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. A. 12.73 amperes C. 20 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? A. 0 A C. 1.5 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 B. 10 V D. 7.07 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 B. 919 D. 1224 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. A. frequency C. peak to peak 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 B. 19.98 V D. 12.73 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? A. 360 degrees C. 180 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 (Eave) 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 B. 19.98 V D. 12.726 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 100πt 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. D.
f = n/2p 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 A. peak value C. r.m.s. 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 A. 1.414 C. 0.707 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. D.
0.5 unity
2
54. The frequency of a sinusoidal signal shown in figure is
1 0 time
A. B. C. D.
it represents ac it represents dc it represents half-wave rectified ac 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 B. 42.4 sin 25πt D. 42.4 sin 50πt 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°) B. 90 sin (ωt – 71.5°) D. 90 sin (ωt - 18.5°) 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. D.
25 kHz 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 disturbance 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. B. Photoelectric effect D.
Thermal energy Crystal
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 Figure 1.1
A. B.
max sin t max cos t
C. D.
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
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
C. D.
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
N max sin t 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 B. 25 Hz D. 75 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 / B. 2 x max. value D. max. value / 2
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 2
78. The average value of sin over a complete cycle is ____ A. +1 C. ½ B. -1 D. zero 79. The average value of sin over a complete cycle is ____. A. zero C. -1 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 B. 1.11 D. 1.5 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 ____. A. 15 V C. 15 /√ 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
0
0
t
t
A. B.
Vm sin Vm sin ( + )
Vm sin ( - ) Vm sin ( - 2)
C. D.
-10 A
-10 A
i 10 A
97. The waveforms of voltage and current shown in Fig. 1.3 would exist in ____ circuit.
i 10 A
0
i
0
t
v
φ
θ
-10 A Figure 1.3
Figure 1.2
A. B.
square wave sinusoidal wave
C. D.
triangular wave saw tooth wave
93. In Fig. 1.2, ____ wave will have the highest average value. i 10 A 0
i 10 A 0
t
t
-10 A
-10 A
i 10 A
i 10 A
0
t
Figure 1.2
saw tooth square
a resistive a capacitive
C. D.
an inductive none of the above
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. D.
triangular 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
I1
I2 3A
Figure 1.4
I3 4A
A. B.
3A 4.33 A
C. D.
9A 3.43 A
103. In Fig. 1.4, I2 + I3 is equal to ____ I2
60° 6A
I3
3A
I1
4A
Figure 1.4
A. B.
7A √ A
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. D.
5A none of the above
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. D.
20 V 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. D.
E1 + E2 - E3 – E4 -E1 + E4
106. In a pure resistive a.c. circuit, the frequency of power curve is ____ that of the circuit frequency. A. half C. thrice B. twice D. same as 107. In a pure resistive circuit, the instantaneous voltage and current are given by: v = 250 sin 314t volts i = 10 sin 314t amperes The peak power in the circuit is A. 1250 W C. 2500 W B. 25 W D. 250 W
111. Power absorbed in a pure inductive circuit is zero because A. reactive component of current is zero B. active component of current is maximum C. power factor of the circuit is zero D. reactive and active component of current cancel out 112. An alternating voltage current equation will be A. ⁄ ) B. (
is applied to a pure capacitive circuit. The C. D.
( (
⁄ ) ⁄ )
113. The capacitive reactance of a circuit is ____ frequency. A. independent of B. inversely proportional to C. directly proportional to D. none of the above 114. An a.c. current given by i = 14.14 sin (t + /6) has an rms value of ____ amperes and a phase of ____ degrees. A. 10, 30 C. 1.96 , -30 B. 14.14, 180 D. 7.07, 210 115. If e1 = A sin t and e2 = B sin (t – ), then A. e1 legs e2, by C. e2 leads e1, by B. e2 lags e1 by D. e1 is in phase with e2 116. From the two voltage equations eA = Em sin 100t and eB = Em sin (100t + /6), it is obvious that
A. B. C. D.
eA leads eB 30 eB achieves its maximum value 1/600 second before e A does eB lags behind eA eA achieves its zero value 1/ 600 before eB
A. B.
119. The r.m.s. value of sinusoidal ac current is equal to its value at an angle of ____ degree. A. 60 C. 30 B. 45 D. 90 120. Two sinusoidal currents are given by the equations: i 1 = 10 sin (t + /3) and i2 = 15 sin (t - /4). The phase difference between them is ____ degrees. A. 105 C. 15 B. 75 D. 60 121. A sine wave has a frequency of 50 Hz. Its angular frequency is ____ radian/second. A. 50/ C. 50π B. 50/2 D. 100 122. An a.c. current is given by i = 100 sin 100. It will achieve a value of 50 A after ____ second. A. 1/600 C. 1/1800 B. 1/300 D. 1/900
C. D.
√ 5
125. The current through a resistor has a wave form as shown in Fig. 1.6. The reading shown by a moving coil ammeter will be ____ ampere.
117. The r.m.s. value a half-wave rectified current is 10 A, its value for full wave rectification would be ____ amperes. A. 20 C. 20/π B. 14.14 D. 40/ 118. A resultant current is made of two components: a 10 A d.c. components and a sinusoidal component of maximum value 14.14 A. The average value of the resultant current is ____ amperes and r.m.s. value is ____ amperes. A. 0, 10 C. 10, 14.14 B. 24, 24.14 D. 4.14, 100
10 0
5A i(t)
0
π
2π
3π
ωt
Fig. 1.6
A. B.
C. D.
√ √
5/π 0
126. A constant current of 2.8 exists in a resistor. The rms value of current is A. 2.8 A C. 1.4 A B. about 2 A D. undefined 127. The rms value of a half-wave rectified symmetrical square wave current of 2 A is A. √ A C. √ A B. 1 A D. √ A 128. The rms value of the voltage v(t) = 3 + 4 cos (3t) is A. √ V C. 7 V B. 5 V D. (3 + 2√ ) V 129. The rms value of the resultant current in a wire which carries a dc current of 10 A and a sinusoidal alternating current of peak value 20 A is A. 14.1 A C. 22.4 A B. 17.3 A D. 30.0 A 130. For the triangular waveform in the figure, the rms value of voltage s equal to v
123. The reactance offered by a capacitor to alternating current of frequency 50 Hz is 10 . If frequency is increased to 100 Hz reactance becomes ____ ohm. A. 20 C. 2.5 B. 5 D. 40 124. A complex current wave is given by i = 5 + 5 sin 100t ampere. Its average value is ____ ampere.
T/2
A. B.
√ √
V V
T
C. D.
3T/2
2T
5T/2
t
1/3 V V √
131. The rms value of the periodic waveform given in the figure is
i A
6A T/2
T
0
√ A √ A
T/2
-A
-6 A
A. B.
i A
C. D.
A √ 1.5 A
T
t
0
π
2π
0
t
t
-A Fig. b
Fig. a
A. B.
A
figure a and b figure b and c
C. D.
Fig. c
figure a and c none of the above
132. If i1 = 120 cos (100πt + 30°) and i1 = -0.1 cos (100πt + 100°) then i2 leads i1 by ____. A. -110 degrees C. -60 degrees B. 60 degrees D. 110 degrees
139. The length of time between a point in one cycle to the same point of the next cycle of an AC wave is the ____. A. frequency C. magnitude B. period D. polarity
133. If v1 = sin (ωt + 30°) and v2 = -5 sin (ωt - 15°) then v1 leads v2 by ____. A. 225 degrees C. 45 degrees B. 30 degrees D. none of the above
140. In an experiment, a sinusoidal wave form is observed to complete 8 cycles in 25 msec. Determine the frequency of the wave form. A. 320 Hz C. 200 Hz B. 40 Hz D. 64 Hz
134. The rms value of a rectangular wave of period T, having a value of +V for a duration, T1 (
A. B.
√ √
C. D.
√ √
138. Which of the waveforms are having unity peak factor?
141. If emf in a circuit is given by e = 100 sin 628t, the maximum value of voltage and frequency is ____. A. 100 V, 50 Hz C. √ V, 50 Hz B. 100 V, 100 Hz D. √ V, 100 Hz 142. A sinusoidal voltage wave has an RMS value of 70.71 V and a frequency of 60 Hz. Determine the value of the voltage 0.0014 second after the wave crosses the ωt axis. A. 70.71 V C. 50 V B. 100 V D. 141.42 V 143. An alternating current varying sinusoidally with frequency of 50 Hz has an RMS value of 20 A. At what time measured from the positive maximum value will the instantaneous current be 14.14 A? A. 1/600 sec C. 1/300 sec B. 1/200 sec D. 1/400 sec 144. The average value of the function i = 50 sin ωt + 30 sin 3ωt is equal to ____. A. 31.8 A C. 38.2 A B. 25 A D. 51.43 A 145. For 200 Vrms value triangular wave, the peak value is equal to ____. A. 200 V C. 282 V B. 222 V D. 346 V
146. Determine the rms value of a semi-circular current wave which has a maximum value of A. A. 0.816A C. 0.866A B. 0.23 A D. 0.707A 147. The rms value of a half-wave rectified current is 100 A. Its value for full-wave rectification would be ____ amperes. A. 141.4 A C. 200/π A B. 200 A D. 400/π A 148. A half-wave rectified sine wave has an average value of 100 amp. What is the effective value? A. 157 A C. 70.71 A B. 444 A D. 100 149. The form factor of a half-wave rectified alternating current is ____. A. 1.11 C. 1.73 B. 1.57 D. 1.0 150. Three alternating currents are (ωt + 90°) A; i3 = 20 cos (ωt current. A. 167.4 sin (ωt + 45.66°) B. 74.6 sin ωt
given by i1 = 141 sin (ωt + 45°) A; i2 = 30 sin – 120°) A. Find the equation of the resultant C. D.
143.8 sin (ωt + 51.4°) 64.7 sin (ωt – 30°)
151. The maximum value of a sine wave AC voltage which will produce heat in a resistor at the same average rate as 115 V of direct current is ____. A. 81.3 V C. 162.6 V B. 115 V D. 230 V 152. A sinusoidal voltage source has a peak value of 150 volts. What equivalent DC voltage source would produce the same heating effect in a 1-ohm resistor? A. 15 V C. 95 V B. 212 V D. 106 V 153. The effective value of v(t) = 100 + A sin ωt is known to be 103.1. The amplitude A of the sine term is ____. A. 25 C. 35.48 B. 4.85 D. 100 154. An alternating current and a direct current flow simultaneously in the same conductor. If the effective of the AC is 8 A and DC is 12 A, what will an AC ammeter read when connected in the circuit? A. 14.42 A C. 11.66 A
B.
12 A
D.
16.49 A
155. Find the reading of an AC voltmeter connected across the series source of 100 sin (ωt – π/2) and 100 sin ωt. A. 100 C. 170.71 B. 130.65 D. 184.78 156. A voltage is given be v = 100 sin 314t. How long does it take this wave to complete one fourth of a cycle? A. 20 ms C. 5 ms B. 10 ms D. 1 ms 157. When a 15 V square wave is connected across a 50 volt AC voltmeter, it will read ____. A. 21.21 V C. 15 V B. 10.61 V D. 9.55 V 158. Calculate the effective value of v(t) = 100 sin 400t + 50 sin 800t + 10 cos 1200t V. A. 79.5 V C. 112.25 V B. 57.9 V D. 121. 52 V 159. The magnetic field energy of an inductor changes from maximum value to minimum value in 5 ms when connected to an ac source. The frequency of the source is A. 20 Hz C. 200 Hz B. 50 Hz D. 500 Hz 160. Non-sinusoidal waveforms are made up of A. different sinusoidal waveforms B. fundamental and even harmonics C. fundamental and odd harmonics D. even and odd harmonics only 161. The positive and negative halves of a complex wave are symmetrical when A. it contains even harmonics B. phase difference between even harmonics and fundamental is 0 or π C. it contains odd harmonics D. phase difference between even harmonies and fundamental is either π/2 or 3π/2 162. The r.m.s. value of the complex voltage given by is √ A. C. √ √ B. 20 D. 192
√
163. In a 3-phase system, ____th harmonic has negative phase sequence of RBY. A. 9 C. 5 B. 13 D. 15 164. A complex current wave is given by the equation The r.m.s. value of the current is ____ ampere. A. 16 C. 10 B. 12 D. 8
.
165. When pure inductive coil is fed by a complex voltage wave, its current wave A. has larger harmonic content B. is more distorted C. is identical with voltage wave D. shows less distortion 166. A complex voltage wave is applied across a pure capacitor. As compared to the fundamental voltage, the reactance offered by the capacitor to the third harmonic voltage would be A. nine times C. one-third B. three times D. one-ninth 167. Which of the following harmonic voltage components in a 3-phase system would be in phase with each other? rd th th A. 3 , 9 , 15 etc. th th th B. 7 , 13 , 19 etc. th th th C. 5 , 11 , 17 etc. nd th th D. 2 , 4 , 6 etc. 168. An alternating voltage is one that A. varies continuously in magnitude B. reverses periodically in polarity C. never varies in magnitude D. both A and B 169. One complete revolution of a conductor loop through a magnetic field is called a(n) A. octave C. cycle B. decade D. alternation 170. For a sine wave, one half cycle is often called a(n) A. alternation C. octave B. harmonic D. period
171. For a sine wave, the number of complete cycles per second is called the A. period C. frequency B. wavelength D. phase angle 172. To compare the phase angle between two waveforms, both must have A. the same amplitude C. different frequency B. the same frequency D. both A and B 173. The value of alternating current or voltage that has the same heating effect as a corresponding dc value is known as the A. peak value C. rms value B. average value D. peak-to-peak value 174. For an ac waveform, the period refers to A. the number of complete cycles per second B. the length of time required to complete one cycle C. the time it takes for the waveform to reach its peak value D. none of the above 175. The wavelength of a radio wave is A. inversely proportional to its frequency B. directly proportional to its frequency C. inversely proportional to its amplitude D. unrelated to its frequency 176. Unless indicated otherwise, all sine wave ac measurements are in A. peak-to-peak values C. rms values B. peak values D. average values 177. A unit step voltage is applied across an inductor. The current through the inductor will be A. zero for all time B. a step function C. a ramp function D. a delta (impulse) function 178. A ramp current flowing through an initially relaxed capacitor will result in a voltage across it that A. varies inversely with time B. remains constant C. varies directly with time D. varies as the square of time 179. The voltage v(t) = t u(t) volts is connected across a 1 H inductor having an initial current of -1 A. The net current will be zero at time t equal to
A. B.
0
C. D.
√ seconds 1 seconds
180. A voltage waveform v (t) = 12t is applied across 1H Inductor for t ≥ 0, with initial current through it being zero. The current through the inductor for t ≥ 0 is given by 3 A. 12t C. 12t 3 B. 24t D. 4 t
B. SERIES CIRCUITS 186. REE Board Exam September 2003 The following are in series R = 1,000 Ω, L = .100 μH and C = 20,000 pF. The voltage across the circuit is 100 V, 60 kHz. What is the total impedance expressed in ohms? A. 1882 ohms C. 2132 ohms B. 1000 ohms D. 1885 ohms
181. It is desired to have a constant direct current i(t) through the ideal inductor L. The nature of the voltage source v(t) must A. constant voltage B. linearly increasing voltage C. an ideal impulse D. exponentially increasing voltage
187. REE Board Exam October 2000 A series circuit has an applied voltage of v = 220 sin (ωt + 30°) and draws a current of i = 10 sin (ωt - 30°). What is the average power and power factor of the circuit? A. 1,905 W, 86.6% lagging C. 2,200 W, 100% B. 1,905 W, 86.6% lagging D. 1,100 W, 50% lagging
√ seconds
2
182. For the current and voltage waveforms, identify the element & its value.
A. B.
L, 25 H C, 25 F
C. D.
L, 2 H C, 2 F
183. The voltage and current waveforms for an element are shown in the figure. Find the circuit element and its value.
A. B.
L and 25 H C and 25 F
C. D.
L and 1 H C and 1 F
184. What is the rms value of a square wave with an amplitude of 10 A and frequency of 1 Hz? A. 0 A C. 5 A B. 10 A D. 7.07 A 185. What is the frequency in kHz of a radio signal whose wavelength is 15 m? A. 10,000 C. 15,000 B. 20,000 D. 20,500
188. REE Board Exam September 2001 A coil has an impedance of 75.4 Ω when connected a across a source of 60 Hz. The same coil yields an impedance of 54.8 Ω when connected across a source having a different frequency of 30 Hz. What is the coil’s inductance? A. 245.7 mH C. 158.6 mH B. 512.8 mH D. 341.7 mH 189. REE Board Exam April 1996 A circuit consists of a 4 ohms resistor and a 300 μF capacitor in series. It is connected across a 60 Hz voltage source with a 500 V peak voltage. What is the phasor form of the current? A. A C. A B. A D. A 190. REE Board Exam September 2000 Find the power in a circuit if i(t) = 10 sin (ωt - 30) and v(t) = 220 sin (ωt + 30). A. 550 watts C. 1900 watts B. 2200 watts D. 1500 watts 191. REE Board Exam April 1997 A current of 2.5 A flows through a series circuit consisting of a 100 Ω resistor and an unknown capacitor across a source of 460 V, 50 Hz. What is the value of the capacitive reactance? A. XC = 91.86 Ω C. XC = 154.45 Ω B. XC = 39.19 Ω D. XC = 184.0 Ω 192. REE Board Exam April 1995
In a series RC circuit the voltage across the capacitor and the resistor are 60 volts and 80 volts respectively. The total voltage is A. 70 C. 140 B. none of these D. 100 193. EE Board Exam October 1984 An industrial coil has a resistance of 32 ohms and reactance of 24 ohms and rated 440 volts at 60 Hz. A factory will connect the coil to a 440 V, 50 Hz supply. Solve for the value of a series resistor needed to avoid over-current condition. A. 2.07 ohms C. 2.44 ohms B. 2.64 ohms D. 2.25 ohms 194. REE Board Exam October 1998 Two relays each with 20 ohms resistance and 0.16 H inductance are connected in series. What is the equivalent impedance? A. 20 + j102.2 Ω C. 40 + j120.63 Ω B. 20 + j95.32 Ω D. 40 + j25.32 Ω 195. EE Board Exam October 1990 An inductive coil takes a current of 2 A and consumes 160 W when connected to a 240 V ac supply. A second coil when connected across the same supply takes 3 A and 500 W. Find the total power when the two coils are connected in series to this supply, A. 144.56 W C. 150.22 W B. 134.31 W D. 128.35 W 196. EE Board Exam October 1985 A coil draws 1875 watts when connected to a 150 V dc source. It consumes 30.72 watts when use on a 240 V, 60 Hz ac source. Find the inductance of the coil. A. 0.0255 H C. 0.0153 H B. 0.0341 H D. 0.0240 H 197. REE Board Exam October 1994 A current of 10 A and a power factor of 0.8 lagging is taken form a single phase 250 volt supply. The reactive power of the system is A. 1500 vars C. 2500 vars B. 2000 vars D. none of these 198. REE Board Exam October 1996 The resistor of 6 Ω and unknown impedance coil in series draws 12 A from a 120 V, 60 Hz line. If the real power taken from the line is 1152 watts, what is the coil inductance? A. 15.9 mH C. 20 mH
B.
10 mH
D.
