Essential University Physics, 3e (Wolfson)Chapter 28 Alternating-Current Circuits

28.1 Conceptual Questions

1) An ac source of period T and maximum voltage V is connected to a single unknown ideal element that is either a resistor, and inductor, or a capacitor. At time t = 0 the voltage is zero. At time t = T/4 the current in the unknown element is equal to zero, and at time t = T/2 the current is I = -Imax, where Imax is the current amplitude. What is the unknown element?A) a resistorB) an inductorC) a capacitorD) an inductor or a capacitorAnswer: CVar: 1

2) A resistor is connected to an ideal ac power supply. (a) The phase angle between the current and voltage is

A) 0B) π/2 radians.C) -π/2 radians.D) π radians.E) 3π/4 radians.

(b) The current in the resistor A) leads the voltage across the resistor by 90°.

B) lags the voltage across the resistor by 90°.C) is in phase with the voltage across the resistor.D) the voltage across the resistor by 45°.E) lags the voltage across the resistor by 45°.

(c) How does the average power dissipated in the resistor change as the frequency in the ac power supply decreases? A) It decreases.

B) It increases.C) It does not change.D) It increases or decreases depending on the sign of the phase angle.

Answer: (a) A (b) C (c) CVar: 1

3) When an LRC series circuit is at resonance, which one of the following statements about that circuit is accurate? (There may be more than one correct choice.)A) The impedance has its maximum value.B) The reactance of the inductor is zero.C) The reactance of the capacitor is zero.D) The reactance due to the inductor and capacitor has its maximum value.E) The current amplitude is a maximum.Answer: EVar: 1

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4) In a series LRC circuit, the frequency at which the circuit is at resonance is f0. If you double the resistance, the inductance, the capacitance, and the voltage amplitude of the ac source, what is the new resonance frequency?A) 4 f0B) 2 f0C) f0D) f0/2E) f0/4Answer: DVar: 1

5) Which one of the phasor diagrams shown below best represents a series LRC circuit driven at resonance?

A) 1B) 2C) 3D) 4E) 5Answer: CVar: 1

6) When an LRC series circuit is driven at resonance, which of the following statements about the circuit are correct? (There may be more than one correct choice.)A) The impedance of the circuit is zero.B) The impedance of the circuit has its maximum value.C) The impedance of the circuit has its minimum value.D) The inductive reactance and the capacitive reactance are both zero.E) The inductive reactance and the capacitive reactance are exactly equal to each other.Answer: C, EVar: 1

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28.2 Problems

1) (a) In an ac circuit, if the peak value of the voltage is 100 V, what is the rms value of the voltage?

A) 141 VB) 100 VC) 210 VD) 71 VE) 120 V

(b) In an ac circuit, if the rms value of the current is 100 mA, what is the peak value of the current?

A) 141 mAB) 100 mAC) 210 mAD) 71 mAE) 120 mA

Answer: (a) D(b) AVar: 1

2) An alternating current is supplied to an electronic component with a warning that the voltage across it should never exceed What is the highest rms voltage that can be supplied to this component while staying below the voltage limit in the warning?A) 6 V

B) 12 VC) 144 VD) 6 VAnswer: AVar: 11

3) The inductor in a radio receiver carries a current of amplitude 200 mA when a voltage of amplitude 2.40 V is across it at a frequency of 1400 kHz. What is the value of the inductance?A) 1.43 µHB) 1.36 µHC) 9.20 µHD) 4.42 µHE) 1.97 µHAnswer: BVar: 1

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4) The 60-Hz ac source of the series circuit shown in the figure has a voltage amplitude of 120 V. The capacitive reactance is 790 Ω, the inductive reactance is 270 Ω, and the resistance is 500Ω.

