Deck 21: Alternating Current

Question 1

What is the peak (maximum) power dissipated by a 150 W light bulb attached to a 120 V rms ac line?

A) 300 W
B) 212 W
C) 150 W
D) 106 W
E) 75.0 W

Answer 1

300 W

Question 2

For a capacitor in an ac circuit, how much energy is stored in the capacitor at the instant when current is zero?

A) 0.707 maximum
B) half
C) zero
D) maximum

Answer 2

maximum

Question 3

Two 100 W bulbs differ in that one is designed for the North American 120 V rms electric supply, while the other is designed for the European 220 V rms. Which bulb has the greater resistance, and what is that resistance?

A) North American, 288 Ω
B) North American, 144 Ω
C) European, 484 Ω
D) European, 242 Ω
E) they are the same, 265 Ω

Answer 3

European, 484 Ω

Question 4

In an ac circuit, the current in a capacitor

A) leads the voltage by 90°.
B) lags the voltage by 90°.
C) is in phase with the voltage.
D) leads the voltage by π radians.
E) lags the voltage by π radians.

Question 5

What is maximum number of 150 W light bulbs that can run on a 130 V (rms) circuit protected by a 20 A (rms) circuit breaker?

A) 18
B) 16
C) 17
D) 15

Question 6

What is the capacitive reactance of an 8.00 μF capacitor attached to 120 V rms at 60.0 Hz?

A) 166 Ω
B) 332 Ω
C) 663 Ω
D) 480 Ω
E) 960 Ω

Question 7

The voltage supplied to an ac circuit is given by v(t) = (120 V) sin (377t). What is the voltage at t = 3.00 × 10⁻³ s?

A) 0.00 V
B) 2.37 V
C) 63.0 V
D) 109 V
E) 119 V

Question 8

A 150 W light bulb is operating on a 120 V rms ac line. What is the rms current in the bulb?

A) 2.50 A
B) 1.67 A
C) 1.50 A
D) 1.25 A
E) 0.883 A

Question 9

What is the average power for an 8.00 mF capacitor attached to a 120 V rms 60.0 Hz source?

A) 240 W
B) 120 W
C) 85.0 W
D) 60.0 W
E) 0

Question 10

What is the capacitance of a capacitor with a reactance of 20.0 Ω at a frequency of 60.0 Hz?

A) 50.0 mF
B) 50.0 μF
C) 133 mF
D) 133 μF
E) 833 μF

Question 11

A 2.2 k Ω resistor and a 2.0 μF capacitor are connected in series in an ac circuit. The rms voltages across each are equal. What is the frequency?

A) 23 Hz
B) 15 Hz
C) 72 Hz
D) 36 Hz
E) There is insufficient information to solve.

Question 12

What is the period for a frequency of 60 Hz?

A) 60 s
B) (1/60) s
C) 120 s
D) (1/120) s
E) (1/377) s

Question 13

A 1500 W hair dryer is run on a 120 V rms circuit. Which of the following is the lowest-rated current breaker that won't open the circuit?

A) 10 A
B) 15 A
C) 20 A
D) 30 A
E) 60 A

Question 14

The voltage supplied to an ac circuit is given by v(t) = (120 V) sin (60t). What are the rms voltage and the frequency?

A) 120 V, 60 Hz
B) 120 V, 380 Hz
C) 170 V, 9.5 Hz
D) 85 V, 9.5 Hz
E) 240 V, 30 Hz

Question 15

A lightbulb is connected to a 120 V (rms), 60 Hz source. How many times per second does the current reverse directions?

A) 60
B) 130
C) 120
D) 30

Question 16

The average value of sin²ωt for a complete cycle is

A) 1.
B) 0.
C) 0.707.
D) 0.500.
E) 0.250.

Question 17

What is the rms current for an 8.0 μF capacitor attached to a 120 V rms 60 Hz source?

A) 2.8 A
B) 1.4 A
C) 0.72 A
D) 0.36 A
E) 0.18 A

Question 18

A 150 W light bulb is designed for an ac voltage of 120 V rms. What is the resistance of the bulb?

A) 150 Ω
B) 144 Ω
C) 96 Ω
D) 68 Ω
E) 48 Ω

Question 19

A bulb is designed for 100 W at 130 V rms. What is the power dissipated by this bulb if it is used in a 120 V rms circuit?

A) 169 W
B) 130 W
C) 100 W
D) 85 W
E) it will blow out

Question 20

The difference between the highest and lowest voltage of a household "120 V emf" is

A) 120 V.
B) 170 V.
C) 240 V.
D) 340 V.
E) 377 V.

Question 21

What is the inductance of an inductor with a reactance of 20 Ω at a frequency of 60 Hz?

