Chapter (33)

Chapter 33

Alternating Current Circuits

Multiple Choice

1. An ac generator with peak voltage 100 volts is placed across a 10-Ω resistor. What is the average power dissipated?

a. 100 W b. 150 W c. 500 W d. 1000 W e. 2000 W

2. An electric heater draws an average power of 1100 Watts when plugged into a 110 V-rms outlet. Calculate the resistance of the heater and the rms current.

a. 11Ω, 10 A (rms) b. 110Ω, 10 A (rms) c. 10Ω, 11 A (rms) d. 10Ω, 110 A (rms) e. 0.09Ω, 11 A (rms)

3. An incandescent lightbulb is rated at 100 Watts when plugged into a 110 V-rms household outlet. Calculate the resistance of the filament and the rms current.

a. 12.2Ω, 0.90 A (rms) b. 10Ω, 1.0 A (rms) c. 110Ω, 1.0 A (rms) d. 121Ω, 0.90 A (rms) e. 11Ω, 1.1 A (rms)

4. A high-voltage powerline operates at 500 000 V-rms and carries an rms current of 500 A. If the resistance of the cable is 0.050Ω/km, what is the resistive power loss in 200 km of the powerline?

a. 250 kW b. 500 kW c. 1 Megawatt d. 2.5 Megawatts e. 250 Megawatts

219

220 CHAPTER 33

5. A 230 000 V-rms powerline carries an average power PAV = 250 MW a distance of 200 km. If the total resistance of the cables is 10 ohms, what is the resistive power loss?

a. 1.0 MW b. 2.5 MW c. 5.4 MW d. 12 MW e. 10 kW

6. Inductive reactance XL is given by

a. Lω b. L/ω c. 1/Lω d. ω/L e. ω2L

7. Capacitive reactance XC is given by

a. 1/ωC b. ωC c. ω/C d. C/ω e. 1/ω2C

8. The total impedance Z of an RLC circuit driven by an ac voltage source at angular frequency ω is,

222 )(

CXLR −+ ω a.

22 )( CL XXR −+ b.

22 )(

1

CL XXR −+ c.

22 )( CL XXR ++d. 22 )( CL XXR +− e.

9. At what frequency will a 12-μF capacitor have a reactance XC = 300Ω?

a. 44 Hz b. 88 Hz c. 176 Hz d. 352 Hz e. 278 Hz

Alternating Current Circuits 221

10. At what frequency will a 50-mH inductor have a reactance XL = 700Ω?

a. 352 Hz b. 777 Hz c. 1.25 kHz d. 2.23 kHz e. 14 kHz

11. A 2-μF capacitor in series with a 2-kΩ resistor is connected to a 60-Hz ac source. Calculate the impedance of the circuit.

a. 1500 ohms b. 1800 ohms c. 2100 ohms d. 2400 ohms e. 8600 ohms

12. A 10-μF capacitor is plugged into a 110 V-rms 60-Hz voltage source, with an ammeter in series. What is the rms value of the current through the capacitor?

a. 0.202 A (rms) b. 0.415 A (rms) c. 0.626 A (rms) d. 0.838 A (rms) e. 0.066 A (rms)

13. A 0.5-H inductor is connected into a 110 V-rms 60-Hz voltage source, with an ammeter in series. What is the rms value of the current through the inductor?


14. An LC circuit is to have resonant oscillations at 5.0 MHz. Find the value of a capacitor which will work with a 1.0-mH inductor.

a. 2 mF b. 1 μF c. 0.02 μF d. 1 pF e. 40 pF

15. The inductance of a tuning circuit of an AM radio is 4 mH. Find the capacitance of the circuit required for reception at 1200 kHz.

a. 2.1 pF b. 4.4 pF c. 21.2 pF d. 43.4 pF e. 27.6 pF

222 CHAPTER 33

16. Find the resonant frequency for a series RLC circuit where R = 10Ω, C = 5 μF, and L = 2 mH.

a. 998 Hz b. 1.592 kHz c. 2.45 kHz d. 11.3 kHz e. 2.53 kHz

17. The voltage 8.00 sin (400t) is applied to a series RLC circuit, with R = 200Ω, L = 0.100 H, and C = 1.00 μF. What are the impedance Z and the phase angle θ ?