(a) What is the capacitance of the capacitor?(b) What is the inductance of the inductor?Answer: (a) 3.4 µF (b) 720 mHVar: 1

5) If the voltage amplitude across an 8.50-nF capacitor is equal to 12.0 V when the current amplitude through it is 3.33 mA, the frequency is closest to:A) 32.6 MHzB) 5.20 MHzC) 32.6 kHzD) 5.20 kHzE) 32.6 HzAnswer: BVar: 1

6) An ac series circuit consists of a voltage source, an 880-Ω resistor, and an inductance L. (There is no capacitance in the circuit.) The current amplitude is 0.60 A, and the phase angle between the source voltage and the current has a magnitude of 41°(a) Does the source voltage lag or lead the current?(b) What is the voltage amplitude of the source?Answer: (a) The source voltage leads the current. (b) 700 voltsVar: 1

7) An LRC series circuit has R = 15.0 Ω, L = 25.0 mH, and C = 30.0 μF. The circuit is connected to a 120-V (rms) ac source with frequency 200 Hz.(a) What is the impedance of the circuit?(b) What is the rms current in the circuit?(c) What is the rms voltage across the resistor?(d) What is the rms voltage across the inductor?(e) What is the rms voltage across the capacitor?Answer: (a) 15.8 Ω (b) 7.61 A (c) 114 V (d) 239 V (e) 202 VVar: 1

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8) An ac circuit is shown in the figure. The rms current in the circuit is measured to be 1.8 A. What is the capacitance of the capacitor?

A) 23 μFB) 24 μFC) 21 μFD) 19 μFE) 18 μFAnswer: AVar: 1

9) The 60-Hz ac source of a series circuit has a voltage amplitude of 120 V. The resistance, capacitive reactance, and inductive reactance are as shown in the figure. What is the rms current in the circuit?

A) 0.097 AB) 0.11 AC) 0.12 AD) 0.14 AE) 0.17 AAnswer: AVar: 1

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10) A series ac circuit consists of an inductor having a reactance of 80 Ω and an inductance of 190 mH, a 40-Ω resistor, a capacitor whose reactance is 100 Ω, and an ac source. The rms current in the circuit is measured to be 2.2 A. What is the rms voltage of the source?A) 98 VB) 96 VC) 93 VD) 91 VE) 88 VAnswer: AVar: 1

11) A 120-V rms voltage at 1000 Hz is applied to an inductor, a 2.00-μF capacitor and a 100-Ω resistor, all in series. If the rms value of the current in this circuit is 0.680 A, what is the inductance of the inductor?A) 34.2 mHB) 35.8 mHC) 11.4 mHD) 17.9 mHE) 22.8 mHAnswer: BVar: 1

12) A series LRC circuit has a sinusoidal voltage supplied to it at with a peak voltage of a resistance, a capacitor, and a inductance. What is the peak current

for this circuit?A) 3.5 μAB) 2.3 μAC) 4.2 μAD) 6.6 μAAnswer: AVar: 50+

13) A series circuit consists of a 50-Hz ac source, a 50-Ω resistor, a 0.50-H inductor, and a 60-μF capacitor. The rms current in the circuit is measured to be 3.1 A. What is the voltage amplitude of the source?A) 510 VB) 270 VC) 220 VD) 180 VE) 160 VAnswer: AVar: 1

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14) A series circuit consists of ac source, a 90-Ω resistor, a 0.80-H inductor, and an 80-μF capacitor. The frequency of the source is adjusted so that the capacitive reactance is equal to twice the inductive reactance. What is the frequency of the source?A) 14 HzB) 13 HzC) 16 HzD) 17 HzE) 19 HzAnswer: AVar: 1

15) An LRC series circuit consists of an 85.0-Ω resistor, a 14.0-μF capacitor, a 1.50-mH inductor, and a variable frequency ac source of voltage amplitude 13.25 V. At what angular frequency will the inductive reactance be 4.00 times as large as the capacitive reactance?A) 1.38 × 104 rad/sB) 6.90 × 103 rad/sC) 3.45 × 104 rad/sD) 2.20 × 104 rad/sE) 1.10 × 104 rad/sAnswer: AVar: 1

16) A series ac circuit consists of a voltage source of frequency 60 Hz and source voltage amplitude 345 volts, a resistor, a capacitor, and an inductor of inductance L.(a) What must be the value of L for the phase angle to be zero?(b) When L has the value calculated in part (a), what is the current amplitude in the circuit?Answer: (a) 4.4 H (b) 0.492 AVar: 50+

17) A series LRC circuit consists of an ac voltage source of amplitude 75.0 V and variable frequency, a 12.5-µF capacitor, a 5.00-mH inductor, and a 35.0-Ω resistor.(a) To what angular frequency should the ac source be set so that the current amplitude has its largest value? (b) Under the conditions of part (a), what is the maximum current amplitude?(c) Suppose that the voltage source is set to twice the angular frequency needed in part (a). What will be the current amplitude in this case?Answer: (a) 4.00 × 103 rad/s (b) 2.14 A (c) 1.63 AVar: 1

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18) An ac circuit is shown in the figure. The rms current in the circuit is 1.3 A. What is the peak magnetic energy in the inductance?