1.59 mH
199. REE Board Exam April 1997 Determine the power factor angle in the series circuit which consists of R = 25 Ω, L = 0.2 H, across a power supply of 200 V, 30 Hz. A. 36.4° C. 52.4° B. 46.4° D. 56.4° 200. EE Board Exam April 1993 The impedance coils absorbs 250 watts when connected across 220 V, 60 Hz mains. It is then connected across 110 V, 25 Hz mains and also absorbs 250 watts. What is the inductance of the coil? A. 0.125 H C. 0.154 H B. 0.149 H D. 0.163 H 201. REE Board Exam September 2001 In laboratory experiment, the impedance of the coil was obtained at 60 Hz and 30 Hz. These are 75.48 ohms and 57.44 ohms respectively. What is the inductance of the coil? A. 150 mH C. 42.5 mH B. 182.5 mH D. 2.1 mH 202. REE Board Exam September 2002 A 10 ohms inductive resistor is connected in series with an unknown capacitance. At 60 Hz the impedance of the circuit is 10 + j11.72 ohms. At 30 Hz the impedance of the circuit is 10 – j5 ohms. What is the value of L in millihenrys? A. 50 C. 100 B. 500 D. 250 203. REE Board Exam April 1995 An impedance coil takes 10 A and absorbs 250 W when connected across a 220 V, 60 Hz source. What power will it absorb when connected across 110 V, 25 Hz mains? A. 539 W C. 439 W B. 239 W D. 339 W 204. EE Board Exam October 1984 An industrial coil has a resistance of 32 ohms and a reactance of 24 ohms and rated 440 volts at 60 Hz. A factory will connect the coil to a 440 V, 50 Hz supply. How much percentage over-current will the coil suffer? A. 5% C. 6% B. 10% D. 8% 205. REE Board Exam March 1998
A 25 Ω resistor connected in series with a coil of 50 Ω resistance and 150 mH inductance. What is the power factor of the circuit? A. 85% C. 90% B. 80% D. 75% 206. REE Board Exam April 1997 A current of 2.5 A flows through a series circuit consisting of a 100 ohm resistor and an unknown capacitor across a source of 460 V, 50 Hz. What is the value of the capacitive reactance? A. XC = 91.86 Ω C. XC = 154.45 Ω B. XC = 39.19 Ω D. XC = 184 Ω 207. REE Board Exam October 1998 The ohmic resistance of a large magnetic contactor is measured to be 20 ohms. A 230 V is impressed on the contractor and the current is taken as 3.2 A. Neglecting core loss, determine the inductance of the contractor in mH? A. 261 C. 183 B. 315 D. 251 208. REE Board Exam March 1998 A load of 20 + j35 Ω is connected across a 220 V source. Determine the power factor and the VARS. A. 49.6%, 1042 vars C. 85.3%, 975 vars B. 52.2%, 1023 vars D. 42.3%, 1087 vars 209. EE Board Exam October 1990 Find the total impedance in rectangular form for the following three series impedances: ohm, ohm, 34 ohm. A. 66.52 + j23.46 Ω C. 74.31 + j21.56 Ω B. 68.34 + j20.54 Ω D. 67.70 + j22.04 Ω 210. REE Board Exam October 1997 An impedance draws a current i = 10 cos (ωt – 30°) A from a voltage, v = 220 sin (ωt + 30°) V. What is the impedance? A. 15.6 – j15.6 Ω C. 19.1 – j11.1 Ω B. 15.6 + j15.6 Ω D. 11.0 + j19.1 Ω 211. EE Board Exam April 1990 A series resistance-capacitance (R-C) circuit is connected to a 230 volt 60 cycle source. If the power taken by the circuit is 4,800 watts and the voltage drop across the resistor is 115 volts, calculate the capacitance of the capacitor. A. 540 μF C. 556 μF B. 530 μF D. 503 μF
212. REE Board Exam March 1998 A 50 μF and 100 μF capacitors are connected in series and across a 100 sin (ωt + 30°) voltage. Write the equation of the current. A. 1.26 sin (ωt + 120°) A C. 5.65 sin (ωt + 120°) A B. 1.26 sin (ωt + 90°) A D. 5.56 sin (ωt + 90°) A 213. EE Board Exam April 1993 A V, 120 Hz generator and a V, 60 Hz generator are connected in series with a 60 V battery and a coil. The resistance and inductance of the coil are 3 and 2.65 mH, respectively. Determine the rms current of the coil. A. 42.54 A C. 43.55 A B. 44.24 A D. 40.44 A 214. REE Board Exam October 1996 A series circuit composed of 100-ohm resistor and a 20-microfarad capacitor connected across a 240-V, 60 Hz line. Which of the following answers is WRONG? A. the impedance of the circuit is 167 ohms B. angle between the current and the voltage vectors is 53.1 degrees C. the resulting current is 0.723 ampere D. the voltage across the resistance is 144.6 volts 215. REE Board Exam April 1994 A capacitance is connected to a 115-V, 25 Hz mains and takes 5 A. What current will it take when the capacitance and the frequency are both doubled? A. 2.5 A C. 20 A B. 5 A D. 10 A 216. REE Board Exam October 1996 A capacitor is rated 100 kVAR, 380 V, 50 Hz, What will its rating be at 60 Hz, 220 V? A. 50 kVAR C. 90.9 kVAR B. 40 kVAR D. 57.7 kVAR 217. REE Board Exam October 1992 A resistor and a capacitor are connected in series across a supply of 250 V. When the supply frequency is 50 Hz the current in the circuit is 5 A. When the supply frequency is 60 Hz, the current is 5.8 A. Find the value of the capacitance. A. 58.3 μF C. 60.2 μF B. 69.1 μF D. 70.2 μF
218. EE Board Exam October 1993 A series circuit composed of a 0.2 Henry inductor and a 74-microfarad capacitor is connected to a 60 V variable frequency source. At what frequency is the current be 4 amperes with a lagging power factor? A. 50 Hz C. 48 Hz B. 51 Hz D. 49 Hz 219. REE Board Exam October 1998 The maximum instantaneous voltage and current output of an alternator are 300 V and 20 A, respectively. What is the power output in watts if the voltage leads the current by 30°? A. 2598 C. 5196 B. 3000 D. 6000 220. REE Board Exam October 1998 A 50-microfarad is connected in series with a coil having 50 ohms resistance and 150 mH inductance. The source voltage is 100 sin (ωt – 120°) V. What is the maximum power? A. 199 watts C. 212 watts B. 147 watts D. 165 watts 221. REE Board Exam October 1997 An impedance draws a current i = 10 cos (ωt – 30°) A from a voltage v = 220 sin ωt. What is the maximum power? A. 2200 watts C. 190.5 watts B. 1100 watts D. 1320 watts 222. REE Board Exam April 1995 An incandescent lamp load generally considered to be made up of resistors take 4.8 kW from a 120 V ac source. The instantaneous maximum value of power is A. 4800 W C. 480 W B. 2400 W D. 9600 W 223. ECE Board Exam November 1998 The term used for an out-of-phase, non-productive power associated with inductors and capacitors? A. peak envelope power C. true power B. effective power D. reactive power 224. ECE Board Exam November 2001 What is the capacitive reactance of a 33 microfarad capacitor at 6500 Hz? A. 7.4 0hms C. 0.74 ohms B. 96 0hms D. 1122 ohms
225. ECE Board Exam November 1999 The power dissipated across the resistance in an AC circuit. A. true power C. reactive power B. real power D. apparent power 226. ECE Board Exam April 2000 What is the capacitive reactance of a 33 microfarad capacitor at 500 Hz? A. 1,000,000 ohms C. 0 ohms B. 144 ohms D. 9.55 ohms 227. ECE Board Exam November 1998 What is the reactance of a 25 mH coil at 600 Hz? A. 0.011 ohm C. 785 ohms B. 94,000 ohms D. 94 ohms 228. ECE Board Exam April 1999 Ignoring capacitance effects, what is the impedance of a 250 mH coil with an internal resistance of 55 ohms at 60 Hz? A. 149.2 ohms C. 94.2 ohms B. 109 ohms D. 10,900 ohms 229. ECE Board Exam November 1999 Ignoring any inductive effects, what is the impedance of RC series capacitor made up of a 56 kilo ohms resistor and a 0.033 μF capacitor at a signal frequency of 450 Hz? A. 66,730 C. 10,730 B. 57,019 D. 45,270 230. ECE Board Exam April 2000 Assuming an ideal capacitor, with no leakage, what is the capacitive reactance of 10 microfarad capacitance of DC (0 Hz)? A. 0 ohms B. 16000 ohms C. 1,000,000 ohms D. infinite capacitive reactance 231. ECE Board Exam April 1998 The impedance in the study of electronics is represented by resistance and _____ A. Reactance B. Capacitance C. Inductance D. Inductance and capacitance 232. ECE Board Exam November 2000
One of the following satisfies the condition of Ohm’s Law A. Application to metals which heated up due to flow of current over them B. C. D.
Application to AC circuit having its impedance used in place of resistance Application to semiconductor Application to vacuum radio valves
233. The effective voltage across a circuit element is (20 + j10) and the effective current through the element is 4 – j3 A. Calculate the true and reactive power taken by the element. A. 50 watts & 100 vars lagging B. 50 watts & 100 vars leading C. 110 watts & 20 vars lagging D. 110 watts & 20 vars leading 234. The voltage across a given circuit is 75 + j50 V. What is the power supplied to the circuit if the current through it is (8 – j5) A? A. 850 W C. 750 W B. 550 W D. 350 W 235. Find average power in a resistance R = 10 ohms if the current in series form is i = 10 sin ωt + 5 sin 3ωt + 2 sin 5ωt amperes. A. 65.4 watts C. 546 watts B. 645 watts D. 5.46 watts 236. Across a 230-V, 60 Hz power supply is a 15-ohm non-inductive resistor. What is the equation of the voltage and resulting current? A. e = 398.4 sin 60t and i = 21.6 sin 60t B. e = 325.5 sin 377t and i = 21.6 sin 377t C. e = 230 sin 377t and i = 15.3 sin 377t D. e = 230 sin 120t and i = 15.3 sin 120t 237. A resistor R and a capacitor C are connected in series across a 100 V, 60 cycle source. The reading of an ammeter connected in the circuit is 2 A and the reading of a voltmeter connected across the capacitor is 80 V. Calculate the values of R and C. A. 66 Ω & 30 μF C. 30 Ω & 66 μF B. 30 Ω & 60 μF D. 36 Ω & 60 μF 238. A series circuit consisting of a 66.2 μF capacitor and a variable resistor. For what two values of resistance will the power taken by the circuit be 172.8 watts, if the impressed 60-cycle emf is 120 volts? A. 85.33 & 3.33 ohms C. 5.33 & 3.0 ohms B. 53.33 & 30 ohms D. 83.33 & 5.33 ohms
239. A series circuit composed of 0.2 H inductor and a 74 μF capacitor is connected to a 60 V variable frequency source. At what frequency will the current be 4 A with lagging power factor? A. 47.767 Hz C. 60 Hz B. 74.68 Hz D. 50 Hz 240. A 30 ohm resistor is connected in parallel with an inductor of inductive reactance XL. The combination is then connected in series with a capacitor of reactance XC. What is the value of XL and XC if the total impedance is 1.92 ohms? A. 7.84 and 7.34 C. 44.8 and 84.21 B. 47.4 and 47.3 D. 84.7 and 34.7 241. An impedance of 100 Ω resistance and an unknown inductance is connected across the capacitor. The resulting impedance is a pure resistance of 500 Ω 5 if ω = 10 rad/sec. Calculate the values of inductor and capacitor. A. 1 μF & 2 mH C. 7 μF & 3 mH B. 5 μF & 1 mH D. 0.04 μF & 2 mH 242. The voltage across the resistor, inductor and capacitor in series is 60 V, 90 V and 10 V respectively. What is the voltage across this circuit? A. 160 V C. 100 V B. 140 V D. 50 V 243. The open circuit voltage of an alternator is 127 V and its internal impedance is Ω. Find the voltage across a load of Ω. A. V C. V B. V D. V 244. The maximum values of alternating voltage and current are 400 V and 20 A, respectively. In a circuit connected to 50 Hz supply and these quantities are sinusoidal. The instantaneous values of voltage and current are 283 V and 10 A respectively at t = 0 both increasing positively. What is power factor of the circuit? A. 0.707 C. 0.85 B. 0.83 D. 0.965 245. The potential difference measured across a coil is 4.5 V, when it carries a direct current of 9 A. The same coil when carries an alternating current of 9 A at 25 Hz, the potential difference is 24 V. Find the power when it is supplied by 50 V, 50 Hz supply. A. 45 W C. 63 W B. 54 W D. 30 W
246. Two coils A and B are connected in series across a 240 V, 50 Hz supply. The resistance of A is 5 Ω and the inductance of B is 0.015 H. If the input from the supply is 3 kW and 2 kVAR, find the inductance of A and resistance of B. A. 0.0132 H & 8.3 Ω C. 0.026 H & 12 Ω B. 0.215 H & 3.8 Ω D. 0.031 H & 5.3 Ω
253. A coil has a resistance of 6 ohms and an inductance of 0.02 H. When a noninductive resistor is connected in series with the coil, the current drawn when connected to 220 V DC source is equal to the current drawn by the coil alone across a 220 V, 60 Hz source. Determine the resistance of the non-inductive resistor. A. 3.63 Ω C. 3.69 Ω B. 6.39 Ω D. 3.96 Ω
247. A current of 5 A flows through a non-inductive resistance in series with a choking coil when supplied at 250 V, 50 Hz. If the voltage across the resistance is 120 V and across the coil is 200 V, calculate the power absorbed by the coil in watts. A. 168.75 W C. 51.37 W B. 137.5 W D. 75.31 W
254. A series RL circuit has L = 0.02 H and an impedance of 17.85 Ω. When a sinusoidal voltage is applied, the current lags the voltage by 63.5°. What is the value of the angular frequency? A. 400 rad/sec C. 600 rad/sec B. 500 rad/sec D. 800 rad/sec
248. A single phase, 7.46 kW motor is supplied from a 400 V, 50 Hz AC mains. If its efficiency is 85% and the power factor is 0.8 lagging, find the reactive component of the input current. A. 16.46 A C. 27.43 A B. 21.95 A D. 21 A
255. A 50 resistance is connected in series with a coil having 25 resistance and 150 mH inductance. The circuit is connected to a voltage source of 200 sin t. Calculate the instantaneous current. A. 2.9 sin t C. 2.1 sin (t – 37) B. 1.7 sin (t + 37) D. 5.11 sin (t - 37)
249. A series RLC circuit consists of 20 ohms resistance, 0.2 H inductance and an unknown capacitance. What is the value of the capacitance if the circuit has a leading angle of 45° at 60 Hz? A. 35.18 μF C. 27.8 μF B. 47.9 μF D. 30.7 μF
256. A coil having a resistance of 25 and an inductance of 150 mH is connected in series with a 80 F capacitor across a voltage source of 200 sin 377t. What is its instantaneous current? A. 5.84 cos (377t - 43) C. 5.84 sin (377t + 43) B. 5.84 sin 377t D. 5.84 sin (377t - 43)
250. A 3 HP, 120 V, 60 Hz induction motor operating at 80% efficiency and 0.866 lagging power factor is to be used temporarily with 240 V, 60 Hz source. What resistance in series with the motor will be required for the motor to have 120 V across its terminals at full load? A. 6.68 Ω C. 13.76 Ω B. 4.77 Ω D. 9.54 Ω
257. A coil with a 15 resistance is connected in series with a capacitor. At 60 Hz source, the impedance is measured at 15 + j11.27 while in 30 Hz source it is measured as 15 – j7.24 . Calculate the inductance of the coil. A. 52.7 mH C. 41.2 mH B. 65.8 mH D. 11.27 mH
251. A circuit draws a current of (3 – j8) A from a source of (100 + j37) V. Find the true power of the circuit. A. 4 W C. 300 W B. 596 W D. 296 W
258. An impedance coil has a resistance and inductance of 20 ohms and 0.05 H respectively. What value of dc voltage can be applied to the coil in order that it will take the same power from a 220 V 60 Hz mains? A. 188 V C. 160 V B. 220 V D. 120 V
252. A resistor and a coil are connected in series with a voltage source. If the voltage across the coil is 10 sin (866t + 70°) V and the current flowing through the resistor is 2 cos (866t – 80°) A, what is the resistance of the coil? A. 4.92 Ω C. 5 Ω B. 2.5 Ω D. 4.33 Ω
259. A ½ HP, 110 V, 60 Hz, single-phase induction motor has an efficiency of 88% and a power factor of 0.707 lagging at rated load. This motor is to be connected temporarily on a 220 V, 60 Hz line. Determine the resistance required to be placed in series with the motor in order to prevent the machine from experiencing overcurrent? A. 25.2 ohms C. 19.5 ohms B. 23.5 ohms D. 27.6 ohms
D. 260. Two coils A and B known to have the same resistance are connected in series across a 110 V, 60 cycle line. The current and power delivered by the source are respectively 4.1 A and 300 W. If the voltage across coil A is twice that across coil B, calculate the inductance of coil B. A. 8.63 mH C. 9.02 mH B. 7.36 mH D. 4.49 mH 261. The total voltage in a series RL circuit ____ the current by an angle ____. A. lags, of 90 B. lags, between 0 and 90 C. leads, between 0 and 90 D. leads, between 90 and 180 262. In a series RL circuit, the inductor current ____ the resistor current. A. lags C. leads B. is equal D. is negative 263. The impedance triangle is similar to the ____ triangle with the resistance phasor in place of the ____ A. current, resistor current B. current, resistor voltage C. voltage, impedance D. voltage, resistor voltage 264. In the impedance triangle the inductive reactance and impedance phasor are analogous to the ____ and ____ phasor respectively in the voltage triangle. A. inductive voltage, total voltage B. inductive current, total current C. inductive voltage, resistive current D. inductive current, resistive current 265. In a series RL circuit, phasor diagram, total voltage may be represented by the ____ phasor and the resistor voltage may be represented by the ____ voltage. A. current, voltage B. impedance, resistance C. current, resistance D. impedance, inductance 266. The phase angle of a series RL circuit is the angle between the ____ phasor and the ____ phasor. A. resistance, inductive reactance B. resistance, impedance C. inductive reactance, impedance
none of the above
267. The phase angle of a series RL circuit may be computed ____ as ____ or ____. -1 -1 -1 A. cos R/XL, sin XL/R, tan R/Z -1 -1 -1 B. cos R/Z, sin XL/R, tan R/XL -1 -1 -1 C. cos Z/XL, sin R/Z, tan XL/R -1 -1 -1 D. cos R/Z, sin XL/Z, tan XL/R 268. In the circuit of figure shown the effective value of the resistor voltage is ____ volts. 5Ω
5Ω
Eeff. = 10 V
A. B.
5
√
C. D.
√ 10
269. A(n) ____ stores and returns energy to a circuit while a(n) ____ dissipates energy. A. resistor, impedance C. inductor, resistor B. resistor, inductor D. inductor, reactance 270. For an RL circuit, the power factor cannot be less than ____ or greater than ____. A. 0, 1 C. 0, -1 B. 1, 0 D. –1, 0 271. The voltage across a capacitor ____ the current through it by ____. A. lags, 45 C. leads, 0 B. lags, 90 D. leads, 90 272. If the resistance in a series RC circuit is increased the magnitude of the phase angle A. increases B. remains the same C. decreases D. changes to an indeterminate manner 273. In a series RC circuit, the current ____ the total voltage by an angle. A. lags, of 45 B. lags of 0 C. leads, between 0 and 90
D.
A. B.
leads, of 90
274. The resistance phasor for a series RC circuit points to the right. The capacitive reactance phasor points ____ while the diagonal of the rectangle having there two phasors as sides represents the ____. A. up, impedance C. down, impedance B. left, current D. up, total voltage 275. The phase angle for a series RC circuit is defined as the angle between the ____ and the ____ phasors. A. current, resistance voltage B. current, total voltage C. resistance voltage, capacitor voltage D. R, XC 276. The phase angle for a series RC circuit may be computed as the angle between the ____ and the ____ phasors. A. resistance, impedance B. resistance, reactance C. resistance, impedance D. none of the above 277. If a series RC circuit with 10 ohms and XC = 10 ohms carries a current of 1 ampere effective value the resistor voltage is ____ volts effective and the capacitor voltage is ____ volts effective. A. 10/√ , 10/√ C. 10√ , 10√ B. 10, 10 D. 5, 10 278. The power dissipated in a series RL circuit with R =10 ohms and X C = 10 ohms carrying an effective current of 3 amps is ____ watts. A. 30 C. 90 B. 30√ D. 90√ 279. The magnitude of the power factor of an RC circuit with R = 10 ohms, XC = 10 ohms. I = 2 amp effective is ____. A. 1 C. 0.707 B. 0.5 D. 0.0 280. The power dissipated in the circuit shown is ____ watts. 30 Ω
Eeff. = 100 V
40 Ω
60 80
C. D.
100 120
281. The net reactance in an RLC circuit is A. XL C. XC B. XC – XL D. XL - XC 282. The impedance of a series RLC circuit is ____. A.
√
C.
√
(
)
B.
√
D.
√
(
)
283. In a series RC circuit, the voltage across the capacitor and the resistor are 60 V and 80 V respectively. The input voltage should be A. V C. V B. V D. V 284. The transient current are due to A. voltage applied to circuit B. resistance of the circuit C. impedance of the circuit D. changes in stored energy in inductance and capacitance 285. To a highly inductive circuit, a small capacitance is added in series. The angle between voltage and current will A. increase B. decrease C. remain nearly the same D. become indeterminant 286. In a series R-L circuit. VL ____ VR by ____ degrees. A. lags, 45 C. leads, 90 B. lags, 90 D. leads, 45 287. The voltage applied across an R-L circuit is equal to ____ of VR and VL. A. arithmetic sum C. phasor sum B. algebraic sum D. sum of the squares 288. The power in an a.c. circuit is given by A. VI cos φ C. I² Z B. VI sin φ D. I² XL 289. The p.f. of an R-C circuit is A. often zero
B. C. D.
between zero and 1 always unity between zero and -1.0
298. An R-L-C circuit has R = 10 Ω, XL = 20 Ω and XC = 30 Ω. The impedance of the circuit is given by the expression. A. Z = 10 + j20 C. Z = 10 – j20 B. Z = 10 + j50 D. Z = -10 + j20
290. Which phasor diagram is correct for a series R-C circuit?
I Fig. 1 A. B.
Figure 1 Figure 2
V
V
I
V
Fig. 2 C. D.
I Fig. 3
I
V
Fig. 4
Figure 3 Figure 4
291. In an R-L-C circuit, v(t) = 20 sin (314t + 5π/6) and i(t) = 10 sin (314t + 2π/3). The p.f. of the circuit is ____ and power drawn is ____ watt. A. 0.5 lead, 200 C. 0.866 lead, 173.2 B. 0.886 lag, 186.6 D. 0.5 lag, 50 292. The input of an a.c. circuit having p.f. of 0.8 lagging is 20 kVA. The power drawn by the circuit is ____ kW. A. 12 C. 16 B. 20 D. 8 293. The power factor of an a.c. circuit is given by A. cosine of the phase angle B. tangent of the phase angle C. the ratio R/XL D. the ratio XL/Z 294. In series R-L-C circuit, R = 100 Ω, XL = 300 Ω and XC = 200 Ω. The phase angle Φ of the circuit is _____ degrees. A. 0 C. 45 B. 90 D. -45 295. The phase angle of a series R-L-C circuit is leading if A. XL = 0 C. XC > XL B. R = 0 D. XC < XL 296. In an a.c. circuit, the ratio of kW/kVA represents A. power factor C. form factor B. load factor D. diversity factor 297. If p.f. of a circuit is unity, its reactive power is A. a maximum C. zero B. equal to I²R D. a negative quantity
299. An alternating voltage e = 200 sin 314t is applied to a device which offers an ohmic resistance of 20 Ω to the flow of current in one direction while entirely preventing the flow in the opposite direction. The average value of current will be A. 5 A C. 1.57 A B. 3.18 A D. 1.10 A 300. A 10 mH inductor carries a sinusoidal current of 1 A rms at a frequency of 50 Hz. The average power dissipated by the inductor is A. 0 W C. 0.5 W B. 0.25 W D. 1.0 W 301. A circuit component that opposes the change in circuit voltage is A. resistance C. inductance B. capacitance D. all of the above 302. Power loss in an electrical circuit can take place in A. inductance only B. capacitance only C. inductance and resistance D. resistance only 303. A circuit of zero lagging power factor behaves as A. an inductive circuit C. R-L circuit B. a capacitive circuit D. R-C circuit 304. In an R-L series circuit the power factor is A. leading C. zero B. lagging D. unity 305. When a sinusoidal voltage is applied across an R-L series circuit having R = XL, the phase angle will be A. 90° C. 45° leading B. 45° lagging D. 90° leading 306. An ac source having voltage e = 110 sin (ωt + π/3) is connected in an ac circuit. If the current drawn from the circuit varies as i = 5 sin (ωt - π/3) the impedance of the circuit will be A. 22 Ω C. 30.8 Ω
B.
