
B)85 $\varOmega$
C)99 $\varOmega$
D)120 $\varOmega$
E)310 $\varOmega$

Question 47

The following table gives the reactance and rms voltage across the elements of a series RCL circuit:
What is the rms current in the circuit?

A)0.25 A
B)0.43 A
C)0.50 A
D)0.86 A
E)1.08 A

Question 48

An ac generator supplies an rms (not peak) voltage of 180 V at 60.0 Hz. The generator is connected in series with a 0.50-H inductor, a 6.0-µF capacitor and a 300- $\varOmega$ resistor.

-What is the inductive reactance?

A)150 $\varOmega$
B)190 $\varOmega$
C)360 $\varOmega$
D)390 $\varOmega$
E)440 $\varOmega$

Question 49

The following table gives the reactance and rms voltage across the elements of a series RCL circuit:
What is the average power consumed by the circuit?

A)37.0 W
B)64.5 W
C)73.3 W
D)95.4 W
E)129 W

Question 50

A 14.0-µF capacitor and a 1480- $\varOmega$ resistor are connected in series to a generator operating at 50.0 Hz and producing an rms voltage of 208 V. What is the average power dissipated in this circuit?

A)190 W
B)28.9 W
C)19.7 W
D)4.18 W
E)zero watts

Question 51

An ac generator supplies an rms (not peak) voltage of 180 V at 60.0 Hz. The generator is connected in series with a 0.50-H inductor, a 6.0-µF capacitor and a 300- $\varOmega$ resistor.

-What is the phase angle for this circuit?

A)26°
B)-32°
C)38°
D)-40°
E)50°

Question 52

An ac generator supplies an rms (not peak) voltage of 180 V at 60.0 Hz. The generator is connected in series with a 0.50-H inductor, a 6.0-µF capacitor and a 300- $\varOmega$ resistor.

-What is the average power supplied to the circuit?

A)48 W
B)54 W
C)63 W
D)83 W
E)112 W

Question 53

The following table gives the reactance and rms voltage across the elements of a series RCL circuit:
What is the power factor for this circuit?

A)0.40
B)0.57
C)0.81
D)1.4
E)5.5

Question 54

An ac generator supplies a peak (not rms) voltage of 150 V at 60.0 Hz. The generator is connected in series with a 35-mH inductor, a 45-µF capacitor and an 85- $\varOmega$ resistor.

-What is the inductive reactance for this circuit?

A)13 $\varOmega$
B)23 $\varOmega$
C)59 $\varOmega$
D)85 $\varOmega$
E)99 $\varOmega$

Question 55

An ac generator supplies a peak (not rms) voltage of 150 V at 60.0 Hz. The generator is connected in series with a 35-mH inductor, a 45-µF capacitor and an 85- $\varOmega$ resistor.

-Determine the rms voltage of the generator.

A)220 V
B)110 V
C)82 V
D)75 V
E)53 V

Question 56

An ac generator supplies an rms (not peak) voltage of 180 V at 60.0 Hz. The generator is connected in series with a 0.50-H inductor, a 6.0-µF capacitor and a 300- $\varOmega$ resistor.

-What is the impedance of the circuit?

A)150 $\varOmega$
B)190 $\varOmega$
C)360 $\varOmega$
D)390 $\varOmega$
E)440 $\varOmega$

Question 57

An ac generator supplies an rms (not peak) voltage of 180 V at 60.0 Hz. The generator is connected in series with a 0.50-H inductor, a 6.0-µF capacitor and a 300- $\varOmega$ resistor.

-What is the capacitive reactance?

A)150 $\varOmega$
B)190 $\varOmega$
C)360 $\varOmega$
D)390 $\varOmega$
E)440 $\varOmega$

Question 58

An ac generator supplies a peak (not rms) voltage of 150 V at 60.0 Hz. The generator is connected in series with a 35-mH inductor, a 45-µF capacitor and an 85- $\varOmega$ resistor.

-What is the impedance of the circuit?

A)13 $\varOmega$
B)23 $\varOmega$
C)59 $\varOmega$
D)85 $\varOmega$
E)97 $\varOmega$

Question 59

The following table gives the reactance and rms voltage across the elements of a series RCL circuit:

-What is the impedance of the circuit?

