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Question Bank in AC CircuitsA. SINUSOIDAL VOLTAGE AND CURRENT REE Board Exam September 2000 Find the average current during the half cycle given the instantaneous maximum value of 20 amperes. A. 12 .7 3 amperes C. 20 amperes B. 14 amperes D. 10 amperes REE Board Exam April 19 97 The phase shift betw...

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A. B.

Question Bank in AC Circuits A. 1.

SINUSOIDAL VOLTAGE AND CURRENT REE Board Exam September 2000 Find the average current during the half cycle given the instantaneous maximum value of 20 amperes. C. 20 amperes A. 12.73 amperes B. 14.14 amperes D. 10 amperes

2.

0.89 A 0.75 A

C. D.

0.91 A 0.84 A

8.

EE Board Exam April 1990 A 240-V, 25 Hz sinusoidal generator is connected to a 20 ohms resistor. Determine the instantaneous current when elapsed time is 0.01 second. A. 15.43 A C. 16.97 A B. 16.30 A D. 12.00 A

REE Board Exam April 1997 The phase shift between the current and voltage vectors us due to the following except one A. magnet coils C. power capacitors B. electric flat iron D. fluorescent lamp

9.

REE Board Exam April 1997 A wire carries a current i = 3 cos 314t amperes. What is the average current over 6 seconds? C. 1.5 A A. 0 A B. 3.0 A D. 0.532 A

3.

REE Board Exam April 2001 An alternating rectangular wave has a maximum value of 10 V and a frequency of 1 cycle per second. What is the average value of the wave? A. 5 V C. 0 D. 7.07 V B. 10 V

10. REE Board Exam April 1997 Across a 230-V, 60 Hz power supply is a 15-ohm non-inductive resistor. What is the equation of the resulting current? A. i = 21.68 sin 377t C. i = 15.33 sin 377t B. i = 26.56 sin 377t D. i = 28.16 sin 120t

4.

REE Board Exam October 2000 A sinusoidal current wave has a maximum value of 20 A. What is the average value of one-half cycle? A. 5 A C. 14.14 A B. 12.7 A D. 0

11. EE Board Exam April 1991 Determine the effective value of the circuit current of an emf of 151 sin 377t is connected in series with a DC emf of 110 volts. Both supply a load of 10 + j8 ohms. A. 10.3 A C. 13.8 A B. 12.5 A D. 11.4 A

5.

REE Board Exam October 1996 What is the wavelength of a carrier wave with frequency of 100 megahertz? A. 3.0 m C. 1.5 m B. 7.5 m D. 6.0 m

6.

REE Board Exam April 1997 A chart speed of a recording instrument is 25 mm/sec. One cycle of the signal being recorded extends over 5 mm. What is the frequency of the signal? A. 20 cps C. 50 cps B. 2 cps D. 5 cps

7.

EE Board Exam April 1992 Determine the rms value of the current drawn by a 2 μF condenser, which is connected across a source of potential. The potential has a third and fifth harmonic components, which are 30% and 20% respectively of the fundamental. The fundamental sinusoidal component has a peak value of 1000 volts and 60 Hz frequency.

12. EE Board Exam April 1994 An alternating current and a direct current flow simultaneously in the same conductor. If the effective of the alternating current is 5 A and the direct current is 10 A, what will an AC ammeter read when connected in the circuit? A. 7.5 A C. 11.18 A B. 15 A D. none of these 13. REE Board Exam April 1997 If e = 100 sin (ωt – 30°) – 50 cos 3ωt + 25 sin (5ωt + 150°) and i = 20 sin (ωt + 40°) + 10 sin (3ωt + 30°) – 5 sin (5ωt – 50°). Calculate the power in watts. A. 1177 C. 1043 D. 1224 B. 919 14. ECE Board Exam November 2001 It is the value of sine wave of voltage or current at one particular instant of time. A. average value C. rms value

B.