16 Ω
D.
none of these
307. Which are of the following true of the circuit shown in the given figure? 100 Ω
L
250 2 sin300 t
-
I
1. VR = 2. I = 2 A 3. L = 0.25 H √ V Select the correct answer using the codes given below: Codes: A. 2 and 3 C. 1 and 3 B. 1 and 2 D. 1, 2 and 3 308. The R-L circuit of the figure is fed from a constant magnitude variable frequency sinusoidal voltage source vin. At 100 Hz, the R and L element each has a voltage drop Vrms. If the frequency of the source is changes to 50 Hz, then new voltage drop across R is R
L
+ vin -
A. B.
√ √
Vrms Vrms
C. D.
5 W and 8.66 VAR 20 W and 60 VAR √ W and √ VAR
150 V
VR
+
B. C. D.
√ √
Vrms Vrms
312. In a two-element series circuit, the applied voltage and resultant current are 3 3 respectively, v(t) = 50 + 50 sin (5 x 10 t) and i(t) = 11.2 sin (5 x 10 t + 63.4°). The nature of the elements would be A. R-L C. L-C B. R-C D. neither R, nor L, nor C 313. A series circuit passive elements has the following current and applied voltage: v = 200 sin (2,000t + 50°), i = 4 cos (2,000t + 13.2°) The circuit elements A. must be resistance and capacitance B. must be resistance and inductance C. must be inductance, capacitance and resistance D. could be either resistance and capacitance or resistance, inductance and capacitance 314. A two terminal black box contains one of the R-L-C elements. The black box is connected to a 220 V ac supply. The current through the source is I. When a capacitance of 0.1 F is inserted in series between the source and the box, the current through the source is 2I. The element is A. a resistance B. an inductance C. a capacitance D. it is not possible to determine the element 315. In the following circuit, i(t) under steady state is
310. A square wave is fed to an R-C circuit. Then A. voltage across R is square and across C is not square B. voltage across C is square and across R is not square C. voltage across both R and C is square D. voltage across both R and C is not square 311. The voltage phasor of a circuit is V and the current phasor is A. The active and reactive powers in the circuit are A. 10 W and 17.32 VAR
2H
1Ω
309. An ac source of 200 Vrms supplies active power of 600 W and reactive power of 800 VAR. The rms current drawn from the source is A. 10 A C. 3.75 A B. 5 A D. 2.5 A
1F
5V 10 sin t
A. B.
zero 5
C. D.
i(t)
7.07 sin t 7.07 sin (t – 45°)
316. The source in the circuit is a sinusoidal source. The supply voltages across various elements are marked in the figure. The input voltage is
3V
14 V
321. In the case of the R-L-C circuit shown in the given figure, the voltage across the R, L and C would be respectively
10 V
R
A. B.
10 V 5V
C. D.
15 V (rms)
27 V 24 V
317. In the circuit shown in the given figure, if the power consumed by the 5 Ω resistor is 10 W, then the pf of the circuit is 5Ω
L
10 Ω
50 cos ωt
A. B. C. D.
L
C
V1 20 V (rms)
V2 9 V (rms)
12 V, 16 V and 7 V or 25 V 16 V, 12 V and 7 V or 25 V 7 V, 16 V and 12 V 16 V, 12 V and 25 V
322. Consider the following statements regarding the circuit shown in the figure. j15 / 3
5Ω
A. B.
0.8 0.6
C. D.
0.5 zero
10 6 V
318. In an RL circuit, supplied from an ac source, the reactive power is proportional to the A. the average energy stored in the electric field B. the average energy stored in the magnetic field C. sum of the average energy stored in the electric field and that stored in the magnetic field D. difference of the average energy stored in the electric field and that stored in the magnetic field 319. If a series RLC circuit excited by a voltage e = E sin ωt when LC < 1/ω A. current lags behind the applied voltage B. current leads the applied voltage C. current is in phase with the applied voltage D. voltage across L and C are equal
2
I
If the power consumed by 5 Ω resistor is 10 W then 1. |I| = √ A 2. the total impedance of the circuit is 5 Ω 3. cos θ = 0.866 Which of these statements is correct? A. 1 and 3 C. 1 and 2 B. 2 and 3 D. 1, 2 and 3 323. In an ac circuit if voltage V = (a + jb) and current I = (c + jd), then the power is given by A. ac + ad C. bc - ad B. ac + bd D. bc + ad 324. The reactive power drawn from the source in the network in the given figure is
320. The current in the circuit shown is
+j10 Ω
3Ω
10010 V
A. B.
5A 10 A
C. D.
10 Ω
15 A 25 A
A.
300 VAR
C.
100 VAR
-j10 Ω
B.
200 VAR
D.
zero
325. A series R-L-C circuit, consisting of R = 10 Ω, XL = 20 Ω, XC = 20 Ω is connected across an ac supply of 100 V (rms). The magnitude and phase angle (with reference to supply voltage) of the voltage across the inductive coil are respectively A. 100 V, 90° C. 200 V, -90° B. 100 V, -90° D. 200 V, 90° 326. For a capacitor in a sine wave ac circuit A. vC lags iC by 90° B. iC leads vC by 90° C. iC and vC have the same frequency D. all of the above 327. In a series RC circuit, A. VC leads VR by 90° B. VC and I are in phase
C. D.
VC lags VR by 90° both B and C
328. In a series RC circuit, A. VC and VR are in phase B. VT and I are always in phase C. VR and I are in phase D. VR leads I by 90° 329. When the frequency of the applied voltage increases in a series RC circuit A. the phase angle, θT, becomes more negative B. ZT increases C. ZT decreases D. both A and 330. Inductive reactance, XL A. applies only to non-sinusoidal waveforms or dc B. applies only to sine waves C. applies to either sinusoidal or non-sinusoidal waveforms D. is inversely proportional to frequency 331. For an inductor in a sine wave ac circuit A. VT leads iL by 90° C. VT and iL are in phase B. VT lags iL by 90° D. none of the above 332. In a series RL circuit, A. VT lags VR by 90° B. VT leads VR by 90°
C. D.
VR and I are in phase both B and C
333. In a series RL circuit where XL = R, the phase angle, θZ, is A. -45° C. 90° B. 0° D. 45° 334. In an ac circuit with only series resistances A. VT and I are in phase B. RT =R1 + R2 + R3 + … + etc. C. each voltage drop is in phase with the series current D. all of the above 335. The unit of apparent power is the A. volt-ampere (VA) B. watt (W) C. volt-ampere-reactive (VAR) D. joule (J) 336. In an ac circuit with only series capacitors A. VT leads I by 90° B. VT lags I by 90° C. each capacitor voltage drop leads I by 90° D. both A and C 337. The unit of real power is the A. watt (W) B. volt-ampere (VA) C. joule (J) D. volt-ampere-reactive (VAR) 338. In a series RLC circuit A. XL and XC are 180° out of phase B. IL and IC are 180° out of phase C. XL and XC are 90° out of phase D. XL and XC are in phase 339. The power factor of an ordinary electric bulb is A. zero B. unity C. slightly more than unity D. slightly less than unity 340. The power factor of an ac circuit is equal to A. cosine of the phase angle B. sine of the phase angle C. unity for a resistive circuit D. unity for a reactive circuit
341. If f(t) = sin t + sin √ t is passing through R = 1 ohm, what is the power dissipated in 1 ohm resistor? A. 1 W B. 2 W C. since f(t) in non-periodic, not possible to find power D. none of the above C. PARALLEL CIRCUITS 342. EE Board Exam October 1981 A circuit consists of XL = j5 ohms, XC = -j5 ohms and R = 5 ohms all are connected in parallel. Find the equivalent impedance. A. 5.5 Ω C. 4.8 Ω B. 5.0 Ω D. 5.2 Ω 343. EE Board Exam October 1985 Given: Z1 = -j2.5 ohms; Z2 = j4 ohms; Z3 = 5 ohms; Z4 = 1 + j5 ohms. If the four impedances are connected in parallel, find the equivalent impedance in ohms. A. 4.1 + j0.72 C. 4.2 + j0.35 B. 4.3 + j0.45 D. 4.0 + j0.97 344. EE Board Exam April 1984, April 1987 Three impedances Za = 3 + j4 ohms, Zc = 4 – j4 ohms and Zc = j3 ohms are connected in parallel. Solve for the pf of the combination. A. 0.653 leading C. 0.503 leading B. 0.554 lagging D. 0.620 lagging 345. EE Board Exam October 1993 -6 A pure capacitance of 530.515 x 10 farad and an inductance of 530.515 x -4 10 Henry are connected in parallel across an ac power source. Solve for the resultant impedance assuming that the frequency is 30 Hz. A. 10 Ω C. zero B. infinite D. undefined
A. B.
0.471 lagging 0.471 leading
C. D.
0.573 lagging 0.573 leading
348. REE Board Exam October 1997 A resistor of 50 ohms and an impedance of 100 + j50 ohms are connected in parallel across a 220 volts supply. What is the power factor of the load? A. 96% C. 98% B. 99% D. 95% 349. EE Board Exam October 1992 A capacitor of 3.18 microfarads is connected in parallel with a resistance of 2,000 ohms. The combination is further connected in series with an inductance of 795 mH and resistance of 100 ohms across a supply given by e = 400 sin wt + 80 sin (3wt + 60°). Assume w = 314 radians/sec. Determine the power dissipated. A. 74.66 W C. 80.28 W B. 78.05 W D. 75.66 W 350. EE Board Exam October 1992 A capacitor of 3.18 microfarads is connected in parallel with a resistance of 2,000 ohms. The combination is further connected in series with an inductance of 795 mH and resistance of 100 ohms across a supply given by e = 400 sin wt + 80 sin (3wt + 60°). Assume w = 314 radians/sec. Determine the circuit power factor. A. 0.702 C. 0.633 B. 0.650 D. 0.612 351. EE Board Exam April 1990 A capacitor, an electric resistance heater, and impedance are connected in parallel to a 120 V, 60 Hz system. The capacitor draws 50 var, the heater draws 100 W and the impedance coil draws 269 VA at a pf 0f 0.74 lagging. Determine the system power factor. A. 0.933 leading C. 0.916 lagging B. 0.928 lagging D. 0.911 lagging
346. REE Board Exam March 1998 A coil of a 50-ohm resistance and of 150 mH inductance is connected in parallel with a 50 μF capacitor. What is the power factor of the circuit? A. 80% C. 70% B. 50% D. 60%
352. REE Board Exam October 1996 A bank of capacitors is connected in parallel each rated at 10 kVAR, 380 volts. If one unit is shorted out, what would be the net capacitance of the bank? A. 330 μF C. 220 μF B. 440 μF D. 110 μF
347. EE Board Exam April 1982 Three impedances Za, Zb and Zc are connected in parallel. If at 60 Hz, Za = j8, Zb = -j2 and Zc = 5 ohms. Solve for the resultant power factor.
353. EE Board Exam October 1992 A capacitor of 3.18 microfarads is connected in parallel with a resistance of 2,000 ohms. The combination is further connected in series with an
inductance of 795 mH and resistance of 100 ohms across a supply given by e = 400 sin wt + 80 sin (3wt + 60°). Assume w = 314 radians/sec. Determine the rms value of the total current. A. 0.40 A C. 0.56 A B. 0.33 A D. 0.45 A 354. EE Board Exam June 1990 Three loads, units A, B and C are connected in parallel and take currents that are respectively 12, 10 and 15 A respectively. Assuming Ia to be the reference phasor. Ib leads Ia by 30° and Ic lags behind Ia by 65°, calculate the total (resultant) current. A. 28.33 A C. 26.46 A B. 30.21 A D. 32.10 A 355. EE Board Exam April 1992 Two single-phase motors are connected in parallel across a 120-volt, 60cycle source of supply. Motor A is a split-phase inductance type and motor B is a capacitor type: Motor A B
HP Output ¼ ½
Determine total power factor. A. 0.886 lag B. 0.864 lag
Efficiency 0.60 0.70
C. D.
pf 0.70 lag 0.95 lag
0.817 lag 0.825 lag
356. EE Board Exam April 1992 A 250 V, 30 Hz generator supplies power to a parallel circuit consisting of a 20 HP motor whose efficiency is 90% at 0.80 pf lagging and a second load that draws an apparent power of 7 kVA at unity pf. Determine the system power factor. A. 0.828 lagging C. 0.802 lagging B. 0.831 lagging D. 0.884 lagging 357. EE Board Exam April 1985 A resistance of 5 ohms is connected in series with a capacitor of 442.1 μF. The combination is then connected in parallel with an inductance of 21.22 mH. Solve for the resultant current if the circuit is connected across a 120 V, 60 Hz ac source. A. 9.44 A C. 11.29 A B. 10.68 A D. 10.34 A 358. EE Board Exam April 1993
An inductor L1 is connected in series with a parallel combination of inductor L2 and capacitor C. The impedance of the circuit w = 400 rad/sec is j100 ohms. The circuit is to yield infinite impedance at w = 1,000 rad/sec and zero impedance at w = 2,000 rad/sec. Determine the value of C. A. 1.28 μF C. 2.06 μF B. 1.67 μF D. 1.32 μF 359. EE Board Exam April 1992 A sinusoidal current source, 10 cos 1000t, is in parallel both with a 20-ohm resistor and the series combination of a 10-ohm resistor and a 10-mH inductor. Find the equation of the voltage across the 10-ohm resistor. A. 63.25 cos (1000t – 18.43°) B. 61.32 cos (1000t – 20.34°) C. 59.36 cos (1000t – 17.45°) D. 60.12 cos (1000t – 19.38°) 360. EE Board Exam April 1993 A 1-hp, 220 V, 60 Hz capacitor-start motor has main and auxiliary winding impedance at starting of 3.5 + j2.5 ohms and 8.6 + j2.5 ohms, respectively. Determine the value of the starting capacitance that will place the main and auxiliary winding currents 90 apart at starting, A. 186.75 μF C. 182.43 μF B. 174.35 μF D. 170.67 μF 361. EE Board Exam October 1990 Two impedances A and B are connected in parallel across a 120 V ac supply. The total current and the current in each impedance is adjusted to 20 A. The power drawn by A is doubled that of B and the power factor is lagging. Determine the power factor of A. A. 0.650 lagging C. 0.841 lagging B. 0.704 lagging D. 0.677 lagging 362. REE Board Exam March 1998 A coil of 50-ohm resistance and of 150-mH inductance is connected in parallel with a 50-μF capacitor. If the source voltage is 100 sin (ωt + 30°), what is the equation of the line current? A. 1.91 sin (ωt + 52.5°) C. 1.82 sin (ωt - 62°) B. 1.25 sin (ωt + 75.5°) D. 1.32 sin (ωt – 75.5°) 363. EE Board Exam October 1984 A resistor R is connected in parallel with a 10-ohm inductive reactance. The combination is then connected in series with a 4-ohm capacitive reactance. The whole combination is connected across a 100-volt, 60 Hz supply, How much is R if the angle between the supply voltage and the total current is 45 degrees?
A. B.
12 ohms 25 ohms
C. D.
16 ohms 20 ohms
364. EE Board Exam April 1980 Three impedances Z1 = 1 - j4 ohms, Z2 = – j6 ohms and Z3 = 4 + j3 ohms are connected in series-parallel. Z1 is connected in series with the parallel combination of Z2 and Z3. Determine the equivalent impedance of the combination. A. 4.32 – j1.21 ohms C. 6.76 – j5.68 ohms B. 2.23 – j3.32 ohms D. 5.42 – j7.21 ohms 365. EE Board Exam October 1984 A 5-ohm resistor is connected in parallel with a 10-ohm inductive reactance. The combination is then connected in series with a 4-ohm capacitive reactance. The whole combination is connected across a 100-volt, 60 Hz supply. How much is the total current drawn by the circuit? A. 22.36 A C. 23.16 A B. 20.45 A D. 19.89 A 366. EE Board Exam April 1983 A non-inductive resistor R is connected in parallel with an inductive reactance of 10 ohms. The combination is then connected in series with a capacitive reactance of 5 ohms. The whole combination is connected across a 100-volt, 60 Hz ac source. If R is equal to 5 ohms, solve for the voltage across the parallel combination. A. 87.53 V C. 89.44 V B. 88.34 V D. 91.87 V 367. EE Board Exam April 1980 Three impedances Z1 = 1 - j4 ohms, Z2 = – j6 ohms and Z3 = 4 + j3 ohms respectively are connected in series-parallel. Z1 is connected in series with the parallel combination of Z2 and Z3. If this circuit is connected across a 230 V, 60 Hz source, determine the voltage across the parallel combination of Z 2 and Z3. A. 156.3 V C. 135.7 V B. 146.8 V D. 163.2 V 368. EE Board Exam October 1980 Given three impedances: Z1 = 10 + j0 ohms, Z2 = 3 + j4 ohms and Z3 = 8 – j6 ohms. Impedance Z2 and Z3 are connected in parallel and the combination is connected in series with impedance Z1 across a 120 V single-phase 60 Hz source. Find the total power drawn by the impedance. A. 1008 W C. 1038 W B. 1204 W D. 1103 W
369. EE Board Exam October 1993 If admittance Y = 0.06 – j0.08 mho, then conductance G equals A. -0.06 C. 0.08 B. 0.06 D. -0.08 370. EE October 1986, April 1993 A parallel circuit consists of a resistor having a conductance of 4 mhos, an inductive reactor having a susceptance of 8 mhos and a capacitive reactor having a susceptance of 5 mhos. What is the impedance of the circuit? A. 0.11 + j0.13 ohms C. 0.12 + j0.16 ohms B. 0.13 + j0.11 ohms D. 0.16 + j0.12 ohms 371. REE Board Exam October 1994 A capacitor branch having a ratio of XC to R of 5 is paralleled with impedance consisting of a 4 Ω resistance and a 3 Ω inductive reactance. The power factor of the resulting circuit is 0.8 leading. Find the size of the capacitor in μF if the frequency is 60 Hz. A. 879.9 μF C. 978.9 μF B. 1078.9 μF D. 778.9 μF 372. ECE Board Exam November 2000 A parallel-LC circuit can store energy fed to it power source and produces an output which is a continuous A.C. wave. It is often called a ____. A. Tank circuit C. Storage circuit B. Store circuit D. Power circuit 373. ECE Board Exam November 2001 What is the impedance relationship between the output of one circuit and the input of another circuit will provide maximum power transfer? A. very low impedance C. lower impedance B. higher impedance D. equal impedance 374. The series circuit of R = 30 Ω & X = 4 Ω and a parallel circuit of R’ and X’ have the same impedance and power factor. Calculate the value of R’ and X’. A. 8.33 Ω and 6.25 Ω C. 7.47 Ω and 7.51 Ω B. 2.56 Ω and, 3.83 Ω D. 5.62 Ω and 9.84 Ω 375. A 25 Ω resistor, 2 mH inductor and 30 μF capacitor are connected in parallel across 100 sin (5000t + 45°) V source. Calculate the total current taken by the circuit. A. 4 sin (5000t + 45°) + 5 cos (5000t + 45°) B. 14 sin (5000t) + 15 sin (5000t + 45°) C. 40 sin (5000t + 30°) + 50 cos (5000t + 45°) D. 4 cos (5000t + 45°) + 5 cos (5000t + 45°)
376. A parallel circuit with one branch of R = 5 Ω and a single unknown element in the other branch has the following applied voltage and total current e = 10 cos (50t + 60°) V and i = 5.38 cos (50t – 8.23°) A. The unknown element is ____. A. L = 0.04 H C. C = 10 μF B. L = 0.02 H D. C = 5 μF 377. An impedance of 3 – j3 Ω is connected in parallel with 5 + j2 Ω. The voltmeter connected across 3 Ω resistance measures 45 V. Calculate the total current of the circuit. A. 22.4 A C. 13.4 A B. 41.3 A D. 7.91 A 378. Two impedances ZA = 4 + j6 Ω and ZB are connected in parallel. The apparent power for the impedance B is 1490 VA. Determine the total apparent power. A. 4250 VA C. 2652 VA B. 3290 VA D. 8031 VA 379. A feeder supplies two loads, one at 50 amperes at 50% power factor, the other 150 amperes at unity power factor. The total current supplied by the feeder is approximately ____. A. 180 A C. 175 A B. 200 A D. 150 A 380. A fluorescent lamp and its inductive ballast draw a 1.0 A current at 50% lagging power factor from a 120-V, 60-Hz source. What is the over-all power factor when a 26.5 μF capacitor is connected across the fixture? A. 0.832 lagging C. 0.5 leading B. 0.832 leading D. 0.5 lagging
383. Ten impedances connected in parallel draw the following individual current: , , , , , , , , , . What is the equivalent power factor of the circuit? A. 0.924 C. 0.707 B. 0.866 D. 0.876 384. Ten impedances connected in parallel draw the following individual current: , , , , , , , , , .What element should be connected across the circuit so that the current would be in phase with the source? A. 54 mH C. 13 mH B. 25.4 mH D. 31 mH 385. A small single-phase, 240 V induction motor is tested in parallel with 160 Ω resistor. The motor takes 2 amperes and the total current is 3 amperes. What is the power of the whole circuit? A. 800 W C. 220 W B. 360 W D. 580 W 386. A capacitor is placed in parallel with two inductive loads, one of 20 A at 30° lagging and another of 40 A at 60° lagging. What current in amperes should flow in the capacitor so that the circuit will have a unity power factor? A. 35.8 A C. 28.8 A B. 44.6 A D. 50.2 A 387. A coil of 10 Ω resistance and 0.1 H inductance is connected in parallel with a capacitor of unknown capacitance. If the total impedance of the combination is 100 Ω, determine the value of the capacitance. A. 50 μF C. 150 μF B. 100 μF D. 200 μF
381. Ten impedances connected in parallel draw the following individual current: , , , , , , , , , . What is the effective value of the total current? A. 48.444 A C. 25.345 A B. 34.255 A D. 84.389 A
388. An impedance equal to Ω is connected across a 220 V source. What should be the value of the second impedance in parallel with the first, if the total power delivered to the circuit is to be 16.5 kW and the overall power factor is to be unity? A. Ω C. Ω B. Ω D. Ω
382. Ten impedances connected in parallel draw the following individual current: , , , , , , , , , .What is the equivalent impedance that could replace the impedances if the source voltage is 100 sin 150t V? A. Ω C. Ω B. Ω D. Ω
389. An inductive reactance of 8 ohms is connected in parallel with a capacitive reactance of 18 ohms. This combination is then connected in series with a variable resistance. For what value of resistance will the power factor be 0.5? A. 8.314 Ω C. 13.81 Ω B. 3.318 Ω D. 1.381 Ω
390. Two impedances Z1 = 3 + j4 and Z2 = 5 – j8.66 ohms respectively are connected in parallel. If the combination is connected across a 240 V AC source, how much is the total current? A. 44.4 A C. 40.6 A B. 42.1 A D. 39.9 A
D.