A) 12 H
B) 19 H
C) 3.0 H
D) 53 mH
E) 27 mH

Question 22

An ac circuit has a 20 μF capacitor, an 80 mH inductor, and a 60 Ω resistor in series. If the voltage source has an angular frequency of 1000 rad/s, what is the phase constant for the circuit?

A) 27°
B) 53°
C) 45°
D) 63°
E) 88°

Question 23

What is the inductive reactance of a 200 mH inductor attached to a 120 V rms, 60.0 Hz source?

A) 12.0 Ω
B) 75.4 Ω
C) 188 Ω
D) 940 Ω
E) 24.0 Ω

Question 24

What is the rms current in a 200 mH inductor attached to a 120 V rms, 60.0 Hz source?

A) 600 A
B) 12.0 A
C) 1.59 A
D) 100 A
E) 1.00 A

Question 25

A series LR circuit dissipates an average power of 60 W. The circuit is powered by a 120 V rms 60 Hz supply. If the current is 2.0 A rms, what is the inductance?

A) 0.10 H
B) 0.15 H
C) 0.20 H
D) 0.25 H
E) 0.30 H

Question 26

For an ideal inductor in an ac circuit, how much energy is stored in the inductor at the instant when the current is zero?

A) maximum
B) half
C) 0.707 maximum
D) zero

Question 27

A series LR circuit dissipates an average power of 60 W. The circuit is powered by a 120 V rms 60 Hz supply. If the current is 2.0 A rms, what is the power factor?

A) 0
B) 0.25
C) 0.50
D) 0.75
E) 1.0

Question 28

A series RLC ac circuit has a capacitive reactance of 55 Ω, an inductive reactance of 25 Ω, and a resistance of 40 Ω. What is the impedance of this circuit?

A) 12 Ω
B) 95 Ω
C) 70 Ω
D) 10 Ω
E) 50 Ω

Question 29

What capacitance is needed in series with a 30 Ω resistor at 1.0 kHz for a total impedance of 45 Ω?

A) 34 μF
B) 15 μF
C) 4.7 μF
D) 0.037 μF

Question 30

In an RLC ac circuit the current in the inductor and the current in the resistor are

A) out of phase by 90° with the current in the inductor leading.
B) out of phase by 90° with the current in the resistor leading.
C) in phase with each other.
D) out of phase by an amount proportional to frequency.
E) out of phase by an amount inversely proportional to frequency.

Question 31

A series RLC circuit has R = 200 Ω, L = 40.0 mH, and C = 120 pF. What is the impedance of this circuit at resonance?

A) 18.0 kΩ
B) 36.0 kΩ
C) 400 Ω
D) 300 Ω
E) 200 Ω

Question 32

A capacitor is connected to the terminals of a variable frequency oscillator. The peak voltage of the source is kept fixed while the frequency is increased. Which statement is true?

A) The rms current through the capacitor decreases.
B) The rms current through the capacitor increases.
C) The phase angle between the current and source voltage changes.
D) The current becomes zero when the frequency is large enough.

Question 33

A series LR circuit dissipates an average power of 60 W. The circuit is powered by a 120 V rms 60 Hz supply. If the current is 2.0 A rms, what is the phase constant?

A) 14°
B) 25°
C) 60°
D) 70°
E) 76°

Question 34

In an ac circuit, the current in an inductor

A) leads the voltage by 90°.
B) lags the voltage by 90°.
C) is in phase with the voltage.
D) leads the voltage by π radians.
E) lags the voltage by π radians.

Question 35

At what frequency is the reactance of a 20.0 mH inductor equal to 18.8 Ω?

A) 75.0 Hz
B) 150 Hz
C) 1500 Hz
D) 15.0 Hz

Question 36

The capacitive reactance of an RLC circuit is 64 Ω. If the frequency is doubled, what is the new capacitive reactance?

A) 18 Ω
B) 64 Ω
C) 32 Ω
D) 8.0 Ω
E) 4.0 Ω

Question 37

An ac circuit has a resistance of 120 Ω and an impedance of 200 Ω. What is the power factor for this circuit?

A) 53°
B) 32°
C) 0.60
D) 1.7
E) 1.3

Question 38

A series LR circuit dissipates an average power of 60 W. The circuit is powered by a 120 V rms 60 Hz supply. If the current is 2.0 A rms, what is the circuit resistance?

A) 50 Ω
B) 60 Ω
C) 15 Ω
D) 10 Ω
E) 24 Ω

Question 39

If the power factor for a series RLC circuit is 1.0, what is the phase constant?

A) 0.0°
B) 30°
C) 45°
D) 60°
E) 90°

Question 40

A series RLC ac circuit has a capacitive reactance of 55 Ω, an inductive reactance of 25 Ω, and a resistance of 40 Ω. What is the phase constant of this circuit?