a. 200 Ω, –37° b. 566 Ω, +87° c. 2470 Ω, –85.4° d. 2540 Ω, –88.8° e. 393 Ω, –63°

18. If an R = 1-kΩ resistor, a C = 1-μF capacitor, and an L = 0.2-H inductor are connected in series with a V = 150 sin (377t) volts source, what is the maximum current delivered by the source?

a. 0.007 A b. 27 mA c. 54 mA d. 0.308 A e. 0.34 A

19. If the input to an RLC series circuit is V = Vm cos ωt, then the current in the circuit is

RVm cos ωt a.

b. 222 LR ω

cos tVm ω

+

c. 22

sin tVm

ωω

ω

)1( CLR ++

d. 22 )1(

)cos(

CLR

tVm

ωω

ω

−+

−φ

e. Vm ( ) tCLR ωωω cos1 22 −+

20. An RLC series circuit has R = 100 ohms, C = 25 μF, and L = 0.16 H. For what angular frequency of an ac voltage is the current flow maximum?

a. 251 rad/s b. 500 rad/s c. 757 rad/s d. 884 rad/s e. 79.6 rad/s


21. Determine the rms voltage for the circuit.

1 kΩ

1 H

1 μF

V = 140 sin (500 t)

a. 99 V (rms) b. 140 V (rms) c. 196 V (rms) d. 70 V (rms) e. 110 V (rms)

22. Determine the impedance for the circuit.

1 kΩ

1 HV = 140 sin (500 t)

1 μF

a. 600 Ω b. 1200 Ω c. 1800 Ω d. 2300 Ω e. 1100 Ω

23. Determine the rms current for the circuit.

1 kΩ

1 HV = 140 sin (500 t)

1 μF a. 55 mA b. 77 mA c. 99 mA d. 0.190 A e. 61 mA

224 CHAPTER 33

24. Determine the resonant frequency of the circuit.

1 kΩ

1 H

1 μF

V = 140 sin (500 t)

a. 159 Hz b. 32 Hz c. 5 Hz d. 500 Hz e. 79.5 Hz

25. Determine the rms voltage drop across the resistor in the circuit.

1 kΩ

1 HV = 140 sin (500 t)

1 μF a. 55 V b. 77 V c. 9.9 V d. 5.5 V e. 61 V

26. Determine the rms voltage drop across the inductor in the circuit.

1 kΩ

1 HV = 140 sin (500 t)

1 μF a. 11 V b. 27.5 V c. 33 V d. 38.5 V e. 30.5 V


27. Determine the rms voltage drop across the capacitor in the circuit.

1 kΩ

1 H

1 μF

V = 140 sin (500 t)

a. 55 V b. 77 V c. 110 V d. 154 V e. 198 V

28. A current I = 3 sin (400 t) amperes flows in a series RL circuit in which L = 1 mH and R = 100Ω. What is the average power loss?

a. 225 W b. 450 W c. 980 W d. 1.12 kW e. 900 W

29. What is the average power dissipation in a series RC circuit if R = 5 kΩ, C = 2 μF, and V = 170 cos (300t)?

a. 0.93 W b. 2.60 W c. 28.2 W d. 157 W e. 5.20 W

30. What is the average power dissipation in an RLC series circuit with R = 10Ω, L = 0.1 H, C = 10 μF when driven at resonance by a 100 V-rms source?

a. 100 W b. 500 W c. 1000 W d. 2 kW e. 700 W

31. A series RLC circuit has an impedance of 120Ω and a resistance of 64Ω. What average power is delivered to this circuit when Vrms = 90 volts?

a. 36 W b. 100 W c. 192 W d. 360 W e. 12 W

226 CHAPTER 33

32. A transformer is to be designed to increase the 30 kV-rms output of a generator to the transmission-line voltage of 345 kV-rms. If the primary winding has 80 turns, how many turns must the secondary have?