effective value

D. instantaneous value

15. ECE Board Exam November 1998 If the combination of an ac voltage and a dc voltage has an instantaneous voltage that varies through a range from -2 V to +10 V, what is the peak ac voltage of the combination? A. 10 V C. 6 V B. 16 V D. 12 V 16. ECE Board Exam April 2001 Measured in Hertz, it is the number of cycles of alternating current per second. C. peak to peak A. frequency B. period D. wavelength 17. ECE Board Exam April 2000 If an ac signal has an average voltage of 18 V, what is the rms voltage? A. 16.2 V C. 25.38 V D. 12.73 V B. 19.98 V 18. ECE Board Exam April 2000 If an ac signal has a peak voltage of 55 V, what is the average value voltage? A. 61.05 V C. 34.98 V B. 38.86 V D. 86.35 V 19. ECE Board Exam April 1999 What is the phase relationship between current and voltage in an inductor? A. in phase B. current lags voltage by 90° C. voltage lags current by 90° D. current lags voltage by 180° 20. ECE Board Exam November 1995 If sine wave voltage varies from 0 to 200 V, how much is its instantaneous voltage at 90°? A. 100 V B. minimum voltage C. 200 V D. half of its maximum voltage 21. ECE Board Exam November 2000 How many degrees are there in one complete wave cycle? C. 180 degrees A. 360 degrees B. 90 degrees D. 720 degrees

22. ECE Board Exam April 1998 When comparing rms voltage and average voltages, which of the following statement is true, assuming sine waves? A. Either the rms voltage or the average voltage might be larger. B. The average voltage is always greater than the rms voltage. C. There will always be a very large difference between the rms voltage and the average voltage. D. The rms voltage is always greater than the average voltage. 23. ECE Board Exam November 1999 It is the maximum instantaneous value of a varying current, voltage, or power equal to 1.414 times the effective value of a sine wave. A. rms value C. effective value B. peak to peak value D. peak value 24. ECE Board Exam November 1999 It is the description of two sine waves that are in step with each other going through their maximum and minimum points at the same time and in same direction. A. stepped sine waves B. sine waves in coordination C. phased sine waves D. sine waves in phase 25. ECE Board Exam April 1999 What is the average voltage (E ave) output of a full wave rectifier with an output of 100 volts peak? A. 63.7 volts C. 141.4 volts B. 14.14 volts D. 6.37 volts 26. ECE Board Exam November 1997 The relation of the voltage across an inductor to it current is ____ A. Lagging the current by 90 degrees B. Leading the current by 90 degrees C. In phase with the current D. Leading the current by 180 degrees 27. ECE Board Exam April 1999 If two equal frequency ac signals of exactly 5 V each are combined with one of the signals 180 degrees out of phase with the other, what will be the value of the resultant voltage? A. 2.25 V C. 0 V B. 5 V D. 10 V

28. ECE Board Exam November 1998 Kind of electric current where amplitude drops to zero periodically normally produced by rectifier circuits A. alternating current B. varying direct current C. damped alternating current D. pulsating direct current 29. ECE Board Exam April 2000 If an ac signal has an average voltage of 18 V, what is the rms voltage? A. 16.2 V C. 25.38 V D. 12.726 V B. 19.98 V 30. ECE Board Exam April 2001 In electronic circuit the current that flows over a capacitor _____. A. In phase with the voltage B. Leads the voltage by 180 degrees C. Lags the voltage by 90 degrees D. Leads the voltage by 90 degrees 31. Two current sources deliver current to a common load. The first source delivers a current whose equation is 25 sin 100πt amperes while the second delivers a current whose equation is 15 cos 100 πt amperes. What is the rms value of the current in the load? A. 29.15 A C. 20.6 A B. 40 A D. 10 A 32. Two alternators A and B delivers 100 A and 150 A, respectively to a load. If these currents are out of phase by 30 electrical degrees, determine the total current drawn by the load. A. 201.5 A C. 215.4 A B. 250.0 A D. 241.8 A 33. When using circuit laws and rules we must use A. maximum value C. effective value B. average value D. peak to peak value 34. A 60 Hz frequency would cause an electric light to A. turn on and off 120 times per second B. flicker noticeable C. turn on and off 180 times per second D. turn on and off 60 times per second 35. The relationship between frequency f, number of revolutions per second n and pair of poles p is given by

