Deck 21: Alternating-Current Circuits

Question 1

A circular coil of radius 10 cm and a separate square coil of side 20 cm are both rotated in a magnetic field of 1.5 T. If the circular coil is rotated at a frequency of 60 Hz, then at what frequency must the square coil be rotated in order for both coils to have the same maximum induced voltage?

A) 47 Hz
B) 60 Hz
C) 76 Hz
D) 30 Hz
E) 19 Hz

Answer 1

47 Hz

Question 2

The rms value of house voltage in much of Europe is 220 V. What is the maximum voltage?

A) 440 V
B) 310 V
C) 220 V
D) 160 V
E) 120 V

Answer 2

310 V

Question 3

If you double the rms voltage in an AC circuit, the peak voltage

A) increases by a factor of 2.
B) decreases by a factor of 2.
C) increases by a factor of .
D) decreases by a factor of .
E) does not change.

Answer 3

increases by a factor of 2.

Question 4

A square coil with 12 turns and side 5 cm is rotated in a uniform magnetic field of 1.2 T at an angular frequency of 90 radians per second. What is the maximum voltage induced in the coil?

A) 10 V
B) 3.2 V
C) 0.51 V
D) 0.27 V
E) None of the above.

Question 5

A circular coil with 20 turns and radius 5 cm is rotated in a uniform magnetic field of 3.2 T. If the maximum voltage induced in the coil is 5 V, calculate the number of rotations of the coil per minute.

A) 600 revs per minute
B) 15 revs per minute
C) 5 revs per minute
D) 95 revs per minute
E) 200 revs per minute

Question 6

How much does the maximum EMF produced by a generator a rotating coil) change if the area of the coil is doubled and the angular frequency halved?

A) It is the same.
B) It is increased by a factor of 2.
C) It is increased by a factor of 8.
D) It is decreased by a factor of 4.
E) It is impossible to tell given the information provided.

Question 7

If you were to plug a 1200-W heater and a 600-W toaster into a 110-V electrical outlet, what total rms current would these two appliances draw if the wiring is parallel?

A) 5.45 A
B) 10.9 A
C) 11.6 A
D) 16.4 A
E) 23.1 A

Question 8

A flat, rectangular coil measuring 0.10 m by 0.20 m and containing 50 turns of wire is rotating at a constant speed of 100π rad/s in a magnetic field of 0.20 T. The maximum EMF induced in this coil is approximately

A) 1.0 V.
B) 10 V.
C) 63 V.
D) 44 V.
E) 0.13 V.

Question 9

How much does the maximum EMF produced by a generator a rotating coil) change if the period of rotation is doubled?

A) It is the same.
B) It is doubled.
C) It is quadrupled.
D) It is halved.
E) It is quartered.

Question 10

As the frequency in this simple AC circuit increases, the rms power dissipated by the resistor

A) increases.
B) does not change.
C) may increase or decrease depending on the magnitude of the original frequency.
D) may increase or decrease depending on the magnitude of the resistance.
E) decreases.

Question 11

If you double the peak voltage in an AC circuit, the rms voltage

A) increases by a factor of 2.
B) decreases by a factor of 2.
C) increases by a factor of .
D) decreases by a factor of .
E) does not change.

Question 12

An AC generator supplies 22 rms volts to a 30-Ω resistor at 50 Hz. What is the maximum current in the resistor?

A) 3.3 mA
B) 21 mA
C) 0.52 A
D) 0.73 A
E) 1.0 A

Question 13

An AC motor can be turned into an AC generator by

A) reversing the poles of the permanent magnets.
B) applying a reverse voltage to the terminals of the motor.
C) mechanically rotating the coils instead of applying a voltage to the coil.
D) replacing the magnet with an armature coil and vice versa.
E) applying a DC voltage instead of an AC voltage.

Question 14

A simple generator consists of a single rectangular loop of wire rotating between two magnetic pole faces as shown. Which curve in the graph correctly represents the EMF as a function of the angle between the normal to the plane of the coil and the direction of the magnetic field?

A) 1
B) 2
C) 3
D) 4
E) None of these is correct.

Question 15

How much does the maximum EMF produced by a generator a rotating coil) change if the area of the coil is quadrupled?

A) It is the same.
B) It is increased by a factor of 16.
C) It is increased by a factor of 8.
D) It is increased by a factor of 4.
E) It is impossible to tell given the information provided.

Question 16

How much does the maximum EMF produced by a generator a rotating coil) change if its magnetic field is halved?