A) 0.32 JB) 0.16 JC) 0.48 JD) 0.64 JE) 0.80 JAnswer: AVar: 1

19) A 120-V rms voltage at 60.0 Hz is applied across an inductor, a capacitor, and a resistor in series. If the peak current in this circuit is 0.8484 A, what is the impedance of this circuit?A) 200 ΩB) 141 ΩC) 20.4 ΩD) 120 ΩE) 100 ΩAnswer: AVar: 1

20) A 25.0-mH inductor, a 2.00-μF capacitor, and a certain resistor are connected in series across an ac voltage source at 1000 Hz. If the impedance of this circuit is 200 Ω, what is the resistance of the resistor?A) 100 ΩB) 184 ΩC) 200 ΩD) 552 ΩE) 579 ΩAnswer: BVar: 1

21) A series circuit has a resistance of 4.0 Ω, a reactance (due to the capacitance) of 21.0 Ω, and a reactance (due to the inductance) of 17.0 Ω. Find the impedance of the circuit.A) 5.7 ΩB) 27 ΩC) 8.0 ΩD) 42 ΩAnswer: AVar: 1

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22) The phase angle of an LRC series circuit with an inductive reactance of 200 Ω and a capacitive reactance of 100 Ω is 40.0°. What is the value of the resistor in this circuit?A) 100 ΩB) 119 ΩC) 156 ΩD) 200 ΩE) 265 ΩAnswer: BVar: 1

23) The phase angle of an LRC series circuit with an inductive reactance of 200 Ω, a resistor of 200 Ω and a certain capacitor at 1000 Hz is 40.0°. What is the value of the capacitance in this circuit?A) 1.95 µFB) 2.95 µFC) 3.95 µFD) 4.95 µFE) 5.95 µFAnswer: DVar: 1

24) The phase angle of an LRC series circuit with a capacitive reactance of 40 Ω, a resistor of 100 Ω and a certain inductor at 1000 Hz is 40.0°. What is the value of the inductance in this circuit?A) 11.8 mHB) 124 mHC) 212 mHD) 61.9 mHE) 19.7 mHAnswer: EVar: 1

25) An LRC series circuit has voltage supplied to it at a frequency of 13.0 kHz with a phase difference between the current and the voltage of magnitude 0.20 rad. If the circuit has a capacitance of 5.0 μF and an inductance of 0.050 H find the resistance of the circuit.A) 20 kΩB) 0.99 kΩC) 9.0 kΩD) 0.32 kΩAnswer: AVar: 1

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26) A series LRC ac circuit has a resistance of 4.0 kΩ, a capacitance of 33.0 μF, and an inductance of 23.0 H. If the frequency of the alternating current is 2.0/π kHz, what is the phase angle between the voltage and the current?A) 1.5 radB) -1.6 radC) 23 radD) 3.1 radAnswer: AVar: 1

27) An LRC ac series circuit has R = 15 Ω, L = 25 mH, and C = 30 μF. The circuit is connected to a 120-V (rms) ac source with frequency 200 Hz.(a) What is the average power dissipated by the circuit?(b) What is the power factor for the circuit?Answer: (a) 870 W (b) 0.95Var: 1

28) An LRC ac series circuit with R = 15 Ω, L = 25 mH, and C = 30 μF, is attached to a 100-V (rms) ac power supply. The frequency of the power supply is adjusted so that the circuit is in resonance.(a) What is the rms current in the circuit?(b) What is the power dissipated by the circuit?Answer: (a) 6.7 A (b) 670 WVar: 1

29) What is the average power dissipated by a 25-Ω resistor in an LRC series ac circuit for which the power factor is equal to 0.25 and the maximum voltage of the ac source is 8.0 V?A) 0.040 WB) 0.32 WC) 0.16 WD) 0.62 WE) 0.080 WAnswer: EVar: 1

30) A series LRC ac circuit has a peak voltage of and a peak current of If the current lags the voltage by what is the average power of the circuit?A) 91 WB) 182 WC) 78 WD) 156 WAnswer: AVar: 50+