A. B.

f = n/p f = np

C. f = n/2p D. f = 2np

36. The difference between the peak positive value and the peak negative of an a.c. voltage is called the A. maximum value C. average value B. effective value D. peak to peak value 37. The greatest value attained during one half of the cycle is called the C. r.m.s. value A. peak value B. average value D. effective value 38. The root mean square (r.m.s.) value of a.c. is the same as A. instantaneous value C. effective value B. average value D. maximum value 39. The r.m.s. value of a sine wave is equal to A. 0.637 maximum value C. 0.707 maximum value B. 0.506 maximum value D. 1.414 maximum value 40. Form factor is defined as A. r.m.s. value/peak value B. maximum value/r.m.s. value C. r.m.s. value/average value D. effective value/ r.m.s. value 41. The value of form factor for a pure sine wave is A. 1.414 C. 0.707 B. 0.637 D. 1.11 42. The value of peak factor for a pure sine wave is C. 0.707 A. 1.414 B. 0.637 D. 1.11 43. If the current and voltage are out of phase by 90 , the power is A. 1.1 VI C. Maximum B. minimum D. zero 44. If e1 = A sin t and e2 = B sin (t - ) then A. e1 lags e2 by  C. e2 lags e1 by  B. e2 leads e1 by  D. e1 leads e2 by  45. Which of the following statements concerning the graph of figure below is most correct?

A. B.

3

infinite zero

C. 0.5 D. unity

2

54. The frequency of a sinusoidal signal shown in figure is

1 0 time

A. it represents ac B. it represents dc C. it represents half-wave rectified ac D. it represents sum of ac and dc 46. Average value of a sine wave is √ times the maximum value A. True B. False 47. The equation for 25 cycles current sine wave having rms value of 30 amperes will be A. 30 sin 25t C. 30 sin 50t 50πtt B. 42.4 sin 25πt D. 42.4 sin 50 48. The voltage v = 90 cos (ωt – 161.5°) may be represented as a sine function by A. 90 sin (ωt + 18.5°) C. 90 sin (ωt + 71.5°) D. 90 sin (ωt - 18.5°) B. 90 sin (ωt – 71.5°) 49. Which of the following frequencies has the longest period? A. 1 Hz C. 1 kHz B. 10 Hz D. 100 kHz 50. RMS value and the mean value is the same in case of A. square wave B. sine wave C. triangular wave D. half-wave rectified sine wave 51. If emf in a circuit is given by e = 100 sin 628t, the maximum value of voltage and frequency are A. 100 V, 50 Hz C. 100 V, 100 Hz B. 50√ V, 50 Hz D. 50√ V, 100 Hz 52. When the sole purpose of an alternating current is to produce heat, the selection of conductor is based on A. average value of current C. rms value of current B. peak value of current D. any of the above 53. The form factor of dc supply voltage is always

A. B.

500 Hz 1 kHz

C. 25 kHz D. 500 kHz

55. The period of the voltage 2 cos 4500πt + 7 sin 7500πt is A. 2.51 s C. 2.51 ms B. 2.51 ns D. 2.51 μs 56. The a.c. system is preferred to d.c. system because ____ A. a.c. voltages can easily be changed in magnitude B. d.c. motors do not have fine speed control C. high-voltage a.c. transmissions is less efficient D. d.c. voltage cannot be used for domestic appliances 57. In a.c. system, we generate sine wave form because ____ A. it can be easily drawn B. it produces lest d disturbance isturbance in electrical circuits C. it is nature’s standard D. other waves cannot be produced easily 58. ____ will work only on d.c. supply. A. Electric lamp C. Heater B. Refrigerator D. Electroplating 59. ____ will produce a.c. voltage. A. Friction C. Thermal energy Crystall B. Photoelectric effect D. Crysta 60. In Fig. 1.1, the component of flux that will contribute to e.m.f. in the coil is ____

Coil of N turns

ω rad/sec

φmax

68. An alternating current given by i = 10 sin 314t. Measuring time from t = 0, the time taken by the current to reach +10 A for the second time is ____. A. 0.05 second C. 0.025 second B. 0.1 second D. 0.02 second