398. The power taken by the circuit shown in Fig. 13.1 is IT
391. A resistance of 20 ohms and an unknown capacitance are connected in parallel across a 110 V, variable frequency AC source. When the frequency is 60 Hz, the current drawn by the circuit is 6 A. At what frequency will the current drawn fall to 5.8 A? A. 42. 33 Hz C. 46.02 Hz B. 50.12 Hz D. 44.18 Hz 392. Two parallel branches have admittances 0.3 + j0.4 and 0.2 – j0.25 S, respectively. If the current in the first branch is 10 A, determine the total current supplied to the parallel combination. A. 10.44 A C. 15.32 A B. 12.10 A D. 11.24 A
none of the above
Fig. 13.1
A. B.
470 W 1920 W
C. D.
396. Domestic appliances are connected in parallel across ac mains because A. it is a simple arrangement B. operation of each appliance becomes independent of each other C. appliances have same current ratings D. this arrangement occupies less space 397. When a parallel ac circuit contains a number of branches, then it is convenient to solve the circuit by A. phasor diagram B. phasor algebra C. equivalent impedance method
1200 W none of these
399. The active component of line current in Fig. 13.1 is IT
395. The impedances of two parallel branches of a circuit are (10 + j10) and (10 – j10) respectively. The impedance of the parallel combination is A. 20 + j0 C. 5 – j5 B. 10 + j0 D. 0 – j20
R= 30 Ω
XL = 30 Ω
240 V
393. An inductive reactance of 3 ohms is connected in parallel with a capacitive reactance of 4 ohms. If the combination is connected in series with a 4 ohm resistance, solve for the power factor of the whole combination. A. 0.333 C. 0.567 B. 0.409 D. 0.316 394. An R-L circuit has Z = (6 + j8) ohm. Its susceptance is ____ siemens. A. 0.06 C. 0.1 B. 0.08 D. -0.08
IR
IL
IR
IL
R= 30 Ω
XL = 30 Ω
240 V
Fig. 13.1
A. B.
8A 4A
C. D.
5.3 A none of these
400. The power factor of the circuit shown in Fig. 13.1 is IT 240 V
IR
IL
R= 30 Ω
XL = 30 Ω
Fig. 13.1
A. B.
0.707 lagging 0.5 lagging
C. D.
0.866 lagging none of these
401. The total line current drawn by the circuit shown in Fig. 13.1 is
IT
IT
IR
IL
R= 30 Ω
XL = 30 Ω
240 V
IL
XL = 40 Ω
240 V
√ A 16 A
C. D.
√ A none of these
402. The power consumed in the circuit shown in Fig. 13.2 is IT
A. B.
13 A 6A
C. D.
IR XL = 40 Ω
240 V
XC = 80 Ω
IC XC = 80 Ω
R= 60 Ω
5A none of these
405. The power factor of the circuit shown in Fig. 13.2 is IT
IL
IC R= 60 Ω
Fig. 13.2
Fig. 13.1
A. B.
IR
IL
IR XL = 40 Ω
240 V
IC R= 60 Ω
XC = 80 Ω
Fig. 13.2 Fig. 13.2
A. B.
480 W 960 W
C. D.
1200 W none of these
403. The active component of line current in Fig. 13.2 is IT 240 V
A. B.
0.8 0.5
C. D.
406. The impedance of the circuit shown in Fig. 13.2 is IT
IL
IR XL = 40 Ω
IC XC = 80 Ω
R= 60 Ω
0.707 none of these
IL
240 V
IR XL = 40 Ω
IC R= 60 Ω
XC = 80 Ω
Fig. 13.2 Fig. 13.2
A. B.
6A 3A
C. D.
13 A 4A
404. The line current drawn by the circuit shown in Fig. 13.2 is
A. B.
180 ohms 24 ohms
407. The circuit shown in Fig. 13.2 is
C. D.
48 ohms none of these
IT
IR
IL
XL = 40 Ω
240 V
IT
IC R= 60 Ω
I2 R1 = 4 Ω
XC = 80 Ω
120 V
R2 = 3 Ω
I1 XC = 4 Ω
XL = 3 Ω Fig. 13.2
A. B.
resistive capacitive
C. D.
Fig. 13.3
inductive in resonance
408. If in Fig. 13.2, XL is made equal to XC, the line current will be IT 240 V
IR
IL
XL = 40 Ω
A. B.
24 A 70 A
C. D.
411. The circuit shown in Fig. 13.3 is
IC
IT
XC = 80 Ω
R= 60 Ω
48 A 30 A
I2 R1 = 4 Ω
120 V
R2 = 3 Ω
I1 XC = 4 Ω
XL = 3 Ω Fig. 13.2
A. B.
10 A 6A
C. D.
4A none of these
Fig. 13.3
409. The power consumed in the circuit shown in Fig. 13.3 is IT 120 V
capacitive inductive
R2 = 3 Ω
resistive in resonance
IT
I1 XL = 3 Ω
C. D.
412. If the source frequency of Fig. 13.4 is low, then
I2 R1 = 4 Ω
A. B.
R
XC = 4 Ω
V
I1
I2
C
L
Fig. 13.3
A. B.
8400 W 3600 W
C. D.
4000 W none of these
410. If the circuit shown in Fig. 13.3 is connected to 120 V dc, the current drawn by the circuit is
Fig. 13.4
A. B. C. D.
coil takes a high lagging current coil takes a low lagging current capacitor takes a leading current circuit offers high impedance
413. If the source frequency of Fig. 13.4 is high, then
R=6Ω IT R V
I1
XL = 8 Ω
I2
C
L
Fig. 13.6
A. B.
Fig. 13.4
A. B. C. D.
coil takes a high lagging current capacitor takes a high leading current capacitor takes a low leading current circuit offers high impedance
10 S 14 S
C. D.
418. The conductance of the circuit shown in Fig. 13.6 is R=6Ω
414. The circuit shown in Fig. 13.5 is
XL = 8 Ω IT
100 V
R= 3Ω
I1
I2 XL = 4Ω
XC = 4Ω
Fig. 13.5
A. B.
in resonance resistive
C. D.
inductive capacitive
Fig. 13.6
A. B.
14 S 0.6 S
C. D.
100 V
R=6Ω XL = 8 Ω
R= 3Ω
I1
Fig. 13.6 I2
XL = 4Ω
XC = 4Ω
1200 W 2400 W
A. B.
8S 0.8 S
C. D.
0.08 S none of these
420. The circuit shown in Fig. 13.7 is
Fig. 13.5
A. B.
0.06 S none of these
419. The inductive susceptance of the circuit shown in Fig. 13.6 is
415. The circuit shown in Fig. 13.5 will consume a power of IT
0.1 S none of these
C. D.
500 W none of these
416. If the admittance of a parallel ac circuit is increased, the circuit current A. remains constant C. is increased B. is decreased D. none of these
100 V
417. The admittance of the circuit shown in Fig. 13.6 is
G= 0.01 S
-B
Fig. 13.7
A.
resistive
C.
capacitive
inductive
D.
none of these
421. The power loss in the circuit shown in Fig. 13.7 is
100 V
G= 0.01 S
-B
Fig. 13.7
A. B.
100 W 10,000 W
C. D.
10 W none of these
422. The conductance and susceptance components of admittance are A. series elements B. parallel elements C. series-parallel elements D. none of the above 423. The impedance of a circuit is 10 ohms. If the inductive susceptance is 1 siemen, then inductive reactance of the circuit is A. 10 ohms C. 100 ohms B. 1 ohm D. none of these 424. The conductance and inductive susceptance of a circuit have the same magnitude. The power factor of the circuit is A. 1 C. 0.707 B. 0.5 D. 0.866 425. The admittance of a circuit is (0.1 + j0.8) S. The circuit is A. resistive C. inductive B. capacitive D. none of these 426. In a parallel ac circuit, power loss is due to A. conductance alone B. susceptance alone C. both conductance and susceptance D. none of the above 427. The admittance of a parallel circuit is S. The circuit is A. inductive C. resistive B. capacitive D. none of these
428. A circuit have an impedance of (1 – j2) ohms. The susceptance of the circuit is A. 0.1 S C. 0.4 S B. 0.2 S D. none of these 429. A circuit has admittance of 0.1 S and conductance of 0.08 S. The power factor of the circuit is A. 0.1 C. 0.08 B. 0.8 D. none of these 430. When an sinusoidal voltage is applied across R-L parallel circuit so that R = XL the phase angle will be A. 45° lagging C. 90° lagging B. 45° leading D. 90° leading 431. In a parallel R-L circuit if IR is the current in resistor and IL is the current in the inductor, then A. IR lags IL by 90° C. IL leads IR by 270° B. IR leads IL by 270° D. IL lags IR by 90° 432. The current read by the ammeter A in the ac circuit shown is the given figure is A
1A
A. B.
9A 5A
C. D.
3A
5A
3A 1A
433. In the given figure, the admittance values of the elements in siemens are Y R = 0.5 + j0, YL = 0 – j1.5 and YC = 0 + j0.3 respectively. The value of I as a phasor when the voltage E across the elements is √ V is YR
I
A. B.
1.5 + j-.5 5 – j18
C. D.
YL
YC
E 100 V
B.
0.5 + j1.8 5 – j12
434. For the circuit shown in the figure, how much the voltage across the inductor leads the voltage across the capacitor?
L E ω = 2 rad/s
0.5 F
V 20
17/6 Ω
3Ω
1Ω
-j4 Ω
A. B.
45° 90°
C. D.
135° 180°
435. In the circuit shown in the figure, v = cos 2t, Z2 = 1 + j. C1 is chosen so that i = cos 2t. The value of C1 is I VS
C1
A. B.
6 + j0 Ω 7 + j0 Ω
C. D.
3Ω
j4 Ω
0 + j8 Ω 6 + j8 Ω
439. A resistance of 40 ohms and an inductive reactor of 30 ohms are joined in parallel to a 120 volts supply as shown in the figure. The power factor of the circuit is
Z2
I1
R = 40 Ω
I2
X = 30 Ω
I
A. B.
2F 1F
C. D.
0.5 F 0.25 F
120 volts
436. For the given ac circuit, what is the value of I? v(t) = 120 sin ωt
I
A. B.
A. B.
60
440. In a parallel RC circuit, A. IC lags IR by 90° B. IR and IC are in phase
C. D.
2-j 0 + j0
437. For the network shown in the given figure Z(0) = 3 Ω and Z(∞) = 2 Ω. The values of R1 and R2 will respectively be 1Ω
R1
A. B.
2 Ω, 1 Ω 1 Ω, 2 Ω
C. D.
0.8 unity
C. D.
IC leads IR by 90° IR leads IC by 90°
-j120 j60
1+j 1 + j0
Z(s)
0.6 0.7
1F
C. D.
R2
3 Ω, 2 Ω 2 Ω, 3 Ω
438. The total impedance Z(jω) of the circuit shown is
1F
441. In a parallel RC circuit, A. VC and IR are in phase B. VC and IC are in phase C. IC and IR are in phase D. VC and IR are 90° out of phase 442. When the frequency of the applied voltage increases in a parallel RC circuit A. the phase angle, θT, increases B. ZEQ increases C. ZEQ decreases D. both A and C 443. In a parallel RL circuit, A. iL lags iR by 90° B. iL leads iR by 90°
C. D.
iL and iR are in phase iR lags iL by 90°
444. In a parallel RL circuit, A. VT and IL are in phase B. IL and IR are in phase C. VT and IR are in phase D. VT and IR are 90° out of phase 445. When the frequency of the applied voltage decreases in a parallel RL circuit A. the phase angle, θI, becomes less negative B. ZEQ increases C. ZEQ decreases D. both A and B 446. When the frequency of the applied voltage increases in a parallel RL circuit A. θZ increases C. ZT increases B. ZT decreases D. both A and C 447. In an ac circuit with only parallel inductors A. IT lags VT by 90° C. VT and IT are in phase B. VT lags IT by 90° D. none of the above 448. In a parallel ac circuit with XL and XC A. IL and IC are 90° out of phase B. IL and IC are in phase C. IL and IC are 180° out of phase D. XL and XC are 90° out of phase D. RESONANCE 449. REE Board Exam October 2000 A series circuit consists of a 20-ohm resistance, a 150 mH inductance and an unknown capacitance. The circuit is supplied with a voltage v = 100 sin 377t. Find the value of capacitance at resonance. A. 42 μF C. 34.65 μF B. 47 μF D. 72.57 μF 450. REE Board Exam April 2001 A 5 mH pure inductance is connected in parallel with one microfarad capacitor. What frequency will the circuit be antiresonance? A. 250 Hz C. 60 Hz B. 2250 Hz D. 100 Hz 451. EE Board Exam April 1993
Capacitor of 30-microfarad capacitance is in series with a coil across an 8,000 cycle supply. What inductance is required for resonance? A. 13.34 μH C. 13.19 μH B. 10.45 μH D. 12.55 μH 452. REE Board Exam October 1998 -9 One leg of a radio tuned circuit has a capacitance of 1 x 10 F. It is tuned at 200 kHz. What is the inductance of the other leg in Henry? -4 -5 A. 6.33 x 10 C. 8.25 x 10 -3 -3 B. 20 x 10 D. 120 x 10 453. EE Board Exam April 1988 A loud speaker whose inductance through a condenser of 2 μF combination be resonant? A. 110 Hz C. B. 108 Hz D.
is 1.15 Henry is coupled to a power tube capacity. To what frequency will the 105 Hz 100 Hz
454. REE Board Exam April 1995 What capacitance must be placed in series with an inductance of 0.05 Henry so that at 100 Hz, the impedance becomes equal to the ohmic resistance? A. 50.7 μF C. 70.7 μF B. 35.5 μF D. 87.0 μF 455. EE Board Exam April 1989 A coil has a resistance of 50 ohms and a reactance of 100 ohms, is shunted by a capacitor, which has practically no losses in order that the voltage across the coil be in phase with the total current supplied to the parallel combination. What is the impedance of the parallel combination under the given condition? A. 250 ohms C. 230 ohms B. 200 ohms D. 220 ohms 456. EE Board Exam April 1983 A non-inductive resistor R is connected in parallel with an inductive reactance of 10 ohms. The combination is then connected in series with a capacitive reactance of 5 ohms. Solve for R at which the power factor of the given circuit would be unity. A. 10 Ω C. 13 Ω B. 12 Ω D. 11 Ω 457. EE Board Exam October 1982 Two impedances Z1 = 15 + j20 and Z2 = 5 – jXC are connected in parallel. Solve for the values of XC so that the total current drawn by the combination will be in phase with any supply voltage V.
A. B.
28.54 30.43
C. D.
33.12 29.55
458. EE Board Exam April 1985 A resistance of 5 ohms is connected in series with a capacitor of 442.1 μF. The combination is then connected in parallel with an inductance of 21.22 mH. Solve for the frequency of the impressed voltage with which the inductive reactance is equal to the capacitive reactance in magnitude. A. 50 Hz C. 52 Hz B. 51 Hz D. none of these 459. EE Board Exam April 1989 A coil has a resistance of 50 ohms and a reactance of 100 ohms, is shunted by a capacitor, which has practically no losses. What must be the reactance of the capacitor in order that the voltage across the coil is in phase with the total current supplied to the parallel combination? A. 120 ohms C. 125 ohms B. 127 ohms D. 132 ohms 460. EE Board Exam April 1982 Three impedances Za, Zb and Zc are connected in parallel. If at 60 Hz, Za = j8, Zb = -j2 and Zc = 5 ohms, Solve for the frequency at resonance. A. 30 Hz C. 36 Hz B. 34 Hz D. 28 Hz 461. EE Board Exam April 1981 A resistor R is connected in parallel with a 20-ohm inductive reactive. The combination is then connected in series with a 5-ohm capacitive reactance. Solve the value of R at which the power factor of the resultant impedance is unity. A. 10.05 ohms C. 11.55 ohms B. 9.15 ohms D. 10.73 ohms
464. EE Board Exam October 1998 In a series resonant RLC circuit, all of the following statements are correct EXCEPT one. Which one is this? A. The resonant frequency is dependent on the resistance of the circuit. B. The phase angle between the voltage and the current vectors is zero. C. The impedance is a minimum. D. The current is a maximum. 465. EE Board Exam April 1994, October 1993 The current in RLC series circuit at resonance is A. maximum C. minimum B. zero D. infinity 466. ECE Board Exam April 2001 Ignoring the capacitive effects, what is the impedance of a 100 mH coil (with an internal resistance of 45 ohms) in parallel with 4,700 ohms resistor at a frequency of 500 Hz? A. 317 ohms C. 5014 ohms B. 237 0hms D. 314 ohms 467. ECE Board Exam November 1996 ____ frequency is reached when the capacitive and inductive reactance in a tuned circuit are equal. A. zero C. infinite B. pulsating D. resonant 468. ECE Board Exam November 1998 Find the Q of a circuit when the resonant frequency is 4.468 MHz, the inductance is 47 microhenry and the resistance is 180 ohms parallel. A. 0.136 C. 0.00735 B. 13.30 D. 7.35
462. EE Board Exam October 1998 A coil has a resistance of 50 ohms and a reactance of 70 ohms. A capacitor is connected in parallel to produce resonance. The source voltage is 120 V. What is the power drawn by the circuit? A. 162 W C. 132 W B. 97 W D. 52 W
469. ECE Board Exam November 2000 In an “IDEAL” resonant circuit, what is the relationship between the current and the impedance? A. current high, impedance low B. current low, impedance low C. current low, impedance high D. current high, impedance high
463. EE Board Exam April 1995 A coil is supplied with 200 volts and takes a current (rms) of 2 amperes at 0.707 lagging. The quality factor (Q) of the coil is A. 25 C. 10 B. 1 D. 100
470. ECE Board Exam November 1997 What condition does resonance occurs in an electrical circuit? A. When the power factor is at minimum
B. C. D.
When the square root of the sum of the capacitive and inductive reactances is to the resonant frequency When the inductive and capacitive reactances are equal none of the above
471. ECE Board Exam November 2001 What is the relationship between frequency and the value of XC? A. frequency has no effect B. XC varies directly with frequency C. XC varies inversely with frequency D. XC varies indirectly with frequency 472. ECE Board Exam April 2001 When is the line current minimum in a parallel LC circuit? A. at the broadcast frequency B. at the circuit frequency C. at the resonant frequency D. at the highest frequency 473. ECE Board Exam November 1999 Find the half-power bandwidth of a parallel resonant circuit which has a resonant frequency of 7.1 MHz and Q of 150. A. 16.5 kHz C. 21.1 kHz B. 211 kHz D. 47.3 kHz 474. ECE Board Exam November 1997 It is the term for the phenomena which occurs in an electrical circuit when the inductive reactance balances with the capacitive reactance. A. reactive equilibrium C. reactive quiescence B. resonance D. high Q 475. ECE Board Exam April 1998 What is the resonant frequency of a circuit when L of 25 microhenrys and C of 10 picofarads are in parallel? A. 68.7 kHz C. 68.7 MHz B. 10.1 kHz D. 10.1 MHz
If you need an LC circuit to be resonant at 2,500 Hz and use a 150 mH coil, what should the capacitance value be? A. 0.015 μF C. 27 μF B. 0.15 μF D. 0.027 μF 478. ECE Board Exam April 1999 What is the resonant frequency of a circuit when L is 40 microhenrys and C is 6 picofarads are in series? A. 6.63 MHz C. 6.63 kHz B. 10.3 MHZ D. 10.3 kHz 479. ECE Board Exam April 1998 What is the resonant frequency of a circuit when L of 3 microhenrys and C of 40 picofarads are in series? A. 14.5 MHz C. 1.33 kHz B. 1.33 MHz D. 14.5 kHz 480. ECE Board Exam November 2001 ____ refers to reactive power. A. power consumed in circuit Q B. power consumed in wire resistance in an inductor C. wattles, non-productive power D. power lost because of capacitor leakage 481. ECE Board Exam November 1998 How do you call the nature of a circuit during series resonance? A. unstable C. resistive B. capacitive D. inductive 482. ECE Board Exam April 1999 What is the resonant frequency of a circuit when L is 200 microhenrys and C is 10 picofarads are in series? A. 7.96 MHz C. 3.56 MHz B. 6 MHz D. 7.96 kHz
476. ECE March 1996 What is the effect in terms of bandwidth when the Q of a single-tuned stage is doubled? A. halved C. doubled B. the same D. four times
483. ECE Board Exam April 2000 In a series resonant LC circuit, what is the impedance at resonant frequency? A. Infinity B. Determined solely by the dc resistance C. The maximum impedance value D. Zero
477. ECE Board Exam November 1999
484. ECE Board Exam April 1999
What is the characteristic of the current flow in a parallel R-L-C circuit at resonance? A. The current circulating in the parallel elements is dc B. The current circulating in the parallel elements is zero C. The current circulating in the parallel elements is at a maximum D. The current circulating in the parallel elements is at a minimum 485. ECE Board Exam March 1996 What is the responsible for the phenomenon when voltages across reactances in series can often be larger than the voltage applied to them? A. Capacitance C. Conductance B. Resistance D. Resonance 486. ECE Board Exam March 1996 Term used for resonance in an electrical circuit. A. The frequency at which power factor is at a minimum B. The frequency at which capacitive reactance equals inductive reactances C. The highest frequency that will pass current D. The lowest frequency that will pass current 487. ECE Board Exam November 1998 Ignoring any effects of dc resistance, what is the total reactance of a 250 mH coil in series with a 4.7 F capacitor at a signal frequency of 1000 Hz? A. 1604 C. 1536 B. 35 D. 1570 488. ECE Board Exam November 1996 The _____ the Q of a circuit, the narrower is its bandwidth. A. Lower C. Higher B. Broader D. Selective
Find the half-power bandwidth of a parallel resonant circuit which has a resonant frequency of 3.6 MHz and a Q of 218. A. 58.7 kHz C. 16.5 kHz B. 606 kHz D. 47.3 kHz 492. ECE Board Exam November 1998 What is the resonant frequency of a circuit when L is 3 microhenrys and C is 40 picofarads are in parallel? A. 14.5 kHz C. 14.5 MHz B. 13.1 kHz D. 13.1 MHz 493. ECE Board Exam November 1998 What is the resonant frequency of a circuit when L is 15 microhenry and C is 5 picofarads are in series? A. 2.12 kHz C. 18.4 kHz B. 18.4 MHz D. 2.12 MHz 494. ECE Board Exam November 1998 What is the resonant frequency of a circuit when L is 2 microhenry and C is 15 picofarads are in series? A. 29.1 MHz C. 29.1 kHz B. 5.31 MHz D. 5.31 kHz 495. ECE Board Exam April 1998 Characteristic of the current flow in a series R-L-C circuit at resonance A. it is zero B. it is dc C. it is at a maximum D. it is at a minimum
489. ECE Board Exam March 1996 Find the half-power bandwidth of a resonant circuit which has a resonant frequency of 1.8 MHz and a Q of 95. A. 58.7 kHz C. 189 Hz B. 18.9 kHz D. 1.89 kHz
496. ECE Board Exam April 2001 What is the term for the number of times per second that a tank circuit energy is stored in the inductor of capacitor? A. Non-resonant frequency B. Broadcast frequency C. Circuit frequency D. Resonant frequency
490. ECE Board Exam November 1998 What is the resonant frequency of a circuit when L is 5 microhenrys and C is 9 picofarads are in series? A. 23.7 kHz C. 23.7 MHz B. 3.54 kHz D. 3.54 MHz
497. ECE Board Exam November 1995 An LC circuit resonates at 2000 kHz, and has a Q of 100. Find the lower and upper cut-off frequencies. A. 1950 kHz, 2050 kHz C. 1980 kHz, 2020 kHz B. 1990 kHz, 2010 kHz D. 1900 kHz, 2100 kHz
491. ECE Board Exam April 1998
498. ECE Board Exam November 1998
What is the resonant frequency of a circuit when L is 50 microhenrys and C is 10 picofarads are in parallel? A. 3.18 kHz C. 7.12 MHz B. 3.18 MHz D. 7.12 kHz 499. ECE Board Exam November 1999 What is the cause of a minimum Q on a single-tuned LC circuit? A. Decreased shunt resistor B. Decreased capacitance C. Increased shunt resistor D. Decreased series resistor 500. ECE Board Exam November 1998 ____ is another term for quality factor or Q of the resonant circuit. A. Noise factor C. White noise B. Noise figure D. Figure of merit 501. ECE Board Exam November 2000 What is the biggest advantage of using crystals in resonant circuits? A. less fragile B. cost C. size D. greater accuracy and stability 502. ECE Board Exam April 2001 What is the impedance of a crystal at its resonant frequency when it is used in the parallel mode? A. 70 percent C. minimum B. 50 percent D. maximum 503. ECE Board Exam April 1998 _____ is a parallel LC circuit. A. Hartley circuit B. Static circuit C. Tank circuit D. Parallel resisting circuit 504. There will ____ be a frequency, called the ____ frequency at which ____. A. sometimes, natural; XL = XC B. always, natural; R = 0 C. always, resonant; XL = XC D. sometimes, resonant; R = 0 505. The formula for the resonant frequency is f = ____. A. √ C. √
B.