a. 6 b. 70 c. 920 d. 9200 e. 12

33. The primary winding of an electric train transformer has 400 turns and the secondary has 50. If the input voltage is 120V(rms) what is the output voltage?

a. 15 V (rms) b. 30 V (rms) c. 60 V (rms) d. 2.4 V (rms) e. 960 V (rms)

34. A step-up transformer has an input voltage of 110V(rms). There are 100 turns on the primary and 1500 on the secondary. What is the output voltage?

a. 1600 V (max) b. 1650 V (rms) c. 3260 V (max) d. 165 kV (rms) e. 7.3 V (rms)

35. A primary current of 6 A exists in an ideal iron-core transformer at a primary voltage of 100 volts. If the current in the secondary is 0.75 A, calculate the output voltage.

a. 12.5 V b. 40 V c. 400 V d. 800 V e. 200 V

36. An ideal step-down transformer has 200 primary turns and 50 secondary turns. If 440 volts (rms) is placed across the primary, what is the current in the secondary when the load resistance is 7 ohms?



37. Calculate Vout/Vin for the circuit if R = 2 kΩ, C = 0.02 μF and V = 140V sin(50 000t)

R

Vin C Vout

a. 0.02 b. 0.45 c. 0.80 d. 0.98 e. 2.23

38. The impedance of the parallel RLC circuit shown is given by

V0 sin ωt R L C

R1

a. + Lω

1+ ωC

b. ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

21R

⎜⎝⎛ −+2

1L

Cω

ω–1/2

R1

c. + ⎟⎠⎞

⎝−

CL ωω11

⎜⎛

22 1

⎟⎠⎞

⎜⎝⎛ −+

CLR

ωωd.

⎥⎦⎢⎣−+

LC

R ωω2

⎤⎡ 11e.

39. The rms current from the voltage source is

V0 sin ωt R L C

a. VrmsZ b. Vrms/Z c. Vrms/R d. Vrms/(R +XL –XC ) e. Vrms/(2Z)

228 CHAPTER 33

40. The phase angle between V and I is

V0 sin ωt R L C

a. tan–1 ⎥⎦⎣ LC XX

⎤⎡−

RR⎢

b. tan–1 ⎟⎟⎠

⎜⎝ − LC XX

⎞⎛ R⎜

c. tan–1 ⎟⎞⎛ − XX LC

⎠⎝ R⎜

d. tan–1 22 )( XXR

R

−+ CL

e. tan–1 22 )( CL XXR −+

41. For driving voltage V = Vm sin ωt, the current through the resistor is

V sin ωt R0 L C

a. Vm sin (ωt + φ) b. Vm cos (ωt + φ)

RVm sin (ωt + φ) c.

ZVm sin (ωt + φ) d.

e. R

Vm sin ωt

42. If R = 10 ohms, L = 0.1 henry, C = 10 μF, what is the resonant frequency for the parallel RLC-circuit?

a. 1000 Hz b. 333 Hz c. 159 Hz d. 53 Hz e. 500 Hz


43. An alternating current circuit has resistance R, inductance L and capacitance C in series with a voltage source. Which statement is correct?

a. The voltage across the capacitor leads the voltage across the inductor by 90°. b. The voltage across the inductor leads the voltage across the capacitor by 90°. c. The voltage across the inductor leads the voltage across the resistor by 180°. d. The voltage across the inductor leads the voltage across the capacitor by

180°. e. Both voltages lead the voltage across the resistor by 90°.

44. The power output, Pout, of an ideal step-up transformer that receives power input, Pin, and which has N1 turns in the primary and N2 turns in the secondary coil is given by

a. Pout = Pin.

b. Pout = 1

2

NN

Pin.

c. Pout = 2

1

NN

Pin.

d. Pout = 2

1

2

N ⎟⎟⎠

⎜⎜⎝

N ⎞⎛ Pin.

e. Pout = 2

1N⎟⎟⎞

⎜⎜⎛

2N ⎠⎝ Pin.