A) 37°
B) −37°
C) 53°
D) −53°
E) 66°

Question 41

An RLC series circuit has a 400 Ω resistance, a 2.50 mH inductor, and a capacitor. If the resonant frequency is 30.0 kHz, and the circuit is attached to a 20 mV rms power supply, what is the rms current at resonance?

A) 60 μA
B) 40 μA
C) 30 μA
D) 50 μA
E) 25 μA

Question 42

In a series RLC circuit the rms voltage across the resistor is 80.0 V, across the capacitor is 120 V, and across the inductor is 60.0 V. If 1.50 A rms current is flowing in this circuit, what is the average power dissipated?

A) 200 W
B) 120 W
C) 80.0 W
D) 60.0 W
E) 40.0 W

Question 43

In a series RLC circuit the rms voltage across the resistor is 80 V, across the capacitor is 120 V, and across the inductor is 60 V. What is the phase constant for this circuit?

A) 27°
B) −27°
C) 37°
D) −37°
E) −41°

Question 44

The inductive reactance of an RLC circuit is 36 Ω. If the frequency is doubled, what is the new inductive reactance?

A) 72 Ω
B) 36 Ω
C) 19 Ω
D) 6.0 Ω
E) 3.0 Ω

Question 45

A series RLC circuit has resistance 200 Ω, inductance 0.200 H, and capacitance 0.500 μF. If the circuit is at resonance with a 120 V rms source, what is the average power dissipated?

A) 144 W
B) 120 W
C) 77.0 W
D) 72.0 W
E) 100 W

Question 46

As the ac frequency in an RLC circuit is increased to very high values, which of the contributions to the impedance dominates?

A) the capacitive reactance
B) the inductive reactance
C) the resistance
D) the combined capacitive reactance and the resistance
E) More information is needed.

Question 47

What inductance is needed in series with a 4.7 μF capacitor for a resonant frequency of 10 kHz?

A) 22 μH
B) 54 μH
C) 0.66 μH
D) 5.3 mH

Question 48

A series RLC circuit has a resistance of 500 Ω, an inductance of 20.0 mH, and a capacitance of 2.00 μF. The source provides a voltage of v(t) = (170 V) sin (377t). What is the peak current in this circuit?

A) 92.4 mA
B) 101 mA
C) 121 mA
D) 170 mA
E) 240 mA

Question 49

A series RLC circuit has a capacitive reactance of 16 Ω and an inductive reactance of 4.0 Ω at 30 Hz. What frequency would result in resonance for this circuit?

A) 12 Hz
B) 60 Hz
C) 15 Hz
D) 7.5 Hz
E) Resonance is not possible in this case.

Question 50

An RLC series circuit has a 200 Ωresistance, a 3.0 mH inductor, and a 100 μF capacitor. What is the resonant frequency for this circuit?

A) 1.8 kHz
B) 1.8 MHz
C) 290 Hz
D) 290 kHz
E) 11 kHz

Question 51

What is the resonant frequency of a 1.0 μF capacitor and a 15 mH inductor in series?

A) 15 kHz
B) 1.3 kHz
C) 0.87 kHz
D) 57 kHz

Question 52

An RLC series circuit has a 400 Ω resistance, a 2.5 mH inductor, and a capacitor. If the resonant frequency is 30.0 kHz, and the circuit is attached to a 20 mV rms power supply, what is the average power dissipated by the circuit at resonance?

A) 1.0 μW
B) 2.0 μW
C) 24 mW
D) 1.2 μW
E) 1.2 mW

Question 53

An RLC series circuit has a 22 Ω resistor, a 3.0 H inductor, and a capacitor. What capacitance would result in resonance at 60 Hz?

A) 55 mF
B) 0.33 F
C) 65 μF
D) 15 mF
E) 2.3 μF

Question 54

An RLC series circuit has a 400 Ω resistance, a 2.5 mH inductor, and a capacitor. If the resonant frequency is 30 kHz, what is the capacitive reactance at resonance?

A) 4.0 × 10² Ω
B) 6.2 × 10² Ω
C) 4.7 × 10² Ω
D) 71 Ω
E) 0.00

Question 55

An RLC series circuit has a 400 Ω resistance, a 2.5 mH inductor, and a capacitor. If the resonant frequency is 30.0 kHz, and the circuit is attached to a 20 mV rms power supply, what is the rms voltage across the inductor at resonance?

A) 20 mV
B) 24 mV
C) 16 mV
D) 48 mV
E) 0.00

Question 56

A series RLC circuit has a resistance of 500 Ω, an inductance of 20.0 mH, and a capacitance of 2.00 μF. The source provides a voltage of v(t) = (170 V) sin (377t). What is the impedance of this circuit?