√
D.
√
506. For a series RLC circuit, a circuit at resonance the current amplitude is ____ for a fixed voltage amplitude and the power factor is ____. A. minimum, zero C. maximum, zero B. minimum, unity D. maximum, unity 507. In an RLC circuit, the impedance at resonance is A. maximum C. infinity B. minimum D. zero 508. The current in RLC series circuit, i.e., at resonance is A. maximum C. infinity B. minimum D. zero 509. In RLC circuits, the current at resonance is A. the maximum in series circuit and minimum in parallel circuit B. maximum in parallel circuit and minimum in series circuit C. maximum in both the circuits D. minimum in both the circuits 510. A series resonant circuit is capacitive at f = 100 Hz. The circuit will be inductive somewhere at A. f = 100 Hz B. f > 100 Hz C. f = 100 Hz by increasing the value of the resistance D. none of these 511. At a frequency less than the resonant frequency A. series circuit is capacitive and parallel circuit is inductive B. series circuit is inductive and parallel circuit is capacitive C. both circuits are inductive D. both circuits are capacitive 512. In series as well as parallel resonant circuits, increasing the value of resistance would lead to A. increase in the bandwidth of both the circuits B. decrease in the bandwidth of both the circuits C. increase in bandwidth in series circuit and decrease in parallel circuit D. decrease in bandwidth in series circuit and increase in parallel circuit 513. The value of current at resonance in a series RLC circuit is affected by the value of A. R C. C B. L D. all of these
514. In resonant circuits, the power factor at resonance is A. zero C. 1 B. 0.5 D. 0.707
A.
C.
B.
D.
515. Which of the following statements is true for a series RLC circuit tuned at resonant frequency? A. the voltage across C > applied voltage B. the voltage across L > applied voltage C. the voltage across L and C > applied voltage D. the voltage across L and C = applied voltage
520. To a series RLC circuit, a voltage of 10 V is applied. If Q of the coil at resonant frequency is 20, the voltage across the inductor at resonant frequency will be A. 200 V C. 75 V B. 100 V D. 50 V
516. At anti-resonance for the given circuit, the frequency is given by
521. The currents flowing in L and C at parallel resonance are A. zero C. infinite B. equal D. different
A. B.
√
√
√
√
R1
R2
L
C
C. D.
522. The exact natural frequency of free oscillation in an oscillatory circuit with capacitance of 0.055 μF, inductance 2 μH and resistance 1 ohm will be A. 478 kHz C. 272 kHz B. 337 kHz D. 192 kHz √ √
√ √
517. The frequency at which maximum voltage occurs the inductance in RLC series circuits is A. B.
√ √
C. √
D. √
518. The frequency at which maximum voltage occurs across the capacitance in RLC series circuits is A.
√
B.
C. √
D. √
√
519. If f1 and f2 are half power frequencies and f0 be resonance frequency, the selectivity of RLC series circuit is given by
523. A coil with large distributed capacitance has a A. low resistance B. low Q C. low resonant frequency D. high resonant frequency 524. In a series R-L-C circuit, resonance occurs when A. R = XL - XC C. XL = 10 XC or more B. XL = XC D. net X > R 525. The p.f. of a series R-L-C circuit at its half-power point is A. unity C. leading B. lagging D. either B and C 526. A resonance curve for a series circuit is a plot of frequency versus ____. A. voltage C. current B. impedance D. reactance 527. At half-power points of a resonance curve, the current is ____ times the maximum current. A. 2 C. √ B. D. 1/2 √ 528. Higher the Q of a series circuit, A. greater its bandwidth
B. C. D.
sharper its resonance broader its resonance curve narrower its pass band
529. As the Q-factor of a circuit ____, its selectivity becomes ____. A. increases, better C. decreases, better B. increases, worse D. decreases, narrower 530. An R-L-C circuit has a resonance frequency of 160 kHz and a Q-factor of 100. Its bandwidth is A. 1.6 kHz C. 16 MHz B. 0.625 kHz D. none of the above 531. In a parallel resonant circuit there is practically no difference between the condition for unity power factor and the condition for maximum impedance so long as Q is A. very small of the order of 5 B. small of the order of 20 C. large of the order of 1000 D. none of these 532. A parallel AC circuit in resonance will A. act like a resistor of low value B. have a high impedance C. have current in each section equal to the line current D. have a high voltage developed across each inductive and capacitive section 533. A parallel resonant circuit can be used A. to amplify certain frequencies B. to reject a small band of frequencies C. as a high impedance D. both B and C 534. The Q-factor of a 2-branched parallel circuit is given by the ratio A. Ic/IL C. I/IL B. I/Ic D. L/C 535. Like a resonant R-L-C, a parallel resonant circuit also A. has a power factor of unity B. offers minimum impedance C. draws maximum current D. magnifies current
536. At resonant frequency an R-L-C circuit draws maximum current due to the reason that A. the difference between capacitive reactance and inductive reactance B. C. D.
the impedance is more than resistance the voltage across the capacitor equals the applied voltage the power factor is less than unity
537. Consider the following statements with respect to a series R-L-C circuit under resonance condition: 1. All the applied voltage appears across R. 2. There is no voltage across either L or C. 3. The voltage across L and C is equal and equal to their maximum values. Of these statement A. 1 alone is correct C. 1 and 3 are correct B. 2 alone is correct D. 1 and 2 are correct 538. A series R-L-C circuit will have unity power factor if operated at a frequency of 2 A. 1/LC C. 1/ω LC B. D. √ √ 539. A series resonant circuit implies A. zero pf and maximum current B. unity pf and maximum current C. unity pf and minimum current D. zero pf and minimum current 540. Consider the following statements: In a network of resonance: 1. the admittance is maximum 2. the power factor is unity irrespective of the network 3. the Q of a series RLC resonant circuit is independent of R Of these statements A. 1 and 3 are correct C. 2 and 3 are correct B. 1 and 2 are correct D. 1 alone is correct 541. A circuit with a resistor, inductor and capacitor in series is resonant at f 0 Hz. If all the component values are now doubled the new resonant frequency is A. 2f0 C. f0/4 B. still f0 D. f0/2 542. If the resonant frequency of the circuit shown in Fig. 1 is 1 kHz, the resonant frequency of the circuit shown in Fig. 2 will be
100 Ω
L
547. The resonant frequency of the given series circuit is
C
M=1H Fig. 1 R
L
2H
C L
A. B.
4 kHz 2 kHz
C. D.
0.5 kHz 0.25 kHz
543. In the circuit shown in the given figure, the magnitude of V L and VC are twice that of VR. The inductance of the coil is VR
VL
VC
5Ω
L
C
50 V
A. B.
2.14 mH 5.30 mH
√
2H
Hz
C.
Hz
D.
√ √
Hz Hz
C
Fig. 2
A. B.
√
2F
C. D.
31.8 mH 1.32 mH
544. In a series RLC circuit at resonance, the magnitude of voltage developed across the capacitor A. is always zero B. can never be greater than the input voltage C. can be greater than the input voltage however it is 90° out of phase with the input voltage D. can be greater than the input voltage and is in phase with the input voltage 545. A coil having a resistance of 5 Ω and inductance of 0.1 H is connected in series with a capacitor of capacitance 50 μF. A constant alternating voltage of 200 V is applied to the circuit. The voltage across the coil at resonance is A. 200 volts C. 1,800 volts B. 1,788 volts D. 2,000 volts 546. A series R-L-C circuit, excited by a 100 V variable frequency supply, has a resistance of 10 Ω and an inductive reactance of 50 Ω at 100 Hz. If the resonance frequency is 500 Hz, what is the voltage across the capacitor at resonance? A. 100 V C. 2,500 V B. 500 V D. 5,000 V
548. In a series R-L-C circuit, the maximum voltage across the capacitor occurs at a frequency A. double the resonant frequency B. equal to the resonant frequency C. √ times the resonant frequency D. below the resonant frequency 549. For a series RLC circuit, the power factor at the lower power frequency is A. 0.5 lagging C. unity B. 0.5 leading D. 0.707 leading 550. Q-factor of a series RLC circuit possessing resonant frequency of 10 Hz and bandwidth of 5 Hz is A. 0.5 C. 2.5 B. 2 D. 50 551. The quality factor of RLC circuit will increase if A. R decreases B. R increases C. voltage increases D. voltage decreases 552. When Q-factor of a circuit is high, then A. power factor of the circuit is high B. impedance of the circuit is high C. bandwidth is large D. none of these 553. Consider the following statements regarding the frequency response curve of a series RLC circuit: 1. At half-power frequencies, the current in the circuit is one half of the current at resonant frequencies 2. At half-power frequencies, the power factor angle of the circuit is 45° 3. At resonant frequency, the power factor angle of the circuit is 90° 4. Maximum power occurs at resonant frequency
2 and 4 are correct 1 and 4 are correct
10 Ω
554. An RLC series circuit has f1 and f2 as the half power frequencies and f0 as the resonant frequency. The Q-factor of the circuit is given by: A. C. A. B.
D.
555. Resonant frequency fr of a series RLC circuit is related to half power frequencies f1 and f2 as A. C. B.
√
D.
√
√
556. A series RLC circuit has R = 50 Ω, L = 100 μH and C = 1 μF. The lower half power frequency of the circuit is A. 30.55 kHz C. 51.92 kHz B. 3.055 kHz D. 1.92 kHz 557. For a series RLC resonant circuit, what is the total reactance at the lower half power frequency? A. √ C. R B. √ D. -R 558. A series RLC circuit when excited by a 10 V sinusoidal voltage source of variable frequency, exhibits resonance at 100 Hz and has a 3 dB bandwidth of 5 Hz. The voltage across the inductor L at resonance is A. 10 V C. √ B. D. 200 V √ V 559. An RLC resonant circuit has a resonant frequency of 1.5 MHz and a bandwidth of 10 kHz. If C = 150 pF, then the effective resistance of the circuit will be A. 29.5 Ω C. 9.4 Ω B. 14.75 Ω D. 4.7 Ω 560. The following circuit resonates at
1F +
all frequencies 0.5 rad/s
C. D.
-
5 rad/s 1 rad/s
561. A choke coil of inductance L and series resistance R is shunted by a capacitor. The dynamic impedance of the resonant circuit would be A. R/(LC) C. L/(RC) B. C/(RL) D. 1/(RLC) 562. For the following circuit, the current source is sinusoidal with frequency equal to the resonant frequency of the circuit. What is the value of current through resistor?
I
A. B.
0 0.11
0.1 H
C. D.
10 Ω
0.1 F
1 10.1
563. In the given circuit, at resonance IR amperes is equal to
0.5 H
B.
1F
4H
C. D.
5A
A. B.
0A 10 A
C. D.
R IR
50 μF
Of these statements A. 1, 2 and 4 are correct B. 1, 2 and 3 are correct
5A 0.5 A
564. A circuit has two parallel branches. In one branch, R and L are connected in series while in the other R and C are connected in series. If , which √ of the following is not correct? A. The circuit is in resonance. B. The two branch currents are in quadrature. C. The circuit has an impedance independent of its frequency.
D.
The two branch currents are in phase.
565. A parallel circuit consists of two branches. One branch has R L and L connected in series and the other branch has RC and C connected in series. Consider the following statements: 1. The two branch currents will be in quadrature if RLRC = L/C. 2. The impedance of the whole circuit is independent of frequency, if RL = RC and √ . 3. The circuit is in resonance for all the frequencies if RL = RC. 4. The two branch currents will be in phase at √ . Which of the above statements are correct? A. 1 and 2 C. 1 and 3 B. 2 and 3 D. 3 and 4 566. The value of Z in given figure which is most appropriate to cause parallel resonance at 500 Hz is
5Ω 2H
A. B.
125 mH 304.2 μF
C. D.
Z
2 μF 0.05 μF
567. The value of the capacitance ‘C’ in the given ac circuit to make it a constant resistance circuit or for the supply current to be independent of its frequency is
A. B.
1/16 F 1/12 F
C. D.
4Ω
4Ω
1H
C
1/8 F 1/4 F
568. A coil takes apparent power and reactive power of 100 VA and 80 VAR, respectively. What is the Q factor of the coil? A. 1.33 C. 8 B. 10 D. 6
569. A 50 Ω resistance, a 30 Ω inductive reactance and a 25 Ω capacitive reactance are connected in series across a 100 V, 60 Hz supply. What will be its resonant frequency? A. 65.726 Hz C. 25 Hz B. 53 Hz D. 54.77 Hz 570. A coil having a Q factor of 5 is connected in series with an ideal capacitor across ac source of 60 V. Calculate the voltage across the capacitor at resonance. A. 150 V C. 12 V B. 300 V D. 65 V 571. A coil having an inductance of 50 mH and a resistance 10 Ω is connected in series with a 25 μF capacitor across a 200 V ac supply. Find the value of Q factor? A. 7.4 C. 3.54 B. 4.53 D. 4.47 572. The following data are given connected in parallel: XL = 15 the circuit be in resonance? A. 169 ohms B. 916 ohms
for a series RL and a series RC which are Ω, XC = 25 Ω, RC = 15 Ω. For value of RL will C. D.
16.9 ohms 91.6 ohms
573. A circuit consisting of a capacitor in series with a resistance of 10 ohms is connected in parallel with a coil having a reactance and resistance of 17.32 ohms and 10 ohms respectively. What is the reactance of the capacitor that will draw minimum current from a 230-V, 60 Hz supply? A. 17.32 Ω C. 6.78 Ω B. 10.32 Ω D. 22.18 Ω 574. Series circuit consists of a 20-ohm resistance, a 150 mH inductance and an unknown capacitance. The circuit is supplied with a voltage v = 100 sin 377t. Find the value of capacitance at resonance. A. 42 μF C. 47 μF B. 72.567 μF D. 34.65 μF 575. A coil having a resistance of 0.5 ohm and an inductance of 5.25 mH is connected in parallel with a capacitor across a 220 volt, 60 Hz source. Calculate the value of the capacitance at resonance. A. 125 microfarad C. 125 millifarad B. 1.25 microfarad D. 1.25 millifarad 576. The current in an RL and C parallel circuit at resonance is A. maximum C. minimum
B.
zero
D.
infinity
577. A circuit draws 25 A when connected across a source of frequency f1. Determine the current drawn by the same circuit at resonance if f 1 is half the resonant frequency. A. 12.5 A C. 35.35 A B. 17.68 A D. 50 A 578. A series RLC circuit is connected across a 120-V, 60 Hz source and draws a leading current of 5 A. Determine the voltage across the capacitor at resonance if R = 5 Ω and L = 25 mH. A. 47.12 V C. 236.6 V B. 164.5 V D. 422.6 V 579. The best definition of Q-factor of a coil is A. The ratio of its maximum energy stored to its energy dissipated per cycle B. Its power factor C. The reciprocal of its reactive factor D. The ratio of its resistance to its inductive reactance 580. A coil is to be wound with Q-factor of 8. A lamp rated 120 V, 480 W is connected in series with the coil and connected across 230 V, 60 Hz source. What is the impedance of the coil if the voltage across the lamp is maintained at 120 V? A. Ω C. Ω B. Ω D. Ω 581. An inductive coil having a resistance of 25 ohms and inductance of 0.2 H is connected in parallel with a 100 μF capacitor. Find the frequency at which the total current taken is in phase with the supply voltage. A. 35.6 Hz C. 29.5 Hz B. 46.5 Hz D. 52.9 Hz 582. The resonant frequency of an LC circuit is the frequency where A. XL = 0 Ω and XC = 0 Ω B. XL = XC C. XL and rS of the coil are equal D. XL and XC are in phase 583. The impedance of a series LC circuit at resonance is A. maximum C. minimum B. nearly infinite D. both A and B 584. The total line current, IT, of a parallel LC circuit at resonance is
A. B. C. D.
minimum maximum equal to IL and IC Q times larger than IL or IC
585. The current at resonance in a series LC circuit is A. zero B. minimum C. different in each component D. maximum 586. The impedance of a parallel LC circuit at resonance is A. zero B. maximum C. minimum D. equal to the rS of the coil 587. The phase angle of an LC circuit at resonance is A. 0° C. 180° B. 90° D. -90° 588. Below resonance, a series LC circuit appears A. inductive C. capacitive B. resistive D. none of the above 589. Above resonance, a parallel LC circuit appears A. inductive C. capacitive B. resistive D. none of the above 590. When either L or C is increased, the resonant frequency of an LC circuit A. decreases B. increases C. doesn’t change D. This is impossible to determine. 591. In a low Q parallel resonant circuit, when XL = XC A. IL = IC C. IC is less than IL B. IL is less than IC D. IL is more than IC 592. To double the resonant frequency of an LC circuit with a fixed value of L, the capacitance, C, must be A. doubled B. quadrupled C. reduced by one-half D. reduced by one-quarter
B. 593. A higher Q for a resonant frequency provides a A. dampened response curve B. wider bandwidth C. narrower bandwidth D. none of the above 594. The Q of a parallel resonant circuit can be lowered by A. placing a resistor in parallel with the tank B. adding more resistance in series with the coil C. decreasing the value of L or C D. both A and B 595. The ability of an LC circuit to supply complete sine waves when the input to the tank is only a pulse is called A. tuning C. anti-resonance B. the flywheel effect D. its Q 596. Which of the following can provide a higher Q? A. a higher L/C ratio B. a lower L/C ratio C. more resistance in series with the coil D. either B or C 597. A resonance curve for a series circuit is a plot of frequency versus ____. A. voltage C. current B. impedance D. reactance 598. At half-power points of a resonance curve, the current is ____ times the maximum current. A. 2 C. √ B. D. 1/2 √ 599. A parallel resonant circuit can be used A. to amplify certain frequencies B. to reject a small band of frequencies C. as a high impedance D. both B and C 600. As the Q-factor of a circuit ____, its selectivity becomes ____. A. increases, better C. decreases, better B. increases, worse D. decreases, narrower 601. The half – power frequency of, series RC circuit is A. 1/RC C. R/C
RC
D.
C/R
602. For the given parallel resonant circuit, match the following: A. I at resonance 1. W/R B. IL 2. In phase with voltage C. Dynamic impedance 3. L/CR 4. Lags the applied voltage ABC ABC A. 4 2 3 C. 4 2 1 B. 2 4 3 D. 2 4 1 603. To increase the Q- factor of an inductor, it can be with A. Thicker wire B. Thinner wire C. Longer wire D. Wire with heavy insulation 604. Given Z = jωL + 1/jωC; the magnitude of Z curve will be
A. B.
Figure a Figure b
C. D.
Figure c none of the above
605. The bandwidth of R.C series circuit is A. 1/RC C. ∞ B. RC D. none of the above 606. Consider the following statements: In a series RLC resonant circuit, the bandwidth is 1. directly proportional to resonant frequency 2. Inversely proportional to resonant frequency 3. directly proportional to quality factor 4. Inversely proportional to quality factor A. 2 & 3 are correct C. 1 & 3 are correct B. 2 & 4 are correct D. 1 & 4 are correct 607. An RLC parallel resonant circuit has a resonance frequency of 1.5 MHz and a bandwidth of 1 kHz. If C = 150 pF, then the effective resistance of the circuit will be A. 2.96 MΩ C. 9.5 Ω B. 14.75 Ω D. 4.7 Ω
608. The parallel RL circuit is having quality factor of Q1, when it is connected in series with R, the new quality factor Q2 will be A. Q2 > Q1 C. Q2 = Q1 B. Q2 < Q1 D. none of the above 609. In a series RLC circuit, as R increases 1. Bandwidth decreases 2. Bandwidth increases 3. Resonance frequency increases 4. Lower 3 dB decreases 5. Upper 3 dB increases A. 2, 4 & 5 are correct C. 2, 3, 4 are correct B. 1, 4 & 5 are correct D. none of the above
616. The half power frequency of series RL circuit is A. R/L C. 2R/L B. L/R D. 2L/R 617. In a series RLC circuit, the value of current at resonance is affected by the value of A. only L C. both L & C B. only C D. only R
610. In a series RLC circuit, given R = 10 Ω, L = 14 H, C = 1 F. Find damping ratio. A. 1.33 C. 0.5 B. 0.187 D. none of the above
618. In a series RLC circuit at resonance with Q = 10, and with applied voltage of 100 mV at resonance frequency voltage across capacitor is A. 100 mV C. 10 mV B. 1 volt D. 10 volts 619. Find fR in the circuit shown.