A)11 $\varOmega$
B)22 $\varOmega$
C)349 $\varOmega$
D)486 $\varOmega$
E)1240 $\varOmega$

Question 60

An ac generator supplies a peak (not rms) voltage of 150 V at 60.0 Hz. The generator is connected in series with a 35-mH inductor, a 45-µF capacitor and an 85- $\varOmega$ resistor.

-What is the power factor for this circuit?

A)0.47
B)0.54
C)0.64
D)0.88
E)28.3

Question 61

An oscillating LC circuit has a resonant frequency of 1.2 × 10⁶ Hz. The diagram shows the system at t = 0 s when there is no charge on the capacitor and the current is in the direction shown. At this time, the energy stored in the inductor is 2.5 × 10^-7 J.

-Which one of the following statements is true for this circuit?

A)When the current in the inductor is zero, $\Delta$ I/ $\Delta$ t = 0 A/s.
B)The circuit will allow dc as well as ac current to flow.
C)The magnetic field in the inductor is a maximum at t = 0 s.
D)The charge on the capacitor will be a maximum at t = 4.2 × 10^-7 s.
E)As the current through the inductor decreases, the induced emf in the coil is directed opposite to the direction of the current.

Question 62

In the circuit shown in the drawing, the generator supplies the same amount of rms current at either very small or very large frequencies. What can be deduced about the resistances R₁, R₂, and R₃ from this information?

A)R₁ = R₂ = R₃
B)R₁ = 2R₂
C)R₁ = R₂
D)R₁ = R₃
E)R₂ = R₃

Question 63

A series RCL circuit contains a 222- $\varOmega$ resistor, a 1.40-µF capacitor, and a 0.125-H inductor. The 360-Hz ac generator in the circuit has an rms voltage of 208 V. What is the average electric power dissipated by the circuit?

A)22 W
B)81 W
C)166 W
D)193 W
E)102 W

Question 64

An ac generator supplies an rms (not peak) voltage of 180 V at 60.0 Hz. The generator is connected in series with a 0.50-H inductor, a 6.0-µF capacitor and a 300- $\varOmega$ resistor.

-What is the peak (not rms) voltage across the inductor?

A)120 V
B)180 V
C)190 V
D)260 V
E)290 V

Question 65

Two 250-µF capacitors and a 1.5-mH inductor are connected as shown in the figure. It is desired to "drive" the circuit by placing an ac generator in series with the inductor. Which one of the following generator output voltages will produce the largest current in the above circuit? Assume that V is in volts when t is in seconds.

A)V = 0.6 sin[(1.1 × 10⁶ rad/s)t]
B)V = 0.6 sin[(1.2 × 10³ rad/s)t]
C)V = 1.2 sin[(5.3 × 10⁶ rad/s)t]
D)V = 1.2 sin[(2.3 × 10⁵ rad/s)t]
E)V = 2.8 sin[(4.6 × 10⁶ rad/s)t]

Question 66

What is the inductance of the inductor in a series RCL circuit with a resonant frequency of 640 Hz if the only other element in the circuit is a 1.2-µF capacitor?

A)52 mH
B)74 mH
C)0.12 H
D)2.1 H
E)13 H

Question 67

Which one of the following materials would be in an n-type semiconductor?

A)silicon doped with boron
B)silicon doped with gallium
C)germanium doped with boron
D)silicon doped with phosphorus
E)germanium doped with gallium

Question 68

The graph shows the impedance as a function of frequency for a series RCL circuit. At what frequency will this circuit resonate?

A)f₁
B)f₂
C)f₃
D)f₁ or f₃
E)f₁ or f₂ or f₃

Question 69

A 315- $\varOmega$ resistor is connected in series with a parallel-plate capacitor across the terminals of a 60.0-Hz ac generator. When the gap between the plates is empty, its capacitance is 2.65 µF. Determine the ratio of the rms current in the circuit when the capacitor is empty to that when ruby mica ( $\kappa$ = 5.40) is inserted between the plates?