45. In a typical transmission line, the current I is very small and the voltage V is very large. A unit length of line has resistance R. For a power line that supplies power to 10,000 households, we can conclude that

a. IV = I2R. b. I = V/R. c. IV < I2R. d. IV > I2R. e. I2R = 0.

46. Whenever the alternating current frequency in a series RLC circuit is halved,

a. the inductive reactance is doubled and the capacitive reactance is halved. b. the inductive reactance is doubled and the capacitive reactance is doubled. c. the inductive reactance is halved and the capacitive reactance is halved. d. the inductive reactance is halved and the capacitive reactance is doubled. e. the reactance of the circuit remains the same.

47. The average power input to a series alternating current circuit is minimum when

a. there are only a resistor and capacitor in the circuit. b. there are only a resistor and inductor in the circuit. c. there is only a resistor in the circuit. d. XL = XC and the circuit contains a resistor, an inductor and a capacitor. e. there is only a capacitor in the circuit.

230 CHAPTER 33

48. All three circuits shown below have Ω= 100R , H 1.0=L and emf

E = (5.0 V) sin (377 t). Which statement regarding the angular resonance frequencies Aω , Bω and Cω is correct?

0.50�mF

0.50�mF

0.10 H

100 Ω

E

(B)

1.0�mF

0.10 H

100 Ω

E

(A)

2.0�mF

2.0�mF

0.10 H

100 Ω

E

(C) a. BAC ωωω => b. BAC ωωω =< c. CBA ωωω == d. CAB ωωω =< e. CAB ωωω =>

49. All three circuits below have Ω= 100R , mF 0.1=C and emf

E = (5.0 V) sin (377 t). The inductors in (B) and (C) are placed sufficiently far apart so that they do not alter one another’s inductance. Which statement regarding the angular resonance frequencies Aω Bω Cω, and is correct?

100 Ω

E

(B)

0.10 H 0.20 H

0.05 H

0.05 H

0.20 H

1.0 mF 1.0 mF 1.0 mF

100 Ω

E

100 Ω

E

(C)(A) a. BAC ωωω => b. BAC ωωω =< c. CBA ωωω == d. CAB ωωω =< e. CAB ωωω =

Ω= 0.10R mF 300=

>

50. A 60-Hz ac generator with a peak voltage of 110 V drives a series RC circuit with and C . The peak current in the circuit is

a. 8.24 A. b. 8.84 A. c. 11.0 A. d. 12.4 A. e. 23.5 A.


51. A 60-Hz ac generator with a peak voltage of 110 V drives a series RC circuit with and . The impedance is Ω= 0.10R mF 300=C

a. 4.68 Ω. b. 8.84 Ω. c. 10.0 Ω. d. 13.4 Ω. e. 18.8 Ω.

52. A 60-Hz ac generator with a peak voltage of 110 V drives a series RC circuit with and . The power factor, Ω= 0.10R mF 300=C φcos is

a. –1.00. b. –0.749. c. +0.749. d. +0.834. e. +1.00.

53. A 60-Hz ac generator with a peak voltage of 110 V drives a series RL circuit with and L . The peak current in the circuit is Ω= 0.10R mH 0.10=

Ω= 0.10R mH 0.10=

Ω= 0.10R mH 0.10=

a. 0.963 A. b. 10.3 A. c. 11.0 A. d. 11.9 A. e. 29.2 A.

54. A 60-Hz ac generator with a peak voltage of 110 V drives a series RL circuit with and L . The impedance is

a. 3.77 Ω. b. 9.26 Ω. c. 10.0 Ω. d. 10.7 Ω. e. 13.8 Ω.

55. A 60-Hz ac generator with a peak voltage of 110 V drives a series RL circuit with and L . The power factor, φcos is

a. –1.00. b. –0.936. c. +0.943. d. +0.936. e. +1.00.