611. The power factor of parallel RLC circuit at W > Wo is A. < 1 C. > 1 B. =1 D. 0 612. The phase of even symmetric signal is A. +90° C. 0° B. –90° D. 0° or ±180°
A. B.
613. The power in a series R-L-C circuit will be half of that at resonance when the magnitude of current is equal to A. V/2R C. V/√ R B. V/√ R D. √ V/R 614. In a series RLC high Q circuit, the current peaks at a frequency A. f = fo C. f < fo B. f > fo D. none of these 615. The given series resonant circuit frequency of 20 MHz. It will A. By pass all signals of 20 B. permit flow of signal of 20 time C. Not produce any effect at 20 D. cause moderate attenuation MHz
resonance
at
MHz MHz along the MHz of signal at 20
all frequencies 0.5 rad/ sec
C. D.
5 rad / sec 1 rad/ sec
620. The parallel RLC circuit shown is in resonance.
A. B.
|IR| < 1 mA |IR + IL| >1 mA
C. D.
|IR + IC| < 1 mA |IL + IC| > 1 mA
621. A series RLC ckt has a Q of 100 and an impedance of (100 + j0) Ω at its resonance angular frequency of 107 rad| sec. The values of R & L are A. R = 100 Ω; L = 1 mH C. R = 100 Ω; L = 10 mH B. R = 10 Ω; L = 10 mH D. none of the above 622. The parallel RLC circuit having damping ratio δp is connected in series with same values, then series circuit damping ratio δs is
A. B.
4δp 2δp
C. D.
δp/4 δp/2
C. D.
623. A series LCR circuit consisting of R = 10Ω, |XL| = 20 Ω & |XC| = 20 Ω is connected across an a.c supply of 200 V rms. The rms voltage across the capacitor is A. 200 -90° C. 400 +90 B. 200 +90° D. 400 -90 624. At fR what is K?
A. B.
0.25 0.5
C. D.
0.999 1.0
625. Find Zin at resonance.
A. B.
1.28 Ω 12.8 Ω
628. A series RLC circuit when existed by a 10 V sinusoidal voltage source of variable frequency, exhibits resonance at 100 HZ and has a 3dB band width of 5 Hz. The voltage across the inductor L at resonance is A. 10 V C. 10/√ V B. 10√ V D. 200 V 629. A circuit with a resistor, inductor and capacitor in series is resonant at fR Hz. If all the component values are now doubled, the new resonant frequency is A. 2 fR C. fR/4 B. still fR D. fR/2 630. A coil (series RL) has been designed for high Q performance at a rated voltage and a specific frequency. If the frequency of operation is doubled, and the coil is operated at the same rated voltage, then the Q factor and the active power P consumed by the coil will be affected as follows A. P is doubled, Q is halved B. P is halved, Q is doubled C. P remain constant, Q is doubled D. P decreases 4 times, Q is doubled
C. D.
2Ω 128 Ω
626. For the series RLC circuit, the partial phasor diagram at a certain frequency is shown, the operating frequency of the circuit is
A. B. C. D.
can be greater than the input voltage however, it is 90° out of phase with the input voltage can be greater than the input voltage and is in phase with the input voltage.
631. A series RLC circuit has the following parameter values R = 10 Ω, L = 0.01 H, C = 100 µF. The Q factor of the circuit at resonance is A. 1 C. 0.1 B. 10 D. none of the above 632. At resonance, the parallel circuit of given figure constituted by an iron-cored coil and a capacitor, behaves like.
Equal to resonant frequency less than resonant frequency Greater than resonant frequency none of the above
627. In a series RLC circuit at resonance, the magnitude of the voltage developed across the capacitor A. is always zero B. can never be greater than the input voltage
A. B.
open circuit short
C. D.
pure resistance = R pure resistance > R
633. Find L & C of a parallel RLC circuit to resonate at 1 rad/sec with a Q of 5 and resistance of 1 ohm. A. 1/5 H, 5 F C. 1 H, 1 F B. 5 H, 1/5 F D. 5 H, 5 F 634. In a parallel RLC resonant circuit R = 10 kΩ, C = 0. 47 µF, the bandwidth will be. A. 212.76 rad/sec C. 100 rad/sec 10 B. 2.12 x 10 rad/sec D. none of the above 635. A parallel resonate circuit (RP, L, &C) and a series resonant circuit (RS, L & C) have the same Q. Find the relation between RP & RS 2 A. RS = Q Rp C. RP = RS 2 B. RP = Q RS D. none of the above 636. In a parallel resonant circuit, as R increases, the selectivity will be A. Decreasing C. Constant B. Increasing D. none of the above 637. In a series RLC circuit, the phasor form at some frequency is as shown, then the frequency is
A. B.
R/L L/RC
C. D.
1/RC ω0L/R
641. The Q of a parallel RLC circuit at its resonance frequency ω0 is A. ω0L/R C. ω0RC B. R/ω0C D. ω0LR 642. In a series R-L-C circuit below resonance, the current A. lags behind the applied voltage B. leads the applied voltage C. is in phase with the voltage D. leads or lags behind the applied voltage depending upon the actual values of L and C 643. A high Q coil has A. large bandwidth B. high losses
C. D.
low losses flat response
644. At a frequency below the resonant frequency ____ circuit is capacitive and ____ circuit. A. series, parallel C. parallel, parallel B. parallel, series D. series, series 645. In the following parallel circuit, resonance will never occur, if:
A. B. C. D.
Less than W0 More than W0 equal to W0 none of the above
638. In a series RLC circuit, let Qc be the Q of the coil at resonance and let Qs = (resonance frequency)/bandwidth, then A. Qc and Qs are not related to each other B. Qc > Qs C. Qc < Qs D. Qc = Qs 639. A coil is represented by an inductance L in parallel with a resistance R. The Q of the coil at frequency w is A. R/(ωL) C. ωLR B. ωL/ R D. 1/(ωLR) 640. The half power bandwidth of a series RCL circuit is
A. B. C. D.
2
2
R1 = R2 = L/C 2 R1 < L/C 2 2 R2 > L/C and R1 < L/C 2 2 R1 > L/C and R2 > L/C
646. The circulating current in a parallel LC circuit at any resonant frequency is A. Directly proportional to frequency B. Inversely proportional to frequency C. Independent of frequency D. none of the above 2
647. In series RLC circuit excited by a voltage, e = E sin ωt, where LC < (1/ω ) A. Current lags the applied voltage B. current leads the applied voltage C. current is in phase with the applied voltage D. voltages across L and C are equal
648. A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q = 100. If each of R, L and C is doubled from its original value, the new Q of the circuit is A. 25 C. 100 B. 50 D. 200
A. B.
R√ R√
C. D.
1/R√ 1/R√
656. A practical inductor can be replaced by the following equivalent circuit at low to medium frequency.
649. What is the bandwidth of parallel RLC circuit at resonance? A. RC C. R/C B. 1/RC D. C/R 650. The current bandwidth of RC series circuit is A. 1/RC C. ∞ B. RC D. none of the above 651. The circuit shown acts as an ideal current source with respect to terminals AB, when the frequency is
A. B.
zero 1 rad/sec
C. D.
4 rad/sec 16 rad/sec
652. A series RLC circuit is excited by an ac voltage v(t) = sin t. If L = 10 H and C = 0.1 F, then the peak value of the voltage across R will be A. 0.707 B. 1 C. 1.414 D. indeterminate as the value of R is not given
A. B.
Figure a Figure b
C. D.
Figure c Figure d
657. A coil of wire has inductive impedance. At high frequencies the impedance will be represented by
A. B.
Figure a Figure b
C. D.
Figure c Figure d
658. In a series RLC circuit R= 2 kΩ, L = 1 H, and C = 1/ 400 microfarads. The resonant frequency is 4 4 A. 2 x 10 Hz C. 10 Hz 4 4 B. (1/π) x 10 Hz D. 2π x 10 Hz 659. In the circuit shown in the figure, Vs = Vm sin 2t and Z2 = 1 – j. The value of C is shown such that the current I is in phase with Vs. The value of C in farad is
653. In a parallel RLC circuit, the current source (I) lags voltage across circuit (V) if A. wL > 1/wC C. R > [wL + 1/wC] B. wL < 1/wC D. none of the above 654. At lower half power frequency the total reactance of the series RLC circuit is A. –R C. √ -45° B. √ 45° D. none of the above 655. In a parallel RLC circuit, the quality factor at a resonance is given by
A. B.
1/4 1/2√
C. D.
2 4
660. The circuit shown has i(t) = 10 sin (120πt). The power (time average power) dissipated in R is when L = 1/120π H, C = 1/60π H, R = 1 ohm.
A. B.
A. B.
25 watts 100 watts
C. D.
10/√ watts 50 watts
661. The value of the capacitance C in the given ac circuit to make it a constant resistance circuit or for the supply current to be independent of its frequency is
A. B.
1/16 F 1/12 F
C. D.
1/8 F ¼F
662. A parallel RLC circuit has half power frequencies at 105 M rad/s and 95 M rad/s. Then Q is given by A. 10.5 C. 100 B. 9.5 D. 10 2
663. The system function H(s) = s/(s + 2s + 100). The resonant frequency and the bandwidth in rad/s are given, respectively, by A. 10, 1 C. 100, 2 B. 10, 2 D. 100, 1 E. POWER FACTOR CORRECTION (1-PHASE) 664. EE Board Exam October 1990 A single phase inductive load takes 50 kVA at 0.60 power factor lagging. Solve for the kVAR of a capacitor required to improve the power factor to 1.0. A. 30 kVAR C. 22.5 kVAR B. 20 kVAR D. 40 KVAR 665. REE Board Exam March 1998 A single phase induction motor is rated 5 hp, 75% power factor and 220 volts. What approximate size of capacitor is necessary to raise the power factor to about 95%?
3 kVAR 2 kVAR
C. D.
2.5 kVAR 3.5 Kvar
666. EE Board Exam April 1984 A plant has a load of 290 kilowatt with an average power factor of 70%. The owner requests you to correct the power factor to reduce its power consumption. How much capacitor kVAR is required to increase the power factor to 90%? A. 152.46 C. 150.34 B. 155.39 D. 154.58 667. REE Board Exam October 1996 A single-phase, 60 Hz, 5 hp squirrel cage induction motor draws a current of 53 A at 117 V. If it has a 78.5% electrical to mechanical conversion efficiency, what capacitance should be connected at the terminals of the motor in order to increase the power factor of the load combination to 92%? A. 480 μF C. 320 μF B. 380 μF D. 420 μF 668. EE Board Exam April 1997 A load of 10,000 kVA, 80% pf lagging is connected to a 13,200 volts line. How much capacitive reactive power is needed to correct the power factor to 0.97 lagging? A. 5,156 kVAR C. 2,547 kVAR B. 3,138 kVAR D. 4,395 kVAR 669. In a pure reactive circuit, the power factor is A. lagging C. leading B. zero D. unity 670. Power factor is defined as the ratio of A. volt ampere to watts B. watts to volt amperes C. volt amperes reactive to watts D. watts to volt amperes reactive 671. In a series circuit consisting of resistance and reactance, power factor is defined as the ratio of A. resistance to impedance B. resistance to reactance C. reactance to impedance D. none of these 672. For a parallel circuit consisting of resistance and reactance the value of power factor is the ratio of
A. B. C. D.
impedance to reactance reactance to impedance resistance to impedance impedance to resistance
C. D.
673. It is not easy to find the value of impedance for a parallel circuit but power factor can easily be obtained as a ratio of A. active current to line current B. reactive current to line current C. line current to active current D. none of these 674. The power factor of a.c. circuit containing both a resistor and a conductor is A. more than unity C. between 0 -1 leading B. leading by 90° D. none of these 675. In an a.c. circuits, a low value of reactive volt-ampere compared with watts indicates A. high power factor C. leading power factor B. unity power factor D. none of these 676. In a given circuit when power factor is unity the reactive power is A. a maximum C. zero 2 B. equal to I R D. none of these 677. The capacitor of power factor correction are rated in terms of A. voltage C. kW B. VA D. kVAR 678. Poor power factor results in all of the following except A. overloading of transformers B. overloading of alternators C. reduction in power losses D. reduction in load handling capacity of electrical system 679. Power factor of an inductive circuit can be improved capacitor to it in A. series B. parallel C. either series or parallel D. depends on the value of the capacitor 680. For the same load, if the power factor is reduced, it will A. draw more current B. draw less current
by connecting a
draw same current but less power draw less current but more power
681. The power factor of incandescent bulb is A. 0.8 lagging C. unity B. 0.8 leading D. zero 682. Power factor of the magnetizing component of a transformer is A. unity C. always leading B. 0.8 lagging D. zero 683. One of the reasons for improving the power factor is A. to increase the reactive power B. to decrease the reactive power C. to increase the real power D. to decrease the real power 684. Another reason for improving the power factor is A. to avoid poor voltage regulation B. to keep voltage regulation constant C. to increase the voltage regulation D. to decrease the voltage regulation 685. Power factor improvement may be achieved by the use of A. synchronous motor C. long transmission line B. induction motor D. short transmission line 686. The advantage of using static capacitor to improve the power factor is because they A. are not variable B. are almost loss free C. provide continuous change of power factor D. none of these 687. Many industrial tariffs penalize consumers whose power factor falls A. below 0.8 C. between 0.8 to 0.95 B. below unity D. none of these 688. A factory takes a load of 1000 KW and has a reactive power of 1000 KVAR. Its power factor is A. 0.6 C. 0.8 B. unity D. 0.7 689. A current of 10 amperes at a power factor of 0.8 lagging is taken from 250 V a.c. supply. The reactive power of the system is
2000 watts 2000 VA
C. D.
1500 watts 1500 VAR
695. Consider the following statements: In the circuit shown in the figure, if the equivalent impedance x – x is Zeq then
690. A resistance ‘R’ Ω and inductance ‘L’ H are connected across 240 V, 50 Hz supply. Power dissipated in the circuit is 100 W and the voltage across R is 100 V. In order to improve the pf to unity, the capacitor that is to be connected in series should have a value of A. 43.7 μF C. 437 μF B. 4.37 μF D. 4.37 mF 691. What size of condenser must be placed across an inductance having a resistance of 10 ohms and reactance of 20 ohms to draw minimum current from the line when the combination is connected across a 60-cycle line? (Assume a condenser of negligible resistance). A. 20 μF C. 10 μF B. 106 μF D. 6.33 μF F. AC NETWORK ANALYSIS 692. A segment of a circuit figure VR = 5 V, VC = 4 voltage VL is given by A. 3 – 8 cos 2t B. 32 sin 2t C. 16 sin 2t D. 16 cos 2t 693. Three currents i1, i2 and approaching a node. If + 60°) A and i2 = 10 sin (400t - 60°) A, then i3 is A. 0 C. -10 sin 400t A B. 10 sin 400t A D. √ (
i3 are i1 = 10 sin (400t )A
I1
4Ω
j10 Ω
1. Zeq = 2 + j5 2. Zeq = 2 + j3 Of these statements A. 1 alone is true B. 2 and 4 are correct
3. 4.
I1 = -I2 I1 = I2
C. D.
2 and 3 are correct none of the above
j3 Ω
A
A. B.
j2 Ω
j5.33 V 5.33 V
C. D.
V2
A. B.
0° 45°
C. D.
-45° -90°
B
j4 Ω
-j5.33 V j3.33 V
697. In the circuit shown in given figure, ( ) √ ( ) and ( ) ( ). What is the voltage v(t) across the 1 ohm grounded √ resistor? 1Ω
1Ω
+
+ 1Ω
e1(t)
A. B. C. D.
V (
) V
j1 V
(
e2(t) -
I j10 Ω
j10 Ω
j4 Ω
-
10 Ω
4Ω
696. For the network shown in the figure, the voltage VB will be
694. The phase angle of the current ‘I’ with respect to the V 1 in the circuit shown in the figure is V1 = 100 (1 + j); V2 = 100(1 – j)
V1
I2
x
1A
shown in given sin 2t. The
x
2A
A. B.
)V
698. If all elements in a particular network are linear, then the superposition theorem would hold when the excitation is A. dc only C. either ac or dc B. ac only D. an impulse 699. For the network shown in given figure, the Thevenin equivalent impedance across terminals CD is given by A. B.
[
]
[
]
C. (
D.
700. In the given figure Thevenin impedance seen from X-Y is A. C. B. D.
,
)
,
.
701. In the figure the current source is A, R = 1 ohm, the impedances are ZC = -j ohm, and ZL = j2 ohm, The Thevenin equivalent circuit looking into the circuit across X-Y is A. √ V, (1 + j2) Ω C. V, (1 + j) Ω B. V, (1 + j2) Ω D. √ V, (1 + j) Ω 702. The circuit shown in Fig. 1 is replaced by its Norton’s equivalent circuit in Fig. 2. The value of I will be A. A C. A B. A D. A 703. Consider the following statements: The transfer impedance and admittance of a network remain constant when the position of excitation and response are interchanged if the network 1. is linear 2. consists of bilateral elements 3. has high impedance or admittance as the case may be 4. is resonant Of these statements A. 1 and 2 are correct C. 2 and 4 are correct B. 1, 3 and 4 are correct D. all are correct 704. In a linear network, the ratio of voltage excitation to current response is unaltered when the position of excitation and response are interchanged. The assertions stems from the A. principle of duality B. reciprocity theorem
C. D.
principle of superposition equivalence theorem
705. A certain network N feeds a load resistance as shown in Fig. 1. It consumes a power of ‘P’. If an indicated network is added as shown in Fig. 2. The power consumed by R will be A. less than P C. between P and 4P B. equal to P D. more than 4P 706. In the circuit shown in the figure, the current source I = 1 A, the voltage source V = 5 V, R1 = R2 = R3 = 1 Ω, L1 = L2 = L3 = 1 H, C1 = C2 = 1 F. The currents (in A) through R3 and the voltage source V respectively will be A. 1, 4 C. 5, 2 B. 5, 1 D. 5, 4 707. For loop (1) of the network shown in the given figure, the correct loop equation is A. C. B. D. 708. An ac source of voltage ES and an internal impedance of ZS = (RS + jXS) is connected to a load of impedance ZL = (RL + jXL). Consider the following conditions in this regard. 1. XL = XS if only XL is varied 2. XL = -XS if only XL is varied √ 3. ( ) if only RL is varied 4. |ZL| = |ZS| if the magnitude of ZL is varied, keeping the phase angle fixed Among these conditions, those which are to be satisfied for maximum power transfer from the source to the load would include A. 2 and 3 C. 1, 2 and 4 B. 1 and 3 D. 2, 3 and 4 709. Under the conditions of maximum power transfer from an ac source to a variable load A. the load impedance must be inductive, if the generator impedance is inductive B. the sum of the source and the load impedances is zero C. the sum of the source reactance and the load reactance is zero D. the load impedance has the same phase angle as the generator impedance 710. If the combined generator and line impedance is (5 + j10) Ω, then for the maximum power transfer to a load impedance from a generator of constant generated voltage, the load impedance is given be which of the following?
A. B.
(5 + j10) Ω (5 – j10) Ω
C. D.
(5 + j5) Ω 5Ω
A. B.
1,905 W 3,300 W
C. D.
5,716 W 3,810 W
711. A voltage source having an internal impedance of 8 + j6 Ω supplies power to a resistive load. What should be load resistance for maximum power transferred to it? A. 8 Ω C. 10 Ω B. 6 Ω D. √ Ω
718. REE Board Exam April 1997 A 170 kV, 3-phase electric source delivers 200 MVA to a balanced load, which has a power factor of 90% lagging. What is the line current? A. 257 A C. 402 A B. 502 A D. 679 A
712. The Thevenin equivalent circuit of a network is as shown in the given figure. For maximum power transfer to the variable and purely resistive load R L, its resistance should be A. 60 Ω C. 100 Ω B. 80 Ω D. infinity
719. REE Board Exam October 1997 A three-phase motor is rated 50 hp, 440 volts and 85% power factor. What is its rated current? A. 61.5 A C. 55 A B. 57.5 A D. 59 A
713. Two ac sources fed a common variable load as shown in the given figure. Under the maximum power transfer condition, the power absorbed by the load resistance RL is A. 2200 W C. 1000 W B. 1250 W D. 625 W
720. EE Board Exam April 1985 A balanced 3-phase load draws 120 amperes line current at 230 volts line to line, 0.848 pf lagging. Solve for the real power. A. 40.54 kW C. 41.45 kW B. 42.35 kW D. 43.15 kW
714. REE Board Exam March 1998 Three impedances, -j10, j10 and 10 ohms are wye-connected. Determine the impedance of an equivalent delta. A. 12.5, j12.5, -12.5 Ω C. j8.5, -j12.5, 8 Ω B. 10, j10, -j10 Ω D. 5, j5, -j5 Ω
721. REE Board Exam March 1998 A generator supplies three-phase power to balanced load. The voltage is 230 volts, the current is 18 A and the power factor is 85%. What is the power? A. 3.6 kW C. 6.1 kW B. 1.6 kW D. 1.4 kW
715. A telephone circuit makes power available at a pair of terminals. The open circuit voltage across the terminals is 1 volt and the impedance looking into the terminals is 500 – j500 Ω. What is the maximum power that can be drawn from the circuit? A. 0.002 W C. 0.001 W B. 0.0005 W D. 0.0014 W
722. EE Board Exam April 1984 A balanced 3-phase load draws 75 amperes line current at 230 volts line to line, 0.848 pf lagging. Solve for the reactive power being drawn. A. 15.83 kVAR C. 15.35 kVAR B. 15.26 kVAR D. 15.94 kVAR
G. BALANCED POLYPHASE SYSTEM 716. REE Board Exam April 2002 In a balanced three-phase system, the phase A voltage is 132.8 cis 0°, what is the line to line voltage VCA? A. 230 cis 30° C. 230 cis (-60°) B. 230 cis (-30°) D. 132.8 cis 120°
723. EE Board Exam April 1990 The input power factor to a three-phase, 6-poles, 460 volts., 60 Hz, 50 hp induction motor is 0.62 as 20 A is drawn by the motor. Find the power input to the motor. A. 9,880 W C. 9,895 W B. 9,675 W D. 9,478 W
717. REE Board Exam September 2001 The phase B line voltage and the phase A line current of a balanced three phase system are v = 220 sin (ωt + 210°) and i = 10 sin (ωt + 180°) amperes, respectively. What is the power of the system?
724. EE Board Exam April 1992 A 460 volt, three-phase motor draws 208 A with a power factor of 0.91 lagging. Calculate the kW input to the motor. A. 150.8 C. 152.4
B.
156.3
D.
