Deck 29: Alternating-Current Circuits

Question 1

A 15- $\Omega$ 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

Answer 1

0.19 kW

Question 2

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 sixteen
C)it is increased by a factor of eight.
D)it is increased by a factor of four
E)it is impossible to tell given the information provided

Answer 2

it is increased by a factor of four

Question 3

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 two
C)it is increased by a factor of eight
D)it is decreased by a factor of four
E)it is impossible to tell given the information provided

Answer 3

it is the same

Question 4

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 5

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 sixteen
C)it is decreased by a factor of two
D)it is increased by a factor of four
E)it is impossible to tell given the information provided

Question 6

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

Question 7

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

Question 8

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 9

A 15- $\Omega$ resistor is connected ACross a sinusoidal source that has a peak value of 75 V.The rms current drawn from this source is approximately

A)5.0 A
B)0.20 A
C)7.1 A
D)3.5 A
E)0.28 A

Question 10

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 11

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 12

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 nine
D)it is reduced by one-third
E)it is impossible to tell given the information provided

Question 13

The resistance of the armature windings of DC motor is 5 $\Omega$ .The motor is connected to a 120 V line.When the motor is spinning at full speed,it draws a current of 4 A.The bACk EMF at full speed is

A)20 V
B)100 V
C)120 V
D)40 V
E)80 V

Question 14

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 100 $\pi$ 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 15

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 16

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 17

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 18

An AC generator supplies 22 rms volts to a 30- $\Omega$ 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 19

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.

Question 20

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 21

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 22

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 23

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 24

An inductor with inductance L = 10 mH is connected to a power supply which provides a current I = 5 mA sin $\omega$ t.The maximum back EMF is

A)5 mV
B)10 mV
C)25 V
D)50 V
E)0 V

Question 25

At what frequency would the reactance of a 10-µF capacitor be 100 $\Omega$

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

Question 26

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 27

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 28

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

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

Question 29

The reACtance of an inductor is 10 $\Omega$ 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 30

Use the following figure for the next problem.
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 31

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 32

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 33

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

A)190 $\Omega$
B)1.6 $\Omega$
C)0.62 $\Omega$
D)5.2 $\times$ 10^-3 $\Omega$
E)270 $\Omega$

Question 34

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 35

The reACtance of an inductor is 100 $\Omega$ 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 36

At what frequency is the reACtance of a 1.5-mH inductor equal to 5.0 $\Omega$ ?

A)0.53 kHz
B)0.13 kHz
C)3.3 kHz
D)21 Hz
E)21 kHz

Question 37

At what frequency is the reACtance of a 3.5-mH inductor equal to 10.0 $\Omega$ ?

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

Question 38

Use the following figure for the next problem.
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 39

If you connect a 12-V rms AC power supply that operates at 5.0 kHz to a 20- $\mu$ F 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 40

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 41

The power dissipated per cycle is

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

Question 42

Use the following figure to answer the next problem:
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 43

Use the following figure for the next problem.
The figure shows the voltage and current for a(n)

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

Question 44

An inductor is placed across an AC generator that has a maximum EMF of 170 V.For a frequency of 3000 Hz,the rms current through the inductor is 5.0 A.Find the value of the inductor.

A)8.0 $\times$ 10^-3 H
B)9.2 $\times$ 10^-4 H
C)1.8 $\times$ 10^-3 H
D)1.3 $\times$ 10^-3 H
E)5.6 $\times$ 10^-3 H

Question 45

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 $\times$ 10⁵ Hz
B)7.07 $\times$ 10⁴ Hz
C)2.25 $\times$ 10⁴ Hz
D)3.18 $\times$ 10⁹ Hz
E)2.00 $\times$ 10¹⁰ Hz

Question 46

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 47

Use the following figure for the next problem. The battery has a voltage V = 6 V, the inductance of the inductor L = 12 mH and the capacitance of the capacitor 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 48

Use the following figure to answer the next problem:
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 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

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 k $\Omega$
B)13 k $\Omega$
C)0.60 k $\Omega$
D)47 $\Omega$
E)19 $\Omega$

Question 51

Use the following figure to answer the next problem:
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 52

A 5-µF capacitor is charged to 30 V and is then connected across a 10-µH inductor.The maximum value of the current in this circuit is

A)1.41 A
B)2.25 A
C)8.73 A
D)15.4 A
E)21.2 A

Question 53

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 $\Omega$
B)0.31 $\Omega$
C)6.0 $\Omega$
D)47 $\Omega$
E)19 $\Omega$

Question 54

At what frequency would the reactance of a 1.0-mH inductor be twice that of a 10- $\mu$ F capacitor?

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

Question 55

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

A)2.2 $\times$ 10⁶ Hz
B)1.3 $\times$ 10¹¹ Hz
C)3.6 $\times$ 10⁵ Hz
D)600 Hz
E)none of the above

Question 56

A capacitor is placed across an AC generator that has a maximum EMF of 170 V.For a frequency of 3000 Hz,the maximum current through the capacitor is 12 A.Find the value of the capacitor.