232 CHAPTER 33

56. A 10-μF capacitor in an LC circuit made entirely of superconducting materials ( ) is charged to 100 μC. Then a superconducting switch is closed. At t = 0 s, plate 1 is positively charged and plate 2 is negatively charged. At a later time, . At that time, is

Ω= 0R

Vab V10+= dcV

12

+–�

a d

cb

a. 0 V. b. 3.54 V. c. 5.0 V. d. 7.07 V. e. 10 V.

57. The graphs below show a voltage phasor at different instances of time. The voltage phasor which shows the instantaneous value of the voltage with the largest magnitude is

a. b. c. d. e.

58. The graphs below show a voltage phasor at different instances of time. The voltage phasors which represent negative voltages are

I. II. III. IV. V.

a. I, II and III. b. IV. c. V. d. IV and V. e. III, IV and V.


59. The graphs below represent current and voltage phasors at one instant of time. The solid arrows represent the voltage phasors, ΔV , and the dashed arrows represent the current phasors, .The graph which shows the correct relationship between current and voltage phasors for an inductor in an RL circuit is

Imax

,

a. b. c. d. e.

60. The graphs below represent current and voltage phasors at one instant of time. The solid arrows represent the voltage phasors, ΔVmax

I, and the dashed arrows

represent the current phasors, max .The graph which shows the correct relationship between current and voltage phasors for a capacitoror in an RC circuit is

a. b. c. d. e.

Δ61. The graphs below show the phasors V Imax and max for five RLC series cicrcuits. The graph which represents a circuit where the inductive reactance is greater than the capacitive reactance is

a. b. c. d. e.

234 CHAPTER 33

62. The graphs below show the phasors ΔVmax and for five RLC series cicrcuits. The graph which represents a circuit where the capacitive reactance is greater than the inductive reactance is

Imax

a. b. c. d. e.

63. In a parallel RLC circuit, where IR = IR,max sin(ωt) , the current through the

capacitor, , is IC

a. I = −I sin(ωt) . C C ,max

I = I sin(ωt) . b. C C ,max

I = −I cos(ωtc. C C ,max )

C C ,max

.

I = I cos(ωt) . d.

IC = ax tan(IC ,m ωt)

IR

. e.

IR,max sin(= ω64. In a parallel RLC circuit, where t) , the current through the

inductor, , is IL

IL = −IL ,max sin(ωt) . a.

IL = IL ,max sin(ωt) . b.

IL = −IL ,max cos(ωt)IL = IL ,max cos(

. c.

ωt)IL = IL ,max tan(

. d.

ωt) . e.

Open-Ended Problems

65. Suppose the circuit parameters in a series RLC circuit are: L = 1.0 μH, C = 10.0 nF, R = 100Ω, and the source voltage is 220 V. Determine the resonant frequency of the circuit and the amplitude of the current at resonance.

66. A 10-Ω resistor, 10-mH inductor, and 10-μF capacitor are connected in series with a 10-kHz voltage source. The rms current through the circuit is 0.20 A. Find the rms voltage drop across each of the 3 elements.

67. An ac power generator produces 50 A (rms) at 3600 V. The voltage is stepped up to 100 000 V by an ideal transformer and the energy is transmitted through a long distance power line which has a resistance of 100 ohms. What percentage of the power delivered by the generator is dissipated as heat in the long-distance power line?


Chapter 33

Alternating Current Circuits

1. c

2. a

3. d

4. d

5. d

6. a

7. a

8. b

9. a

10. d

11. d

12. b

13. c

14. d

15. b

16. b

17. c

18. c

19. d

20. b

21. a

22. c

23. a

24. a

25. a

26. b

27. c

28. b

29. b

30. c

31. a

32. c

33. a

34. b

35. d

36. d

37. b

38. b

39. b

40. a

41. e

42. c

43. d

44. a

45. d

46. d

47. e

48. c

49. c

50. a

51. d

52. c

53. b

54. d

55. d

56. e

57. c

58. d

59. a

60. c

61. b

62. a

236 CHAPTER 33

63. d

64. c

65. 1.59 MHz, 2.2 A

66. 2.0 V, 125.6 V, 0.318 V

67. 0.18%

Chapter (33)

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