160.3
725. EE Board Exam April 1993 A wye-connected load has a ohm impedance per phase and is connected across a 120-V three-phase source. Calculate the line current. A. 24 A C. 41.56 A B. 13.85 A D. 15.45 A
731. EE Board Exam June 1990 Two parallel connected loads A and B are supplied by a 440 V, 3-phase, 60 Hz generator. Load A draws an apparent power of 100 kVA at 0.80 pf lagging and load B draws an apparent power of 70 kVA at unity pf. Determine the feeder current. A. 208 A C. 214 A B. 212 A D. 202 A
726. EE Board Exam April 1993 Three condensers, each having capacity of 75 microfarads are connected in star to a 440 volts, 3-phase, 50 cycles supply. Calculate the capacitance of each of the three condensers so that when they are connected in delta to the same supply the line current remains the same. A. 20 μF C. 25 μF B. 28 μF D. 30 μF
732. EE Board Exam April 1990 A three-phase motor takes 10 kVA at 0.67 pf lagging from a source of 230 volts. It is in parallel with a balanced delta load having 16 ohms resistance and 12 ohms capacitive reactance in series in each phase. Determine the total power factor. A. 0.966 lagging C. 0.917 lagging B. 0.896 lagging D. 0.967 lagging
727. EE April 1993 A balanced three-phase load is wye-connected and has an impedance Zp = 4 – j3 ohms per phase. Find the line current if this load is connected across a 220 V three-phase source. A. 25.4 A C. 20.5 A B. 22.3 A D. 26.7 A
733. REE Board Exam March 1998 The phase b line voltage and the phase a line current of a balanced threephase system are v = 220 (sin wt + 210) and i = 10 sin (wt - 30), respectively. What is the power of the system? A. 1905 W C. 5716 W B. 3300 W D. 3810 W
728. REE Board Exam October 1998 Three 10-ohm resistances are connected delta on a balanced three-phase source. If the equation of the phase Van =120 sin ωt. What is the equation of the line current in line a? A. 20.78 sin (ωt + 30°) C. 12 sin (ωt – 56.56°) B. 13.15 sin (ωt - 30°) D. 36 sin ωt
734. EE Board Exam April 1985 A balanced 3-phase load draws 120 amperes line current at 230 volts line to line, 0.848 pf lagging current. Solve for the readings of the two wattmeters used to measure the 3-phase power. A. 25.543 kW, 15.087 kW B. 28.155 kW, 12.385 kW C. 24.365 kW, 16.175 kW D. 27.583 kW, 12.957 kW
729. EE Board Exam October 1994 Three resistors 10, 15 and 30 ohmic values are connected in wyeconfiguration to a balanced 208 volt three-phase supply. Calculate the total power of the system. A. 2644 W C. 3080 W B. 2880 W D. 3280 W 730. REE Board Exam March 1998 Three impedances each 10 + j5 ohms are connected delta on a balanced three-phase source. If the equation of the phase Van =120 sin ωt. What is the equation of the line current through the impedance connected across phase A and B? A. 20.02 sin (ωt - 22°) C. 16.21 sin (ωt + 56.56°) B. 18.59 sin (ωt + 3.44°) D. 21.32 sin (ωt – 8.15°)
735. EE Board Exam April 1988 MERALCO used two wattmeters to measure the balanced 3-phase dynatron elevator motor drive. The coils of the wattmeters are connected to the current transformers, which are lines 1 and 2 respectively. The potential coils are connected to potential transformers, which are across lines 2 and 3 and lines 3 and 1, respectively. The line potentials are 230 V and the line currents are each 150 A. The wattmeters each indicate 19.6 kW. Assume load is wye connected. What is the total power supplied? A. 49.175 kW C. 45.461 kW B. 48.236 kW D. 47.350 kW 736. EE Board Exam April 1992
A 460-volt three-phase motor draws 208 A with a power factor of 0.91 lagging. Calculate the indication of W1 and W2 for the given condition. A. 75.40 kW, 75.40 kW C. 89.56 kW, 61.25 kW B. 91.23 kW, 59.58 kW D. 95.24 kW, 55.57 kW 737. EE Board Exam June 1990 Two wattmeter method is used to test a 25 HP, 230 volt, 1800 rpm, 60 cycle, 3-phase induction motor. When the line voltages are 230 volts, one wattmeter reads +13,400 watts and the other +7,400 watts. Determine motor power factor. A. 0.961 C. 0.894 B. 0.886 D. 0.807 738. In a balanced three phase star connected circuit the line voltages are equal A. to the line current B. to the phase voltage C. and so are line currents D. but the line currents are unequal
743. The advantages of star connections over delta connections for the same voltage is that it gives A. step down current B. extra step up voltage C. extra step up current D. extra step up power 744. Power in a three phase star system is equal to A. √ x VL x IL x power factor B. 3 x Vph x IL x power factor C. √ x VL X Iph X power factor D. 3 x Vph x Iph x power factor 745. Power in a three phase delta system with balanced load is equal to A. √ x VL x IL x power factor B. √ x Vph X Iph X power factor C. 3 x Vph x IL x power factor D. 3 x VL x IL x power factor
739. The type of a.c. distribution system commonly used to supply both light and power is the A. open delta system B. three phase delta system C. three phase star system with neutral wire D. three phase star system without neutral wire
746. In a delta connected system the line current is A. 1.414 times the phase current B. phasor sum of the two phase currents C. equal to the phase current D. 1.732 times the phase current
740. The phase displacement between phasors in polyphase system is always A. 90 degrees B. 120 degrees C. 360 degrees divided by the number of phases D. none of the above
747. Power in star connected system is A. equal to that of delta system B. √ times the delta system C. √ times the delta system D. 3 times of a delta system
741. In a balanced three phase star connected system the line voltage is A. the phasor difference of the two phase voltages B. the phasor sum of the two phase voltages C. 0.707 times the phase voltage D. 1.414 times the phase voltage
748. Electric power is almost exclusively generated, transmitted and distributed, by three phase system because it A. it is more efficient B. uses less material for a given capacity C. costs less than single-phase apparatus D. all of the above
742. In a star connected system line current is A. 0.707 times the phase current B. 1.735 times the phase current C. equal to the phase current D. 1.414 times the phase current
749. The voltages induced in the three windings of a three-phase alternator are ____ degree apart in time phase. A. 120 C. 90 B. 60 D. 30
750. If positive phase sequence of a 3 – phase load is a-b-c the negative sequence would be A. b-a-c C. a-c-b B. c-b-a D. all of the above 751. In the balanced 3-phase voltage system generated by a Y-connected alternator, VYB lags ER by ____ electrical degrees. A. 90 B. 120 C. 60 D. 30 752. The power taken by 3-phase load is given by the expression A. 3 VL IL cos φ C. 3 VL IL sin φ B. √ VL IL cos φ D. √ VL IL sin φ 753. In a balanced 3-phase voltage generator, the difference phase voltages reach their maximum values ____ degree apart. A. 120 C. 240 B. 60 D. 30 754. If the B-phase, Y-connected alternator become reverse connected by mistake, it will not affect. A. V Y B C. V B R B. V R Y D. V B Y 755. Three equal impedances are first connected in star across a balanced 3phase supply. If connected in delta across the same supply. A. phase current will be tripled B. phase current will be doubled C. line current will become one-third D. power consumed will increase three-fold 756. A 3-phase, 4-wire, 230/440-V system is supplying lamp load at 230 V. If a 3phase motor is now switched on across the same supply then, A. neutral current will increase B. all line currents will decrease C. neutral current will remain unchanged D. power factor will be improved 757. Power factor improvement A. does not affect the performance characteristics of the original load B. employs series resonance C. increase the active power drawn by the load D. increases the reactive power taken by the load 758. The chief disadvantage of a low power factor is that
A. B. C. D.
more power is consumed by the load current required for a given load power is higher active power developed by a generator exceeds its rated output capacity heat generated is more than the desired amount
759. In the 2-wattmeter method of measuring 3-phase power, the two wattmeter’s indicate equal and opposite readings when load power factor angle is ____ degrees lagging. A. 60 C. 30 B. 0 D. 90 760. When phase sequence at the 3-phase load is reversed A. phase powers are changed B. phase currents are changed C. phase currents change in angle but not in magnitude D. total power consumed in changed 761. Phase reversal of a 4-wire unbalanced load supplied from a balanced 3phase supply changes A. magnitude of phase currents B. magnitudes as well as phase angle of neutral current C. the power consumed D. only the magnitude of neutral current 762. In a two-phase generator, the electrical displacement between two phase or windings is ____ electrical degrees. A. 120 C. 180 B. 90 D. none of the above 763. In a six-phase generator, the electrical displacement between different phases or windings is ____ electrical degrees. A. 60 C. 120 B. 90 D. 45 764. The torque on the rotor if a 3-phase motor is more constant than that of a single motor because A. single phase motors are not self-starting B. single phase motors are small in size C. 3-phase power is of constant value D. none of the above 765. For the same rating, the size of a 3-phase motor will be ____ single phase motor. A. less than that of C. same as that of B. more than that of D. none of the above
770. The advantage of star-connected supply system is that A. line current is equal to phase current B. two voltages can be used C. phase sequence can easily be changed D. it is a simple arrangement
767. The phase sequence of a three-phase system is RYB. The other possible phase sequence can be A. B R Y C. R B Y B. Y R B D. none of the above
771. In a balanced star connected, line voltages are ____ ahead of their respective phase voltages. A. 30 C. 120 B. 60 D. none of the above
768. If in Fig. 14.1, the phase sequence is RYB, then
772. In a star-connected system, the relation between the line voltage V L and phase voltage Vph is A. C. √ B. D. none of the above √
3-phase line
766. To transmit the same amount of power over a fixed distance at a given voltage, the 3-phase system requires ____the weight of copper required for the single-phase system. A. 3 times C. 1.5 times B. 3/4 times D. 0.5 times
R
60 W
Y
60 W
L1
L2
773. Fig 14.2 shows a balanced star-connected system. The line voltage VRY is given by
R
C B
A. B. C. D.
N
L1 will burn more brightly than L2 L2 will burn more brightly than L1 both lamps will be equally bright none of the above
B
3-phase line
769. If the phase sequence of the 3-phase line in Fig 14.1 is reversed R
60 W
Y
60 W
L1
L2
C B Fig. 14.1
A. B. C. D.
L1 will be brighter than L2 L2 will be brighter than L1 both lamps will be equally bright none of the above
IR
ERN
Fig. 14.1
EBN
EYN Y
VRY IY IB
VBR VYB
Fig. 14.2 A. B. C. D.
VRY = ERN – ENY …..phasor sum VRY = ERN – EYN.....phasor difference VRY = ENR + EYN …..phasor sum none of the above
774. If the load connected to the 3-phase generator shown in Fig. 14.2 has a lagging p.f. of cos , then angle between VRY and IR is
777. The power delivered by the 3-phase system shown in Fig. 14.2 is . Here θ is the phase difference between √
R IR
ERN N B
EYN
EBN
Y
R
VRY VBR
IY
N VYB
IB
B
EYN
EBN
Y
Fig. 14.2 A. B.
30 + ϕ 30 - ϕ
C. D.
60 + ϕ 120 – ϕ
R N B
IR
EYN
EBN
Y
VRY VBR
IY
VYB
IB
90 – ϕ 90 + ϕ
C. D.
60 + ϕ 30 - ϕ
776. Each phase voltage in Fig. 14.2 is 230 V. If connections of phase B are reversed then
A. B. C. D.
B
R
EYN
EBN
Y
VRY = 230 V VRY > 230 V
C. D.
1
IB IR
VRY VBR
IY
2 B
IB
VRY < 230 V VRY = 0 V
Y
IY
VYB
3 Fig. 14.3
Fig. 14.2 A. B.
line voltage and corresponding line current phase voltage and corresponding phase current phase current and line current none of the above
780. Fig. 14.3 shows a balanced delta-connected supply system. The current in line 1 is
IR
ERN
VYB
778. A 3-phase load is balanced if all the three phases have the same A. impedance B. power factor C. impedance and power factor D. none of the above
R N
IB
VBR
779. Three 50-ohm resistors are connected in star across 400 V, 3-phase supply. If one of the resistors is disconnected, then line current will be A. 8 A C. √ A B. 4 A D. √ A
Fig. 14.2 A. B.
VRY IY
Fig. 14.2
775. If the load connected to the 3-phase generator shown in Fig. 14.2 has a leading p.f. of cos , then angle between VRY and IR is
ERN
IR
ERN
A. B. C. D.
IR - IB..... phasor difference IB - IR ….. phasor difference IY - IR - IB ….. phasor difference none of the above
781. In Fig. 14.3, line currents are ____ behind the respective phase currents.
R IB
10 Ω
400 V
1
10 Ω
400 V
IR
10 Ω N
400 V
2 B
Y
IY
Fig. 14.4
3 Fig. 14.3
A. B.
60 30
C. D.
120 none of the above
A. B.
400 V √ V
2 3 Fig. 14.3 A. B.
200 V √ V
C. D.
10 Ω N
400 V Fig. 14.4
Y
IY
10 Ω
400 V
IR B
10 Ω
400 V
1
IB
230 V none of the above
786. The power rating of each resistor in Fig. 14.4 is
782. The delta-connected generator shown in Fig. 14.3 has phase voltage of 200 V on no load. If a connection of one of the phases is reversed then resultant voltage across the mesh is
R
C. D.
A. B.
4000 W 2300 W
C. D.
787. If one of the resistors in Fig. 14.4 were open-circuited, then power consumed in the circuit is
400 V none of the above
785. The voltage rating of each resistor in Fig. 14.4 should be
10 Ω
400 V 10 Ω
400 V
783. If one line conductor of a 3-phase line is cut, the load is then supplied by the ____ voltage. A. single phase C. three phase B. two phase D. none of the above 784. The resistance between any two terminals of a balanced star connected load is 12 . The resistance of each phase is A. 12 C. 6 B. 18 D. 36
4600 W 5290 W
10 Ω N
400 V Fig. 14.4
A. B.
8000 W 4000 W
C. D.
16000 W none of the above
788. The power consumed in the star-connected load shown in Fig. 14.5 is 690 W. The line current is
8Ω
6Ω
400 V
8Ω
6Ω
400 V
8Ω
6Ω
10 Ω
400 V 10 Ω
400 V
10 Ω
400 V
N
400 V Fig. 14.4
A. B.
2.5 A 1A
C. D.
1.725 A none of the above
789. If one of the resistors in Fig. 14.5 is open-circuited, power consumption will be
R
R
Fig. 14.6 A. B.
184 V 138 V
C. D.
792. The power consumed in each phase of the circuit shown in Fig. 14.6 is
8Ω
6Ω
400 V
8Ω
6Ω
400 V
8Ω
6Ω
400 V 400 V
R
Y 400 V
B A. B.
400 V R
Fig. 14.5 C. 345 W D. none of the above
200 W 300 W
790. The power factor of the star-connected load shown in Fig. 14.6 is
8Ω
6Ω
400 V
8Ω
6Ω
400 V
8Ω
6Ω
400 V
Fig. 14.6 A. B.
0.8 lagging 0.6 lagging
C. D.
400 V none of the above
0.75 lagging none of the above
791. The voltage drop across each inductor in Fig. 14.6 is
Fig. 14.6 A. B.
2300 W 4000 W
C. D.
3174 W none of the above
793. Three identical resistances connected in star consume 4000 W. If the resistances are connected in delta across the same supply, the power consumed will be A. 4000 W C. 8000 W B. 6000 W D. 12000 W 794. Three identical resistances, each of 15 , are connected in delta across 400 V, 3-phase supply. The value of resistance in each leg of the equivalent starconnected load would be A. 15 C. 5 B. 7.5 D. 30 795. Three identical capacitances, each of 450 F, are connected in star. The value of capacitance in each phase of the equivalent delta-connected load would be
C. D.
225 F 900 F
802. If the p.f. of the load shown in Fig. 14.7 (phase sequence is RYB) is zero, then
796. Three identical resistances connected in star carry a line current of 12 A. If the same resistances are connected in delta across the same supply, the line current will be A. 12 A C. 8 A B. 4 A D. 36 A
Z
N
W2
W1 will read zero W2 will read zero both W1 and W2 will read zero W1 and W2 will read equal and opposite
Z
Z
W2
IL
Y
VL IL
± ±
C. D.
√ √
( (
IL
Y
B
± ±
Z
Z
Z
) )
VL N
VL ± ±
IL
Fig. 14.7
A. B. C. D.
W1 will give more reading than W2 both W1 and W2 will give equal and positive reading W2 will give more reading than W1 none of the above
804. If the p.f. of the load (phase sequence is RYB) is Fig. 14.7 is 0.5, then
Fig. 14.7
( (
± ±
IL
N
A. B.
W1
R
VL
W2
± ±
803. If the p.f. of the load (phase sequence is RYB) in Fig. 14.7 is unity, then
IL
B
VL IL
Fig. 14.7
A. B. C. D.
801. In the circuit shown in Fig. 14.7, the phase sequence is RYB. If the load p.f. is cos lagging, then reading of wattmeter W2 will be R
IL
Y
B
800. A wattmeter measures ____ power. A. instantaneous C. reactive B. apparent D. average
W1
VL
Z
799. In order to measure power in a 3-phase,4-wire unbalanced load, the minimum number of wattmeters required would be A. 1 C. 4 B. 2 D. 3
± ±
IL
797. Three delta-connected resistors absorb 60 kW when connected to a 3phase line. If the resistors are connected in star, the power absorbed is A. 60 kW C. 40 kW B. 20 kW D. 180 kW 798. If a balanced delta load has an impedance of (6 + j9) ohms per phase, then impedance of each phase of equivalent star load is A. (6 + j9) ohms C. (12 + j18) ohms B. (2 + j3) ohms D. (3 + j4.5) ohms
W1
R
Z
150 F 450 F
Z
A. B.
) )
W1
R
± ±
W1
R
± ±
IL Z
Z
IL VL
N
Z
Z
W2
Z
IL
Y
B
IL
W2
Fig. 14.7
A. B. C. D.
VL ± ±
IL
Fig. 14.7
W2 will give total power W1 will give total power both W1 and W2 will read equal W2 will give negative reading
A. B. C. D.
805. If the p.f. of the load (phase sequence is RYB) is Fig. 14.7 is 0.4, then W1
R
IL
Y
B
VL ± ±
Z
N
VL
± ±
Z
IL VL
total power drawn will change total power drawn will not change power factor of the load remains same none of the above
807. In two wattmeter method, the algebraic sum of the readings of two wattmeters will indicate true power only if A. the load is balanced B. phase sequence remains unchanged C. there is no source unbalance D. neutral wire available does not carry any current
N IL
Z
Y
Z
B
W2
VL ± ±
IL
Fig. 14.7
A. B. C. D.
W2 will give negative reading both W1 and W2 will give negative reading W1 will give negative reading both W1 and W2 will give positive reading
806. If capacitors of equal capacitance are shunted across each phase in Fig. 14.7, then
808. Three-wattmeter method is not used to measure power in a 3-phase circuit because A. it is complicated B. generally neutral is not available or delta load cannot be opened C. it requires three wattmeters D. none of the above 809. Three resistors having the same resistances are connected in star and across 480 V 3-phase lines. To what value should the line voltage be changed to obtain the same line currents with the resistors delta-connected? A. 230 V C. 160 V B. 133 V D. 240 V 810. In the circuit shown in Fig. 14.8, the wattmeter reads 1000 W. The total reactive power drawn by the balanced 3-phase load is
W R
± ±
Z
IR
N Z
Y
Z
B
IY IB
Fig. 14.8
A. B.
1000 VAR 2000 VAR
C. D.
1732 VAR none of the above
811. The most difficult unbalanced 3-phase load to deal with is A. 4-wire star connected unbalanced load B. unbalanced -connected load C. unbalanced 3-wire, Y-connected load D. none of the above 812. In a balanced three-phase system, the line to line voltages are displaced from each other by ____. A. 0° C. 90° B. 30° D. 120° 813. When phase sequence of the three-phase system is reversed ____. A. Phase currents change in angle not in magnitude B. Phase currents are changed C. Total Power consumed is changed D. Phase power are changed 814. A three-phase load is balanced if all the three phases have the same ____. A. Impedance B. Impedance & power factor C. Power factor D. Power 815. In balanced star (wye) connected system, the line voltage is A. 0.707 times the phase voltage B. 1.414 times the phase voltage C. phasor sum of the two phase voltage D. phasor difference of the two phase voltage
816. The phase sequence of a three-phase system is BCA. The other possible phase sequence can be ____. A. CBA C. ACB B. CAB D. none of these 817. Find the line voltage Vab is A. V B. V
C. D.
V and the sequence is BCA. V V
818. Line B of a 230 V ungrounded-wye system touches the ground. What is the voltage between line A and ground? A. 230 V C. 0 B. 115 V D. 132.79 V 819. A system consists of three equal resistors connected in wye and is fed from a balanced three-phase supply. How much power is reduced if one of the resistors is disconnected? A. 33% C. 25% B. 50% D. 0% 820. Three identical wye-connected resistances consume 1,000 watts. If the resistances are connected in delta across the same supply, the power consumed will be ____. A. 3,000 W C. 1,000 W B. 6,000 W D. 333 W 821. A balanced delta connected load draws 10 A of line current and 3 kW at 220 V. The reactance of each phase of the load is ____. A. 38.1 Ω C. 23.5 Ω B. 30 Ω D. 22 Ω 822. A 50-HP, three-phase induction motor with full load efficiency of 85% and power factor of 0.80 is connected to a three phase, 480 V system. The equivalent star connected impedance that can replace this motor is ____ A. C. B. D. 823. Three equal impedances of (20 + j20) ohms re connected in delta to 240 V, three-phase, 60 Hz line. Determine the capacitance of an ideal condenser in wye so that the overall power factor is 0.8 lagging. A. 16.58 μF C. 38.53 μF B. 49.74 μF D. 83.74 μF
824. Find the average power absorbed by a balance three phase load in an ACB circuit in which one line voltage is V and one line current to the load is A. A. 1337 W C. 1719 W B. 1122 W D. 1122 W
831. A 100 KVA balanced three phase load operates at 0.65 power factor lagging at 450 V. If power is measured by two wattmeters, what will be the reading of each wattmeter? A. 20,000 W & 45,000 W C. 10,563 W & 54,437 W B. 25,000 W & 40,000 W D. 65,000 W & 0 W
825. A balanced delta connected load having impedance per phase of ohms is supplied from a balanced 3-phase, 240 V source. Determine the total real power. A. 6824 W C. 7416 W B. 6912 W D. 6740 W
832. The two wattmeter method is applied to a three phase, three-wire, 100 V, ABC system with the meters in lines B and C, W B = 836 watts and WC = 224 watts. What is the impedance of the balanced delta-connected load? A. C. B. D.
826. A balanced three-phase load draws 20 kW at 0.447 pf lagging from a 230 V, 60 Hz three phase transmission line. Find the readings of the two wattmeters properly connected to measure power. A. 18.45 kW, 1.55 kW C. 21.55 kW, -1.55 kW B. 14.25 kW, 5.75 kW D. 25.75 kW, -5.75 kW
833. Two wattmeters are connected are for the two wattmeter method with current coils in lines A and B of a 208 V, ABC circuit that has a balanced delta load. If the meter readings arte 6 kW and -3 kW respectively, find the load impedance per phase. A. C. B. D.