A) 0.402 kΩ
B) 1.33 kΩ
C) 1.25 kΩ
D) 1.41 kΩ
E) 2.15 kΩ

Question 57

An ideal diode in an ac circuit

A) doubles the current.
B) halves the current.
C) permits the current to flow in only one direction.
D) permits the current to flow in one direction and double the current to flow in the other.
E) permits the current to flow in one direction and half the current to flow in the other.

Question 58

An RLC series circuit has a 200 Ω resistance, a 3.0 mH inductor, and a 100 μF capacitor. At resonance, what is the inductive reactance?

A) 21 Ω
B) 5.5 Ω
C) 11 Ω
D) 25 Ω
E) 30 Ω

Question 59

If the inductance and the capacitance both double in an LRC series circuit, the resonant frequency of that circuit will

A) decrease by a factor of 1/2.
B) decrease by a factor of 1/4.
C) increase by a factor of 2.
D) increase by a factor of 4.

Question 60

In a series RLC circuit the rms voltage across the resistor is 80.0 V, across the capacitor is 120 V, and across the inductor is 60.0 V. What is the rms voltage applied to this circuit?

A) 60.0 V
B) 80.0 V
C) 100 V
D) 120 V
E) 140 V

Question 61

What is the power factor for an RLC series at resonance?

A) one
B) its value depends upon the ratio of inductive reactance to impedance
C) its value depends upon the ratio of capacitive reactance to impedance
D) zero

Question 62

As frequency is varied in an RLC series circuit, resonance is reached when

A) the impedance becomes zero.
B) the inductive reactance is equal to the capacitive reactance.
C) the sum of the inductive and capacitive reactances is equal to the resistance.
D) the capacitive reactance is equal to the resistance.
E) the inductive reactance is equal to the resistance.

Question 63

An ac circuit consists of a 220 mH inductor in series with a 25 pF capacitor and a sinusoidal ac generator with an rms voltage of 12 V. If the frequency of the generator is 55 kHz, what will the rms voltage across the inductor be?

A) 5.4 V
B) 23 V
C) 6.6 V
D) 0.20 V

Question 64

An ac circuit consists of a 220 mH inductor in series with a 75 kΩ resistor and a sinusoidal source with an rms voltage of 12 V. At what frequency will the rms voltage across the resistor be equal to that across the inductor?

A) 114 kHz
B) 5.5 kHz
C) 54 kHz
D) 18 kHz

Question 65

An ac circuit consists of a 220 mH inductor in series with a 75 kΩ resistor and a 12 V rms sinusoidal ac generator. If the frequency of the generator is 25 kHz, what is the rms voltage across the inductor?

A) 7.0 V
B) 2.6 V
C) 9.4 V
D) 5.0 V

Question 66

An ac circuit consists of a 220 mH inductor in series with a 25 pF capacitor and a sinusoidal ac generator with an rms voltage of 12 V. If the frequency of the generator is 55 kHz, what will the rms voltage across the capacitor be?

A) 5.4 V
B) 35 V
C) 6.6 V
D) 11.80 V

Question 67

The average power dissipated in an RLC series circuit at resonance is dependent upon

A) the frequency.
B) the capacitive reactance.
C) the inductive reactance.
D) the resistance.

Question 68

A 25 nH inductor is connected to a 12 V rms ac source. At what frequency must the source drive the circuit if the rms current is to be 2.0 mA?

A) 38 GHz
B) 240 GHz
C) 0.15 MHz
D) 0.96 MHz

Question 69

An ac circuit consists of a 220 mH inductor in series with a 75 kΩ resistor and a 12 V rms sinusoidal emf. If the frequency of the emf is 25 kHz, what is the rms voltage across the resistor?

A) 7.0 V
B) 9.4 V
C) 11 V
D) 5.0 V

Question 70

An ac circuit consists of a 220 mH inductor in series with a 25 pF capacitor and an ac source with an rms voltage of 12 V. At what frequency will the rms voltage across the capacitor be equal to that across the inductor?

A) 94 kHz
B) 15 kHz
C) 68 kHz
D) 426 kHz

Question 71

As frequency is varied in an RLC series circuit, resonance is reached when

A) the voltages V_R, V_L and V_C all become equal.
B) the voltages V_L and V_C become zero.
C) the voltage V_R becomes equal to the source voltage.
D) None of the choices are correct.

Question 72

The current in an RLC circuit when driven at resonance depends on

A) the resonance frequency.
B) the resistance.
C) the inductive reactance.
D) the capacitive reactance.
E) More than one of these choices are correct.

Question 73

In an RLC series circuit, which of the following statements is true?

A) The current is in phase with the voltage across the inductor.
B) The current is in phase with the voltage across the resistor.
C) The current is in phase with the voltage across the capacitor.
D) None of the choices are true.