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31) An LRC ac circuit has a reactance (due to its capacitance) of 17 kΩ, a reactance (due to its inductance) of 9.0 kΩ, and a resistance of 28 kΩ. What is the power factor of the circuit?A) 0.96B) 0.28C) 1.04D) 0.48Answer: AVar: 1

32) For an RLC ac circuit, the rms current is 10 A. If the impedance is 12 kΩ when the voltage leads the current by 39°, find the average power of the circuit.A) 930 kWB) 47 kWC) 93 kWD) 190 kWAnswer: AVar: 1

33) A series LRC ac circuit has a peak current of 1.0 A with a frequency of 54 kHz. If the resistance of the circuit is 51 kΩ, the capacitance of the circuit is 19 μF, and the inductance of the circuit is 25 μH, determine the average power of the circuit.A) 26 kWB) 77 kWC) 7.7 kWD) 4.1 kWAnswer: AVar: 1

34) A series circuit consists of a 50-Hz ac source, a 40-Ω resistor, a 0.30-H inductor, and a 60-μF capacitor. The rms current in the circuit is measured to be 1.6 A. What is the power factor of the circuit?A) 0.70B) 0.66C) 0.63D) 0.59E) 0.56Answer: AVar: 1

35) An ac series circuit consists of a voltage source of frequency 60 Hz and voltage amplitude V, a resistor, and a capacitor of capacitance What must be the source voltage amplitude V for the average electrical power consumed in the resistor to be 989 W? There is no inductance in the circuit.Answer: 1300 VVar: 50+

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36) For an LRC series circuit containing a resistance of a capacitance of and an inductance of what frequency is needed to minimize the impedance?A) 0.023 kHzB) 0.14 kHzC) 10 kHzD) 1.7 kHzAnswer: AVar: 50+

37) A series LRC circuit consists of a 100-Ω resistor, a 0.100-μF capacitor and a 2.00-mH

inductor connected across a 120-V rms ac voltage source operating at . At what frequency

will this circuit be in resonance?A) 70.7 kHzB) 17.9 kHzC) 22.5 kHzD) 35.3 kHzE) 11.3 kHzAnswer: EVar: 1

38) An ac source having a maximum voltage output of 30 V is connected in series with a 50-Ω resistor, a 0.60-H inductor, and a 20-µF capacitor. What is the maximum charge on the capacitor when the frequency of the source is adjusted so that the circuit is in resonance?A) 1.0 mCB) 0.00 mCC) 2.1 mCD) 4.2 mCE) 8.4 mCAnswer: CVar: 1

39) A series LRC circuit consists of a 5.00-pF capacitor, a 7.25-mH inductor, a 75.0-Ω resistor, and a 50.0-V ac power source of variable frequency. At what frequency will the impedance of this circuit be equal to 75.0 Ω?Answer: 836 kHzVar: 1

40) A series LRC circuit consists of a 12.0-mH inductor, a 15.0-µF capacitor, a resistor, and a 110-V (rms) ac voltage source. If the impedance of this circuit is 45.0 Ω at resonance, what is its impedance at a frequency twice the resonance frequency?Answer: 61.8 ΩVar: 1

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41) The primary coil of a transformer has 100 turns and its secondary coil has 400 turns. If the ac voltage applied to the primary coil is 120 V, what voltage is present in its secondary coil?A) 100 VB) 30 VC) 70 VD) 480 VE) 400 VAnswer: DVar: 1

42) A transformer changes the 10,000 V power line to 120 V. If the primary coil contains 750 turns, how many turns are on the secondary?A) 3B) 6C) 9D) 63,000E) 21,000Answer: CVar: 1

43) In a transformer, how many turns are necessary in a 110-V primary if the 24-V secondary has 100 turns?A) 458B) 240C) 110D) 22E) 4Answer: AVar: 1

44) When a current of 2.0 A flows in the 100-turn primary of an ideal transformer, this causes 14 A to flow in the secondary. How many turns are in the secondary?A) 700B) 356C) 114D) 14E) 4Answer: DVar: 1

45) An ideal transformer consists of a 500-turn primary coil and a 2000-turn secondary coil. If the current in the secondary is 3.0 A, what is the current in the primary?A) 0.75 AB) 1.3 AC) 12 AD) 24 AE) 48 AAnswer: CVar: 1

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