A) It is the same.
B) It is increased by a factor of 16.
C) It is decreased by a factor of 2.
D) It is increased by a factor of 4.
E) It is impossible to tell given the information provided.

Question 17

A motor sometimes burns out when its load is suddenly increased because the resulting sudden decrease in its rotational frequency causes

A) an increased back EMF and an increased current flow.
B) a decreased back EMF and a decreased current flow.
C) a decreased back EMF and zero current flow.
D) an increased back EMF and a decreased current flow.
E) a decreased back EMF and an increased current flow.

Question 18

As the frequency in this simple AC circuit increases, the rms current through the resistor

A) increases.
B) does not change.
C) may increase or decrease depending on the magnitude of the original frequency.
D) may increase or decrease depending on the magnitude of the resistance.
E) decreases.

Question 19

How much does the maximum EMF produced by a generator a rotating coil) change if the number of turns of the coil is tripled?

A) It is the same.
B) It is tripled.
C) It is increased by a factor of 9.
D) It is reduced by one-third.
E) It is impossible to tell given the information provided.

Question 20

A 200-turn coil rotates in a magnetic field of magnitude 0.25 T at a frequency of 60 Hz. The area of the coil is 5.0 cm². What is the maximum EMF in the coil?

A) 1.5 V
B) 4.5 V
C) 9.0 V
D) 9.4 V
E) 24 V

Question 21

The figure shows the voltage and current for a device. The average power consumed by the device is

A) 2 W.
B) 0.6 W.
C) 1.2 W.
D) 0.3 W.
E) 2.4 W.

Question 22

The main power panel of a modern home is typically rated at 200 A at 120 V. The number of 60 W lightbulbs that can be on at the same time is

A) 120.
B) 240.
C) 360.
D) 400.
E) 600.

Question 23

At what frequency is the reactance ) of a 3.5-mH inductor equal to 10.0 Ω?

A) 1.45 kHz
B) 1.05 kHz
C) 0.865 kHz
D) 0.455 kHz
E) 0.234 kHz

Question 24

The 8000-turn primary of a transformer is connected to a 50-kV transmission line and the secondary has 19 turns. What is the voltage output of this transformer?

A) 21 MV
B) 119 V
C) 110 V
D) 21 kV
E) 220 V

Question 25

What is the resistance of a regular 75-W lightbulb connected to a 120-V AC outlet?

A) 190 Ω
B) 1.6 Ω
C) 0.62 Ω
D) 5.2 × 10^-3 Ω
E) 270 Ω

Question 26

In the U.K. the power companies supply an rms voltage of 240 V to most home outlets. If you were to try and use your standard U.S.-rated 1200-W at 120-V) hair dryer in the U.K. without using a transformer, what would be the average power supplied to the hair dryer?

A) 1200 W
B) 2400 W
C) 4800 W
D) 600 W
E) None of the above.

Question 27

A transformer is used in a converter so that a traveler can use a hair dryer made in the U.S. in their hotel room in Germany. The standard voltage in the U.S. is 120 V. The voltage in Germany is 220 V. The ratio of the number of turns must be

A) 0.545.
B) 1.833.
C) 20.
D) 100.
E) 340.

Question 28

A transformer is used to change

A) capacitance.
B) frequency.
C) voltage.
D) power.
E) None of these is correct.

Question 29

The figure shows the voltage and current for a device. The frequency of the voltage is

A) 0.2 Hz.
B) 0.4 Hz.
C) 1.2 Hz.
D) 2.0 Hz.
E) 2.5 Hz.

Question 30

Two heaters are plugged into the same 120-V AC outlet. If one heater is rated at 1100 W, then what can be the maximum rating of the second heater in order not to exceed the
20 A trip rating on the circuit?

A) 1100 W
B) 1300 W
C) 1200 W
D) 2400 W
E) 920 W

Question 31

The reactance ) of an inductor is 10 Ω at 1 kHz. The inductance of this inductor is

A) 1.00 mH.
B) 1.59 mH.
C) 2.06 mH.
D) 2.86 mH.
E) 3.45 mH.

Question 32

Most calculators operate on 6.0 V. If, instead of using batteries, you obtain 6.0 V from a transformer plugged into 110-V house wiring, what must the ratio of the primary to the secondary turns be in the transformer? Ignore any changes in voltage due to rectification.)

A) 0.054
B) 18
C) 660
D) 0.066
E) 15

Question 33

Electronic devices use electrical energy even when they are on standby. Calculate the percent of energy used per day for the following entertainment equipment in the standby mode assuming that they are plugged in all the time.