Figure 1.1

A. B.

max sin t max cos t

C. D.

max tan t max cot t

61. In Fig. 1.1, the maximum e.m.f. induced in the coil is ____.

Coil of N turns

ω rad/sec

φmax Figure 1.1

A. B.

N max  max

67. A sinusoidal current has a magnitude of 3 A at 120 . Its maximum value will be ____. A. √ A C. √ A B. √ A D. 6 A

C. N max sin t D.  N max

69. An a.c. generator having 10 poles and running at 600 r.p.m. will generate an alternating voltage of frequency _____ A. 25 Hz C. 50 Hz B. 100 Hz D. 200 Hz 70. We have assigned a frequency of 50 Hz to power system because it ____ A. can easily be obtained B. gives best result when used for operating both lights and machinery C. leads to easy calculation D. none of the above

62. A coil is rotating in the uniform field of an 8-pole generator. In one revolution of the coil, the number of cycles generated by the voltage is ____. A. one C. four B. two D. eight

71. An alternating voltage is given by v = 100 sin 314t volts. Its average value will be ____. A. 70.7 V C. 63.7 V B. 50 V D. 100 V

63. An alternating voltage is given by v = 20 sin 157t. The frequency of the alternating voltage is ____. A. 50 Hz C. 100 Hz D. 75 Hz B. 25 Hz

72. An alternating current whose average value is 1 A will produce ____ 1 A d.c. under similar conditions. A. less heat than C. the same heat as B. more heat than D. none of the above

64. An alternating current is given by i = 10 sin 314t. The time taken to generate two cycles of current is ____. A. 0.02 second C. 0.04 second B. 0.01 second D. 0.05 second

73. A sinusoidal alternating current has a maximum value of I m. Its average value will be ____. A. Im/ C. 2Im/ B. Im/2 D. none of the above

65. An alternating voltage is given by v = 30 sin 314t. The time taken by the voltage to reach –30 V for the first time is ____. A. 0.02 second C. 0.03 second B. 0.1 second D. 0.015 second

74. The area of a sinusoidal wave over a half-cycle is ____ A. max. value / 2 C. max. value /  D. max. value / 2 B. 2 x max. value

66. A sine wave has a maximum value of 20 V. Its value at 135 is ____. A. 10 V C. 15 V B. 14.14 V D. 5 V

75. An alternating voltage is given by v = 200 sin 314t. Its r.m.s. value will be ____ A. 100 V C. 141.4 V B. 282.8 V D. 121.4 V

B. 76. The r.m.s. value of sinusoidally varying current is ____ that of its average value. A. more than C. same as B. less than D. none of the above 77. Alternating voltages and currents are expresses in r.m.s. values because ____ A. they can be easily determined B. calculations become very simple C. they give comparison with d.c. D. none of the above 78. The average value of sin2 over a complete cycle is ____ A. +1 C. ½ B. -1 D. zero 79. The average value of sin over a complete cycle is ____. C. -1 A. zero B. +1 D. ½ 80. An alternating current is given by i = Im sin . The average value of squared wave of this current over a complete cycle is ____ A. Im/2 C. 2Im/ B. Im/ D. 2Im 81. The form factor a sinusoidal wave is ____ A. 1.414 C. 2 D. 1.5 B. 1.11 82. The filament of a vacuum tube requires 0.4 A d.c. to heat it. The r.m.s. value of a.c. required is ____. A. 0.4 x √ C. 0.8 / √ B. 0.4 / 2 A D. 0.4 A 83. A 100 V peak a.c. is as effective as ____ d.c. A. 100 V C. 70.7 V B. 50 V D. none of the above 84. The form factor of a ____ wave is 1. A. sinusoidal C. triangular B. square D. saw tooth 85. Out of the following ____ wave is the peakiest. A. sinusoidal C. rectangular

square

D. triangular

86. The peak factor of a sine wave form is ____. A. 1.11 C. 2 B. 1.414 D. 1.5 87. When a 15-V square wave is connected across a 50-V a.c. voltmeter, it will read ____. C. 15 /√ A. 15 V B. 15 x √ D. none of the above 88. The breakdown voltage of an insulation depends upon ____ value of alternating voltage. A. average C. peak B. r.m.s. D. twice the r.m.s. 89. The peak factor of a half-wave rectified a.c. is ____. A. 1.57 C. 1.11 B. 2 D. 1.4142 90. The form factor of a half-wave rectified a.c. is ____ A. 2 C. 1.414 B. 1.11 D. 1.57 91. When 200 V sinusoidal peak-to-peak is connected across an a.c. voltmeter, it will read ____ A. 141.4 V C. 70.7 V B. 50 V D. none of the above 92. In Fig. 1.2, the wave that will produce maximum heat under the similar conditions is ____.