A)2.4 $\times$ 10^-5 F
B)2.6 $\times$ 10^-6 F
C)1.8 $\times$ 10^-5 F
D)3.7 $\times$ 10^-6 F
E)5.6 $\times$ 10^-6 F

Question 57

A 5-µF capacitor is charged to 30 V and is then connected across a 10-µH inductor.The maximum current in this circuit after a long time has passed will be

A)0
B)8.83 A
C)15.4 A
D)21.2 A
E)some value that cannot be determined from the given information.

Question 58

If you place a 40.0- $\mu$ F 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 $\Omega$
B)66 $\Omega$
C)0.38 k $\Omega$
D)19 $\Omega$
E)0.13 k $\Omega$

Question 59

At what frequency would the reactance of a 100-pF capactor be 1000 $\Omega$ ?

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

Question 60

An AC power supply,V = V_o sin $\omega$ t,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 61

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 $\mu$ F,and R = 10 $\Omega$ .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

Question 62

A series RLC circuit is driven by a 1.0-kHz oscillator.The circuit parameters are L = 5.0 mH,C = 4.0 $\mu$ F,R = 10 $\Omega$ .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 63

A 5-µF capacitor is charged to 30 V and is then connected in series with a 10-µH inductor and a 50- $\Omega$ resistor.The potential difference across the resistor 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 64

Use the following figure for the next problem.
The battery has a voltage V = 6 V, the inductance of the inductor L = 12 mH and the capacitance of the capacitor 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 $\mu$ C
B)1.33 $\mu$ C
C)48 $\mu$ C
D)72 $\mu$ C
E)zero

Question 65

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 $\mu$ F,and R = 10 $\Omega$ .Under these conditions the current

A)lags the voltage by 40º.
B)leads the voltage by 40º.
C)lags the voltage by 57.1º.
D)leads the voltage by 57.1º.
E)None of these are correct.

Question 66

A 5-µF capacitor is charged to 30 V and is then connected in series with a 10-µH inductor and a 50- $\Omega$ 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 67

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

A)8.4 $\Omega$
B)10 $\Omega$
C)13 $\Omega$
D)0.24 k $\Omega$
E)81 $\Omega$

Question 68

A series RLC circuit is driven by a 1.0-kHz oscillator.The circuit parameters are L = 5.0 mH,C = 4.0 $\mu$ F,R = 10 $\Omega$ .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 69

A 5-µF capacitor is charged to 30 V and is then connected in series with a 10-µH inductor and a 50- $\Omega$ 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 70

You have a 30-µH inductor and want to form a 1.0-MHz parallel,resonant circuit.You need a capacitor of

A)approximately 0.84 nF.
B)approximately 1.2 nF.
C)approximately 2.1 µF.
D)approximately 33 µF.
E)None of these is correct.

Question 71

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

A)3.77 $\Omega$
B)10 $\Omega$
C)13.8 $\Omega$
D)10.6 $\Omega$
E)none of these is correct

Question 72

A 5-µF capacitor is charged to 30 V and is then connected in series with a 10-µH inductor and a 50- $\Omega$ resistor.The initial current in the circuit will be

A)0
B)0.600 A
C)2.00 A
D)5.00 A
E)some value that cannot be determined from the given information.

Question 73

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

A)10 $\Omega$
B)14 $\Omega$
C)0.10 k $\Omega$
D)5.0 $\Omega$
E)impossible to tell from the given information.

Question 74

A circuit contains a capacitor (C $\mu$ F),an inductor (L mH),and an ohmic resistor (R $\Omega$ )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 75

Use the following figure for the next problem.
The battery has a voltage V = 6 V, the inductance of the inductor L = 12 mH and the capacitance of the capacitor 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 $\mu$ C
B)1.33 $\mu$ C
C)48 $\mu$ C
D)72 $\mu$ C
E)zero

Question 76

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 $\mu$ F,and R = 10 $\Omega$ .Under steady-state conditions,the rms current in the circuit will be

A)0.513 A
B)0.725 A
C)0.919 A
D)1.23 A
E)1.56 A

Question 77

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 $\mu$ F,and R = 10 $\Omega$ .Under steady-state conditions,the rms potential difference across the capacitor will be

A)9.73 V
B)12.2 V
C)18.4 V
D)25.5 V
E)36.6 V

Question 78

You have a 30-µH inductor and a 50-µF capacitor with which you form a parallel,resonant circuit.The frequency of this circuit will be

A)4.11 kHz
B)13.7 kHz
C)25.8 kHz
D)31.7 kHz
E)39.1 kHz

Question 79

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 $\mu$ F,and R = 10 $\Omega$ .Under steady-state conditions,the rms potential difference across the inductor will be

A)5.13 V
B)13.7 V
C)21.9 V
D)32.3 V
E)47.2 V

Question 80

A 5-µF capacitor is charged to 30 V and is then connected in series with a 10-µH inductor and a 50- $\Omega$ resistor.The current in this circuit after a long time has passed will be

A)0
B)8.83 A
C)15.4 A
D)21.2 A
E)some value that cannot be determined from the given information.