A) 0.45%
B) 1.1%
C) 4.8%
D) 5.1%
E) None of these is correct.

Question 34

An inductor with inductance L = 10 mH is connected to a power supply that provides a current I = 5 mA sin ωt. The maximum back EMF is

A) 5 mV.
B) 10 mV.
C) 25 μV.
D) 50 μV.
E) 0 V.

Question 35

The current in the primary of a transformer is changing at the rate of 500 A/s and the EMF in the secondary is 30 V. The coefficient of mutual inductance of this transformer is

A) 30 mH.
B) 60 mH.
C) 17 H.
D) 33 H.
E) 15 kH.

Question 36

You want the output current from the secondary coil of a transformer to be 10 times the input current to the primary coil. The ratio of the number of turns N₂/N₁ must be

A) 100.
B) 10.
C) 1.
D) 0.1.
E) 0.01.

Question 37

A heater is plugged into the same 120-V AC outlet as an 800-W hair dryer. If the total rms current drawn is 16.7 A, then calculate the power rating of the heater.

A) 2000 W
B) 800 W
C) 3200 W
D) 1200 W
E) 2800 W

Question 38

A 500-W toaster is plugged into a 120-V AC outlet. What is the peak current in the toaster?

A) 0.24 A
B) 4.2 A
C) 2.9 A
D) 0.34 A
E) 5.9 A

Question 39

The reactance ) of an inductor is 100 Ω at 2 kHz. The inductance of this inductor is

A) 1.99 mH.
B) 3.98 mH.
C) 7.96 mH.
D) 8.86 mH.
E) None of these answers is correct.

Question 40

A 15-Ω resistor is connected across a sinusoidal source that has a peak value of 75 V. The average power delivered by this source is approximately

A) 75 W.
B) 0.19 kW.
C) 0.38 kW.
D) 0.75 kW.
E) 1.2 W.

Question 41

If you double the frequency in the circuit shown, the inductance of the inductor

A) increases by a factor of 2.
B) does not change.
C) decreases by a factor of 2.
D) increases by a factor of 4.
E) decreases by a factor of 4.

Question 42

At what frequency would the reactance ) of a 10-μF capacitor be 100 Ω?

A) 318 Hz
B) 159 Hz
C) 79.6 Hz
D) 39.8 Hz
E) 25.4 Hz

Question 43

You place a 50-mH inductor across an AC generator that has a maximum EMF of 120 V. The inductive reactance ) when the frequency is 2.0 kHz is approximately

A) 0.63 kΩ.
B) 13 kΩ.
C) 0.60 kΩ.
D) 47 Ω.
E) 19 Ω.

Question 44

A 5-μF capacitor is charged to 30 V and is then connected across a 10-μH inductor. The frequency of oscillation of the energy stored in the electric field of the capacitor and the magnetic field of the inductor is

A) 1.41 × 10⁵ Hz
B) 7.07 × 10⁴ Hz
C) 2.25 × 10⁴ Hz
D) 3.18 × 10⁹ Hz
E) 2.00 × 10¹⁰ Hz

Question 45

For an inductor, the

A) voltage lags behind the current.
B) current lags behind the voltage.
C) current and the voltage are in phase.
D) current-voltage phase angle is greater than 90º.
E) current-voltage phase angle is less than 90º.

Question 46

Which of the following statements about a capacitor that is connected to an AC voltage is true?

A) The average power dissipated by the capacitor is zero.
B) At low frequencies the capacitor behaves like an open circuit.
C) At high frequencies the capacitor behaves like a short circuit.
D) At any given instant the net charges on the capacitor is zero.
E) All the above statements are true.

Question 47

For a capacitor, the

A) voltage lags behind the current.
B) current lags behind the voltage.
C) current and the voltage are in phase.
D) current-voltage phase angle is greater than 90º.
E) current-voltage phase angle is less than 90º.

Question 48

The battery has a voltage V = 6 V, the inductance of the inductor L = 12 mH and the capacitance of the capacitor C = 8 mF. Assume that the inductor and the wires have zero resistance.The switch S was at position a for a long time when it is switched to b. What is the charge on the capacitor at t = 0.487 ms?

A) 0.75 μC
B) 1.33 μC
C) 48 μC
D) 72 μC
E) zero

Question 49

A 5-μF capacitor is charged to 30 V and is then connected across a 10-μH inductor. The maximum value of the energy stored in the electric field of the capacitor is

A) 0.750 mJ.
B) 22.5 mJ.
C) 34.7 mJ.
D) 45.0 mJ.
E) 54.4 mJ.