A)2.87
B)2.32
C)0.430
D)0.348
E)0.253

Question 70

Two series RCL circuits have the same resonant frequency. Circuit A has an inductance of 0.55 H and circuit B has an inductance of 0.15 H. Determine the ratio of the capacitances of the circuits, C_A/C_B.

A)0.44
B)0.27
C)3.7
D)1.8
E)2.4

Question 71

An ac generator supplies an rms (not peak) voltage of 180 V at 60.0 Hz. The generator is connected in series with a 0.50-H inductor, a 6.0-µF capacitor and a 300- $\varOmega$ resistor.

-What is the peak (not rms) voltage across the resistor?

A)120 V
B)140 V
C)190 V
D)260 V
E)290 V

Question 72

A series RCL circuit is comprised of a 3.00-mH inductor and a 5.00-µF capacitor. What is the resonant frequency of this circuit?

A)11.9 Hz
B)69.4 Hz
C)1.06 × 10² Hz
D)8.27 × 10² Hz
E)1.30 × 10³ Hz

Question 73

An oscillating LC circuit has a resonant frequency of 1.2 × 10⁶ Hz. The diagram shows the system at t = 0 s when there is no charge on the capacitor and the current is in the direction shown. At this time, the energy stored in the inductor is 2.5 × 10^-7 J.
Determine the value of the current at the instant shown in the drawing.

A)0.02 A
B)0.03 A
C)0.05 A
D)0.09 A
E)0.12 A

Question 74

An ac generator supplies an rms (not peak) voltage of 180 V at 60.0 Hz. The generator is connected in series with a 0.50-H inductor, a 6.0-µF capacitor and a 300- $\varOmega$ resistor.

-What is the peak (not rms) voltage across the capacitor?

A)120 V
B)180 V
C)190 V
D)210 V
E)290 V

Question 75

Complete the following statement: The main difference between an npn transistor and a pnp transistor is that

A)the bias voltages are reversed.
B)they are made from different materials.
C)one is a bipolar transistor and the other is not.
D)one conducts electricity and the other does not.
E)the current directions are the same while the voltages are reversed.

Question 76

An ac generator supplies a peak (not rms) voltage of 120.0 V at 60.0 Hz. It is connected in series with a 50.0- $\varOmega$ resistor and a 0.500-H inductor.

-What is the rms voltage of the generator?

A)84.9 V
B)138 V
C)151 V
D)169 V
E)240 V

Question 77

An ac generator supplies a peak (not rms) voltage of 120.0 V at 60.0 Hz. It is connected in series with a 50.0- $\varOmega$ resistor and a 0.500-H inductor.

-What is the inductive reactance of the circuit?

A)60 $\varOmega$
B)188 $\varOmega$
C)377 $\varOmega$
D)514 $\varOmega$
E)754 $\varOmega$

Question 78

Which one of the following statements best explains why semiconductors in transistors are doped?

A)Doping makes the charge carriers mobile.
B)Doping makes the charge carriers immobile.
C)Doping makes the semiconducting material non-conducting.
D)Doping increases the conductive properties of the semiconductors.
E)Doping converts the semiconducting material into a metallic material like copper.

Question 79

Which one of the following statements concerning diodes is false?

A)A diode is fabricated by forming junctions between one n-type and two p-type semiconductors or one p-type and two n-type semiconductors.
B)At an n-p junction in a diode that is not connected to a battery, an electric field exists across the junction.
C)A battery can be connected to a diode so that a continual flow of charge results.
D)A diode connected to an ac source allows current to flow only in one direction.
E)Holes move in a diode under a forward-bias condition.

Question 80

An oscillating LC circuit has a resonant frequency of 1.2 × 10⁶ Hz. The diagram shows the system at t = 0 s when there is no charge on the capacitor and the current is in the direction shown. At this time, the energy stored in the inductor is 2.5 × 10^-7 J.
Determine the numerical value of the capacitance.

A)2.4 × 10^-11 F
B)3.6 × 10^-11 F
C)4.4 × 10^-11 F
D)6.8 × 10^-11 F
E)8.8 × 10^-11 F