i 10 A

96. In Fig. 1.3, current is given by i = Im sin . The voltage equation will be ____.

i 10 A

t

0

t

0

A. B.

Vm sin  Vm sin ((  + )

C. Vm sin ( - ) D. Vm sin ( - 2)

-10 A

-10 A

97. The waveforms of voltage and current shown in Fig. 1.3 would exist in ____ circuit.

i 10 A

i 10 A

0

i

0

t

v

φ

θ

-10 A Figure 1.3

Figure 1.2

square wave sinusoidal wave

A. B.

C. triangular wave D. saw tooth wave

93. In Fig. 1.2, ____ wave will have the highest average value. i

i

10 A

0

10 A

0

t

t

-10 A

-10 A

i

i 10 A

10 A

0

t

Figure 1.2

saw tooth square

C. an inductive D. none of the above

a resistive a capacitive

98. An alternating voltage or current is a ____. A. scalar quantity C. phasor B. vector quantity D. none of the above 99. Three parallel circuits take the following currents: i1 = 5 sin 314t, i2 = 30 sin (314t + /2) and i3 = 25 sin (314t - /2). The expression for the resultant current is ____. A. 25 sin (314t + /3) C. 10 sin (314t - /6) B. 5 sin (314t + /2) D. 5√ sin (314t + /4) 100. The sum of the following two e.m.f’s will be ____ e1 = 10 sin t e2 = 10 cos t A. 10 C. 14.14 cos t B. 20 sin t D. 14.14 sin (t + /4)

0

-10 A

A. B.

A. B.

C. triangular D. sinusoidal

94. The average value of a sinusoidal current is 100 A. Its r.m.s value is ____. A. 63.7 A C. 141.4 A B. 70.7 A D. 111 A 95. A current wave is given by i = 4 + 2√ sin 3 + 4√ sin 5. The r.m.s. value of current wave is ____. A. 10 A C. √ A B. 6 A D. 5 A

101. Each of the three coils generates an e.m.f. of 230 V. The e.m.f. of second leads that of the first 120  and the third lags behind the first by the same angle. The resultant e.m.f. across the series combination of the coils is ____. A. 0 V C. 690 V B. 230 V D. none of the above 102. In Fig. 1.4, I1 + I2 is equal to ____ 60° 6A

I2 3A

I3 4A

I1 Figure 1.4

A. B.

3A 4.33 A

C. 9 A D. 3.43 A

103. In Fig. 1.4, I2 + I3 is equal to ____ I2

60° 6A

I3

3A

4A

I1 Figure 1.4

A. B.

108. In a pure resistive circuit, the instantaneous voltage and current are given by: v = 250 sin 314t volts i = 10 sin 314t amperes The average power in the circuit is A. 2500 W C. 25 W B. 250 W D. 1250 W

C. 5 A D. none of the above

7A √ A

104. In Fig. 1.5, E1 + E2 + E3 + E4 is equal to E1 = 9 V

109. An alternating voltage current equation will be A. ⁄ ) ( B.

is applied to a pure inductive circuit. The C. D.

(

(

⁄) ⁄ )

110. The inductive reactance of a circuit is ____ frequency. A. directly proportional to C. independent of B. inversely proportional D. none of the above

E3 = 20 V E2 = 24 V E4 = 6 V Figure 1.5

A. B.

7V 5V

C. 20 V D. none of the above

105. In Fig. 1.5, ____ will have the least value. E1 = 9 V E3 = 20 V E2 = 24 V E4 = 6 V Figure 1.5

A. B.

E1 + E2 + E3 + E4 E1 + E2 + E3 – E4

C. E1 + E 2 - E3 – E4 D. -E1 + E4