Question 50

Which of the following statements about an inductor that is connected to an AC voltage is true?

A) The average power dissipated by the inductor is zero.
B) At low frequencies the inductor behaves like a short circuit.
C) At high frequencies the inductor behaves like an open short circuit.
D) The back EMF produced by the inductor is the maximum when the voltage is at zero part of the cycle.
E) All the above statements are true.

Question 51

You place a 50-mH inductor across an AC generator that has a maximum EMF of 120 V. The inductive reactance ) when the frequency is 60 Hz is approximately

A) 3.0 Ω.
B) 0.31 Ω.
C) 6.0 Ω.
D) 47 Ω.
E) 19 Ω.

Question 52

If you double the frequency in the circuit shown, the capacitive reactance ) of the circuit

A) increases by a factor of 2.
B) does not change.
C) decreases by a factor of 2.
D) increases by a factor of 4.
E) decreases by a factor of 4.

Question 53

The battery has a voltage V = 6 V, the inductance of the inductor L = 12 mH and the capacitance of the capacitor C = 8 mF. Assume that the inductor and the wires have zero resistance.The switch S was at position a for a long time when it is switched to b. What is the charge on the capacitor at t = 0 s?

A) 0.75 μC
B) 1.33 μC
C) 48 μC
D) 72 μC
E) zero

Question 54

If you place a 40.0-μF capacitor across a generator that has a maximum EMF of 120 V, the capacitive reactance ) when the frequency is 60 Hz is approximately

A) 1.5 Ω.
B) 66 Ω.
C) 0.38 kΩ.
D) 19 Ω.
E) 0.13 kΩ.

Question 55

At what frequency would the reactance ) of a 1.0-mH inductor be twice the reactance ) of a 10-μF capacitor?

A) 10 kHz
B) 3.2 kHz
C) 2.2 kHz
D) 1.6 kHz
E) 1.1 kHz

Question 56

The battery has a voltage V = 6 V, the inductance of the inductor L = 12 mH and the capacitance of the capacitor C = 8 mF. Assume that the inductor and the wires have zero resistance.The switch S was at position a for a long time when it is switched to b. Describe the current flow in the right loop.

A) There is no current flow in the loop since it is disconnected from the battery.
B) At the instant the switch is at b, the current starts to flow and then decays exponentially.
C) The current flows in a sinusoidal function with frequency .
D) The current flows in a damped oscillations.
E) None of the above.

Question 57

If you double the frequency in the circuit shown, the inductive reactance ) of the inductor

A) increases by a factor of 2.
B) does not change.
C) decreases by a factor of 2.
D) increases by a factor of 4.
E) decreases by a factor of 4.

Question 58

At what frequency would the reactance ) of a 100-pF capacitor be 1000 Ω?

A) 3.18 MHz
B) 15.9 MHz
C) 1.59 MHz
D) 3.98 MHz
E) 2.54 Mhz

Question 59

If you connect a 12-V rms AC power supply that operates at 5.0 kHz to a 20-μF capacitor, what is the rms current in the circuit neglect any resistance)?

A) 1.2 A
B) 7.5 A
C) 19 A
D) 8.4 A
E) 11 A

Question 60

At what frequency is the reactance ) of a 2-mH inductor equal to the reactance ) of a 100-pF capacitor?

A) 2.2 × 10⁶ Hz
B) 1.3 × 10¹¹ Hz
C) 3.6 × 10⁵ Hz
D) 600 Hz
E) None of the above,

Question 61

A circuit contains a capacitor C μF), an inductor L mH), and an ohmic resistor R Ω) connected in series. If you change the potential across this series combination, the values that change if you neglect thermal effects) are

A) C, L, and R.
B) C and R.
C) C and L.
D) R and L.
E) none of these is correct.

Question 62

A 10-mH inductor has an internal resistance of 10 Ω. The impedance of this inductor for a frequency of 60 Hz is approximately

A) 3.77 Ω.
B) 10 Ω.
C) 13.8 Ω.
D) 10.6 Ω.
E) none of these is correct.

Question 63

An AC power supply, V = V_o sin ωt, is connected in series to an inductor, capacitor, and resistor. The sum of the peak voltages across the inductor, capacitor, and resistor is

A) always equal to V_o.
B) always less than V_o.
C) always greater than V_o.
D) not possible to determine.
E) none of the above.

Question 64

A series RLC circuit is driven by a 1.0-kHz oscillator. The circuit parameters are L = 5.0 mH, C = 4.0 μF, R = 10 Ω. What is the resonance frequency of the circuit?

A) 1.1 kHz
B) 7.1 kHz
C) 11 kHz
D) 36 Hz
E) 36 kHz

Question 65

Use the following figure to answer the next question.
The diagram that correctly represents the phase relationship between the current through the resistor and the voltage across the capacitor in a circuit containing an inductor L, a capacitor C, and a resistor R all connected in series is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 66

A 10-mH inductor has a resistance of 10 Ω. Its impedance in an AC circuit is

A) 10 Ω.
B) 14 Ω.
C) 0.10 kΩ.
D) 5.0 Ω.
E) impossible to tell from the given information.

Question 67

A series RLC circuit is driven by a 1.0-kHz oscillator. The circuit parameters are L = 5.0 mH, C = 4.0 μF, R = 10 Ω. What is the impedance of this circuit?

A) 8.4 Ω
B) 10 Ω
C) 13 Ω
D) 0.24 kΩ
E) 81 Ω

Question 68

Use the following figure to answer the next question.
The diagram that correctly represents the phase relationship between the current through the resistor and the voltage across the inductor in a circuit containing an inductor L, a capacitor C, and a resistor R all connected in series is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 69

A series RLC circuit is driven by a 1.0-kHz oscillator. The circuit parameters are L = 5.0 mH, C = 4.0 μF, R = 10 Ω. If you adjust the frequency of the oscillator so that it is at the resonance frequency of the RLC circuit, and if it supplies 3.0 V rms, what is the rms current in the circuit?

A) 0.23 A
B) 0.36 A
C) 0.21 A
D) 0.30 A
E) 0.42 A

Question 70

Use the following figure to answer the next question.
The diagram that correctly represents the phase relationship between the current through the resistor and the voltage across the resistor in a circuit containing an inductor L, a capacitor C, and a resistor R all connected in series is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 71

A 5-μF capacitor is charged to 30 V and is then connected in series with a 10-μH inductor and a 50-Ω resistor. The potential difference across the capacitor after a long time has passed will be

A) 0.
B) 7 V.
C) 15 V.
D) 30 V.
E) some value that cannot be determined from the given information.

Question 72

The figure shows the voltage and current for an)

A) inductor.
B) capacitor.
C) resistor.
D) inductor and capacitor.
E) inductor and resistor.

Question 73

The diagram that correctly represents the phase relationship between the voltage across the resistor and the voltage across the inductor in a circuit containing an inductor L, a capacitor C, and a resistor R all connected in series is

A) 1).
B) 2).
C) 3).
D) 4).
E) 5).

Question 74

A 5-μF capacitor is charged to 30 V and is then connected in series with a 10-μH inductor and a 50-Ω resistor. The potential difference across the inductor after a long time has passed will be

A) 0.
B) 7 V.
C) 15 V.
D) 30 V.
E) some value that cannot be determined from the given information.

Question 75

The approximate resonant frequency of the circuit shown is

A) 1.5 kHz.
B) 0.25 kHz.
C) 2.4 MHz.
D) 25 kHz.
E) none of these is correct.

Question 76

The power dissipated per cycle is

A) 2 W.
B) 4 W.
C) 6 W.
D) 8 W.
E) zero.

Question 77

At t = 0.25 s, the power input is approximately

A) -2.5 W.
B) 2.5 W.
C) -10 W.
D) 10 W.
E) zero.

Question 78

The diagram that correctly represents the phase relationship between the voltage across the resistor and the voltage across the capacitor in a circuit containing an inductor L, a capacitor C, and a resistor R all connected in series is

A) 1).
B) 2).
C) 3).
D) 4).
E) 5).

Question 79

When you close the switch S in the figure, the potential between A and B drops to zero. The current in the top loop does not immediately drop to zero because

A) the top loop has less resistance than the bottom loop.
B) an EMF is generated in the inductor L.
C) an EMF is generated in the resistor R.
D) the current depends only on the resistance in the circuit.
E) Kirchhoff's junction rule states that the current into a junction must equal the current out of the junction.

Question 80

A series RLC circuit is driven by a 1.0-kHz oscillator. The circuit parameters are V_rms = 12 V, L = 5.0 mH, C = 4.0 μF, and R = 10 Ω. Under steady-state conditions, the rms potential difference across the resistor will be

A) 5.13 V.
B) 9.19 V.
C) 12.3 V.
D) 14.7 V.
E) 18.8 V.