827. A 25 HP induction motor is operating at rated load from a three phase 450 V, 60 Hz system. The efficiency and power factor of the motor are 87% and 90%, respectively. The apparent power in kVA drawn by the motor is ____. A. 23.82 C. 21.44 B. 27.78 D. 19.30 828. A balanced star connected load is supplied from a symmetrical three phase, 400 volts ABC system. The current in each phase is 30 amperes and lags 30° behind the line voltage. What is the total power? A. 18,000 W C. 20,785 W B. 10,393 W D. 31.177 W 829. A balanced delta load with impedances of 15 – j9 ohms is connected to a three phase source by three wires each of which has 2 + j5 ohms impedance. The load phase voltage is 120 V. Find the line voltages of the source. A. 69 V C. 259 V B. 208 V D. 87 V 830. Two-wattmeter method is applied to a three-phase motor running at full load. The two wattmeters indicate 85.5 kW and 34.7 kW, respectively. What is the operating power factor of the motor? A. 87.45% C. 89.49% B. 80.69% D. 94.76%
834. Three equal impedances, each represented by a series R-L circuit are connected to a three phase source. A total power of 7630 watts is measured by the two-wattmeter method. If one wattmeter gives zero deflection, determine the values of R and XL for a line voltage of 230 V. A. 3.2, 10 Ω C. 3.2, 9 Ω B. 5.2, 10 Ω D. 5.2, 9 Ω 835. Three equal impedances of (25 + j30) Ω are connected in wye to 240 V, 60 Hz, three-phase source. Determine the value of the capacitor to be connected in parallel with the load so that the total current drawn by the load is 3 amperes. A. 90 μF C. 70 μF B. 80 μF D. 60 μF 836. A delta-connected load draws 17.28 kW from 240-V, balanced three-phase supply. What is the resistance of the load if the reactance is equal to 5 ohms? A. 5 Ω C. 10 Ω B. 7.5 Ω D. 2.5 Ω 837. Three identical impedances of ohms are connected in star to a threephase, three-wire, 240 V system. The lines between the supply and the load have an impedance 2 + j1 ohms. Find the magnitude of the line voltage at the load. A. 123 V C. 416 V B. 240 V D. 213 V
838. A delta connected load having an impedance of (300 + j210) per phase is supplied from 480 V, three-phase supply through a line having an impedance of (4 + j8) per wire. What is the total power supplied to the load? A. 1418 W C. 454 W B. 473 W D. 1363 W 839. A certain load takes 300 kW at 400 V. A three-phase capacitor bank rated 15 kVA per phase is connected in parallel with the load to raise the power factor of the load to 90% lagging. What is the power factor of the load before correction? A. 99% C. 95% B. 92% D. 88% 840. A factory load draws 100 kW at 75% lagging power factor from a 480 V source. To increase the power factor to 90% lagging, a synchronous motor operating at 80% leading power factor is connected to the load. What is the rating of the motor if it has an efficiency of 80%? A. 54 HP C. 33 HP B. 43 HP D. 35 HP 841. A three-phase, wye-connected induction motor is connected to a 480 V, three-phase supply. It draws a current of 15 amperes at 80% power factor. A delta connected reactance is connected in parallel with the motor and the combination draws 15 amperes. What is the value of the element? A. 57.4 μF C. 28.7 μF B. 122.5 μF D. 245.0 μF 842. A three-phase balanced load is connected across 220 V, three-phase, ACB source. A wattmeter with its current coil in line A and voltage coil across liens A and B reads 800 W. The potential coil is then connected across liens A and C with the current coil in the same line. What is the power factor of the load if the meter reads -800 W? A. 0.5 lagging C. 0.87 lagging B. 0.5 leading D. 0.87 leading 843. In two-wattmeter method, the readings of the wattmeter will be identical when _____. A. load in one of the two phases is zero B. power factor is unity C. power factor is 0.5 D. neutral is earthed 844. A wye-connected, balanced three-phase load draws 75 A from 230 V, 60 Hz source. To measure the total power, two wattmeters are connected in lines A
and C and reads 8,625 W and 17,250 W, respectively. Determine the impedance of the balanced load. A. C. B. D. 845. Two wattmeters are used to measure the power drawn by a balanced threephase load from a 440 V, three-phase source. The wattmeters are connected in lines A and B and reads 10 kW and -2.5 kW. When a capacitor in parallel with the load and the wattmeters reconnected in lines B and C, the wattmeter in line B reads 7.5 kW. What is the power factor of the combined load? A. 33% C. 28% B. 50% D. 72% 846. The ratio of the readings of wattmeters connected to measure the power delivered to an inductive load is 0.75. If the load draws 75 kVA from 440-V supply, determine the impedance per phase of the delta-connected load? A. C. B. D. 847. A balanced three-phase, three-wire, 480 V supply has two loads. The first load is delta connected and takes 30 kW at 80% lagging power factor. The second load is delta connected and uses 24 kVA at 90% leading power factor. Find the readings of the two wattmeters connected in lines A and C. A. 28,940 & 22,660 W C. 30,000 & 21,600 W B. 20,400 & 31,200 W D. 32,680 & 18,920 W H. POWER FACTOR CORRECTION (3-PHASE) 848. EE Board Exam April 1989, October 1989 A three-phase, 60 Hz, 2200 volts induction motor develops 500 HP, 0.8 lagging pf and efficiency of 94%. The power factor is raised to 0.90 lagging by connecting a bank of condensers in delta across the lines. If each of the capacitance unit is built up of four similar 550 V condensers, calculate the required capacitance of each condenser. A. 77.04 μF C. 76.12 μF B. 75.42 μF D. 72.30 μF 849. EE Board Exam October 1987, October 1982 Installed in one of the customer CEPALCO are two single phase transformers each rated 75 kVA are connected V or open delta to serve a 3phase load of 120 kW at 0.8 p.f. lagging. To prevent the overloading of the transformers, determine the size of the capacitor in kVAR. A. 40 C. 39 B. 41 D. 42
850. EE Board Exam October 1983 Three single-phase transformers each rated 75 kVA are banked in delta and supplying a three-phase load drawing 160 kVA at 0.8 lagging power factor. If one transformer is removed for repairs, solve for the minimum amount in kVAR of a capacitor needed to prevent overloading of the remaining units. A. 70.32 C. 72.46 B. 73.64 D. 73.28 851. EE Board Exam October 1982 Two single-phase transformers each rated 75 kVA are connected in V or open delta to serve a 3-phase load of 120 W at 0.8 power factor lagging. Determine the size in kVAR of the capacitor needed to prevent overloading of the transformers. A. 40.25 C. 45.24 B. 41.28 D. 43.50 852. EE Board Exam October 1982 A 150 kVA transformer bank will serve a load expected to draw 135 kW at 0.80 lagging power factor. Solve for the size of the capacitor bank needed to be added in order to prevent overloading of the transformer bank. A. 32.506 kVAR C. 40.391 kVAR B. 35.866 kVAR D. 28.266 kVAR 853. EE Board Exam October 1981 A 3-phase generator has the following 3-phase loads: an inductive load drawing 400 kVA at 0.60 pf power factor and a resistive load drawing 80 kVA at 1.00 power factor. Solve for the size in kVAR of the capacitor bank needed to improve the power factor of the combined loads to 0.85 lagging. A. 120.58 kVAR C. 124.54 kVAR B. 121.68 kVAR D. 122.82 kVAR 854. EE Board Exam April 1986 A short, 3-phase, 3-wire transmission line has a receiving end voltage of 4,160 V phase to neutral and serving a balanced 3-phase load of 998.400 volt-amperes at 0.82 pf lagging. At the receiving end the voltage is 4600 V., phase to neutral and the pf is 0.77 lagging. Solve for the size in kVAR of a capacitor needed to improve the receiving end pf to 0.9 lagging maintaining 4160 V. A. 181 C. 172 B. 175 D. 178 855. REE Board Exam October 1996 A 132 kV line, three-phase system delivers 70.7 MVA of a balanced delta load of power factor 70.7%. Determine the reactance necessary in order to attain unity power factor.
A. 1,092 Ω B. 965 Ω
C. D.
1,142 Ω 1,045 Ω
856. EE Board Exam October 1980 A balanced 500 kVA, 3-phase, 440 volt, 60 Hz, inductive load operates at a pf of 75%. Determine the total capacitive kVAR required improving the pf to 95%. A. 207.46 C. 210.75 B. 176.42 D. 192.21 857. EE Board Exam October 1984 A balanced 3-phase load draws 150 A phase current at 7.5 kV phase to neutral, 0.891 power factor lagging. It is desired to raise the power factor to 0.96 leading. Solve for the amount of capacitor kVAR needed to achieve such pf. A. 2273 kVAR C. 2509 kVAR B. 2409 kVAR D. 2365 kVAR 858. EE Board Exam April 1981 A 3-phase, 3-wire, short transmission line has a resistance of 3 ohms and a reactance of 8 ohms per wire. At the receiving end, a balanced 3-phase load draws a line current of 60 A, at 13,500 volts line to line, 0.90 power factor lagging. Assuming the receiving end voltage is maintained at 13,500 V, solve for the size in kVAR of capacitors needed to raise the power factor at the receiving end to 0.95 leading. A. 1043.5 C. 1026.5 B. 1154.2 D. 1232.2 859. EE Board Exam April 1981 A three-phase balanced load draws a line current of 80 A at 0.90 lagging power factor. Solve for the minimum size in kVAR of the capacitor bank needed to raise the power factor to 0.96 leading, if the line to line voltage is 13,200 volts. A. 1310.15 C. 1247.54 B. 1338.25 D. 1430.12 860. EE Board Exam October 1990 Two Y-connected, 50° rise induction motors are fed by a 4160 V, line to line, 3-phase 60 Hz motor-control center 20 feet away. Motor 1 drives a 600-hp compressor. The efficiency of this motor is 90% and its power factor is 0.5. Instruments of motor 2 indicate 1730 kW, 277 amperes. Determine the capacity in microfarads per phase of a wye-connected bank that is required to correct the power factor of the load to 0.966 lagging. A. 172.4 μF C. 167.2 μF B. 193.8 μF D. 182.1 μF
861. EE Board Exam April 1993 A star-connected 400 HP (metric), 2000 V, 50 c/s motor works at a power factor of 0.7 lagging. A bank of mesh-connected condensers is used to raise the power factor to 0.93 lagging. Calculate the capacitance of each unit required if each is rated 500 V, 50 c/s. The motor efficiency is 85%. A. 194 μF C. 302 μF B. 225 μF D. 233 μF 862. A delta connected induction motor takes 20 kW at 0.8 pf from a 500 V 60 Hz mains. Three delta connected capacitors are used to raise the pf to 0.95. What is the capacitance of each capacitor in F? A. 22.3 F C. 29.8 F B. 28.7 F D. 38.9 F 863. A three-phase induction motor delivers 150 HP while operating at 80% efficiency and a power factor of 0.8 lagging from 480 V lines. A wye connected power factor correction capacitor is to be installed to improve the overall power factor to 0.9 lagging. Determine the capacitance required per phase. A. 428 μF C. 1283 μF B. 142.6 μF D. 3850 μF G. UNBALANCED POLYPHASE SYSTEMS 864. EE Board Exam April 1982 Given a balanced 3-wire, three-phase system serving the following loads:
Determine the current on line b A. 20.34 A C. B. 22.04 A D.
24.36 A 21.57 A
865. EE Board Exam April 1982 Given the following line voltages and two load impedances:
Solve for the current in line c. A. 17.41 A B. 17.95 A
C. D.
16.62 A 18.46 A
866. EE Board Exam April 1988 Three unequal single-phase loads so connected across the lines of a balanced, 3-phase, 230 volts circuit. The first takes 106 A at 0.78 pf lagging
and is connected across lines 1 & 2. The second takes 142 A, at 0.82 pf lagging and is connected across lines 2 & 3. And the third takes 28.4 kW at 0.77 pf lagging and is connected across lines 3 & 1. Find the three line currents. A. 254.40 A, 211.38 A, 252 A B. 231.26 A, 215.20 A, 268 A C. 254.40 A, 215.20 A, 252 A D. 231.26 A, 211.38 A, 268 A 867. EE Board Exam October 1992 A 120-V per phase, three-phase Y-connected source delivers power to the following delta-connected load:
Solve for the three line currents. A. 12.45 A, 9 A, 22.45 A B. 13.49 A, 9 A, 22.45 A C. 13.49 A, 10 A. 20.22 A D. 12.45 A, 10 A, 20.22 A 868. EE Board Exam October 1985 Given:
Solve for the three line currents Ia, Ib and Ic. A. Ia = 45 A, Ib = 43 A, Ic = 20 A B. Ia = 48 A, Ib = 42 A, Ic = 24 A C. Ia = 45 A, Ib = 42 A, Ic = 20 A D. Ia = 48 A, Ib = 43 A, Ic = 24 A 869. EE Board Exam April 1985 A three phase 230-V circuit serves two single-phase loads, A and B. Load A is an induction motor rated 8 hp, 230 V, 0.70 pf, 0.90 efficiency, which is connected across lines a and b. Load B draws 5 kW at 1.0 pf and is connected across lines b and c. Assume a sequence of a-b-c, solve for the current on line b. A. 42.19 A C. 41.08 A B. 27.74 A D. 34.46 A 870. EE Board Exam April 1980 A factory is supplied by a three-phase, 3-wire system with the following characteristics:
B. Find the line current Ib. A. 145.3 A B. 163.3 A
C. D.
184.6 A 166.5 A
871. EE Board Exam April 1988 Three unequal single-phase loads so connected across the lines of a balanced, 3-phase, 230 volts circuit. The first takes 106 A at 0.78 pf lagging and is connected across lines 1 & 2. The second takes 142 A at 0.82 pf lagging and is connected across 2 & 3. And the third takes 28.4 kW at 0.77 pf lagging. Determine total apparent power. A. 94 kVA C. 78 kVA B. 83 kVA D. 101 kVA 872. REE Board Exam October 1996 The following information is given for a delta-connected load of three numerically equal impedances that differ in power factor. Line voltage = 120 volts. , and . Phase sequence of voltages is a-b-c. Using the phase sequence as a guide, calculate the total power drawn by the load. A. 2,624 W C. 2,564 W B. 2,472 W D. 2,731 W 873. EE Board Exam April 1993 In AC circuit, find the total power in kW in an unbalanced three-phase circuit loaded as follows: Phase I = 120 V, 100 A, unity pf. Phase II = 100 V, 230 A, 80% pf and phase III = 110 V, 85 A, 77% pf. A. 37.6 kW C. 32.8 kW B. 35.3 kW D. 38.2 kW 874. EE Board Exam April 1983 Two single-phase transformers are connected in V (open delta) and serving a delta connected impedance load. Each impedance is equal to . If the transformer voltages impressed on the impedances are , , . Solve for the total kVA drawn by the load. A. 6.23 C. 10.8 B. 8.31 D. 11.3 875. EE Board Exam October 1980, October 1982 Three impedances Zan = 20 + j0, Zbn = 16 + j12, Zcn = 5 – j15 ohms, are connected in wye across a 230 V (line to line), 3-phase, 4-wire source. The phase sequence is a-b-c, counterclockwise. Determine the current passing thru the neutral. A. 7.54 A C. 8.81 A
9.12 A
D.
8.02 A
876. EE April 1981 A wye-connected transformer with neutral connection has balanced voltages of 265 V between lines and neutral. The transformer is serving two single phase motors. Motor A (rated 4 hp, 0.90 efficiency, 0.80 power factor lagging) is connected across line a and neutral. Motor B (rated 3 hp, 0.85 efficiency, 0.85 power factor lagging) is connected across line b and neutral. Solve for the neutral current, using Van as reference vector. A. 20.42 A C. 22.45 A B. 25.37 A D. 23.14 A 877. REE Board Exam October 1998 The loads of a wye connected transformer are: Ia = 10 cis (-30°); Ib = 12 cis 215°; Ic = 15 cis 82°. What is the neutral current? A. 1.04 cis 72.8° C. 0.92 cis 62.5° B. 2.21 cis (-30°) D. 3.11 cis 72.6° 878. EE Board Exam April 1980 A factory is supplied by a three-phase, 3-wire system with the following characteristics: Determine the power consumed by the load. A. 42.75 kW C. 40.23 kW B. 48.78 kW D. 45.12 kW 879. EE Board Exam April 1981 The following voltages and line currents were measured to a 3-phase, 3-wire feeder serving a commercial building: Solve for the real power in kW drawn by the commercial building. A. 402.2 C. 419.5 B. 404.5 D. 421.5 880. EE Board Exam October 1981 A 3-phase, 3-wire load draws the following line currents: , and . If the voltages impressed on the load are balanced 3-phase, having a magnitude of 4140 volts line to line, solve for the total power in kW. A. 556.16 C. 536.54 B. 506.85 D. 520.18 881. EE Board Exam October 1983
Given the following load impedances in delta and the impressed voltages as follows:
What will be the reading of the two wattmeters connected to measure total power. Use line a as the common potential point. A. 3.869 kW, 9.031 kW C. 3.125 kW, 6.778 kW B. 2.546 kW, 8.357 kW D. 4.055 kW, 9.848 kW 882. EE Board Exam October 1984 The 3-phase power supply to a factory has the following measurements:
Solve for the total power drawn. A. 60.2 kW C. B. 56.5 kW D.
58.8 kW 62.4 kW
883. EE Board Exam April 1985 A three-phase 230-V circuit serves two single-phase loads, A and B. Load A is an induction motor rated 8 hp, 230 V, 0.70 pf, 0.90 efficiency, which is connected across lines a and b. Load B draws 5 kW at 1.0 pf and is connected across lines b and c. Assume a sequence of a-b-c, solve for the total power factor of the load. A. 0.907 C. 0.864 B. 0.704 D. 0.886 884. EE Board Exam October 1987 A wound rotor motor, 7.5 HP, 230 volts, 3-phase takes a line current of 18.4 ampere, when operating at rated output at an efficiency of 88%. Calculate the indication on the wattmeter when this is inserted to measure power by the T-method. A. 3.179 kW C. 3.361 kW B. 4.401 kW D. 4.042 kW 885. EE Board Exam October 1994 A wattmeter with its current coil in line 2 and potential coil across lines 2 and 3 is connected to a balanced 3-phase system. The only load supplied is a single phase one connected to lines 1 and 2. This load is known to be inductive. If the wattmeter reads zero watts, determine the power factor of the single-phase load. A. 0.707 C. 0.800 B. 0.866 D. 0.900
886. EE Board Exam April 1984 A balanced 3-phase load draws 75 amperes line current at 230 volts line to line and 0.848 lagging power factor. If the two-wattmeter is used, solve for the readings of the two wattmeters. A. 15.32 kW, 10.02 kW C. 16.42 kW, 8.92 kW B. 17.86 kW, 7.48 kW D. 17.24 kW, 8.10 kW 887. EE Board Exam October 1980 Three equal impedances, each having a resistance of 8 ohms and an inductive reactance of 7 ohms are connected in delta to lines a, b and c of a 240 V, 3-phase, 3-wire line, phase sequence a-b-c. What is the reading of a single-phase wattmeter connected with its current coil in line a and the potential coil across lines b and c? A. 6,180 W C. 6,561 W B. 6,324 W D. 6,004 W 888. EE Board Exam October 1992 A 3-phase feeder carries two lagging balanced loads. The power observed by each is measured by two wattmeter method, giving the following readings: First Load: W1 = 160 kW W2 = 96 kW Second Load: W1 = 90 kW W2 = 48 kW What is the combined kVA load on the feeder? A. 434.68 C. 504.35 B. 462.35 D. 420.12 889. EE Board Exam October 1992 National Power Corporation used two wattmeters to measure 3-phase power of a balanced Y-connected lagging power factor motor loads. Each wattmeter indicates 15.4 kW. The voltage coils are connected across lines 2 and 3, and across lines 1 and 3, respectively. The line to line voltages are 230 volts with V12 leading V23 and the line currents are each 120 A. Calculate the total power supplied. A. 37.44 kW C. 39.67 kW B. 30.72 kW D. 34.88 kW 890. EE Board Exam April 1980 A factory is supplied by a three-phase, 3-wire system with the following characteristics: A. B.
0.934 lagging 0.908 lagging
C. D.
0.892 lagging 0.866 lagging
891. EE Board Exam October 1981 A 3-phase, 3-wire load draws the following line currents:
, and . If the voltages impressed on the load are balanced 3-phase, having a magnitude of 4140 volts line to line, solve for the power factor of the load. A. 0.976 C. 0.982 B. 0.999 D. 0.906 892. EE Board Exam April 1995 Three unequal single-phase induction motor loads are connected across the lines and neutral conductor of a balanced, 3-phase, 350 volts circuit. The line to neutral voltages is each 202 volts. The first load takes 20 kW at 0.82 power factor, the second takes 28 kW at 0.75 power factor, and the third takes 36 kW at 0.80 power factor. What is the current in the neutral conductor? A. 105.5 amps C. 125.4 amps B. 86.6 amps D. none of these 893. For an unbalanced load which connection is suitable A. 3 wire open delta B. 4 wire star connection C. 3 wire delta connection D. 3 wire star connection 894. What is the minimum number of wattmeters required for measuring power of a three phase balanced load? A. two C. one B. four D. three 895. The power is to be measured for a balanced delta connected load whose terminals cannot be opened. How many wattmeters do you need? A. four C. two B. one D. three 896. What is the minimum number of wattmeters required to measure unbalanced power for a three-phase system? A. two C. three B. four D. one 897. In two wattmeter method, the readings of the wattmeter will be identical when A. load in one of the phases is zero B. power factor is unity C. power factor is 0.5 D. neutral is earthed 898. Two wattmeters can be used to measure 3-phase for a
A. B. C. D.
balanced and unbalanced load unbalanced load only balanced load only unity power factor only
899. In 2 wattmeter method, the reading of one of the wattmeter will be zero when A. power factor is unity B. power factor is 0.5 C. load in one of the phases is zero D. a neutral wire is not provided 900. For a 3 phase unbalanced load A. the power factor of each phase will be in proportional to the load B. the power factor of each phase will be the same C. the power factor of at least one of the phase must be leading D. the power factor of each phase may be different 901. A wattmeter is installed in a balanced 3-phase system. The wattmeter will measure R Y B
A. B.
total power real power
C. D.
active power reactive power
902. A three-phase, three-wire, 240 V, CBA system supplies power a wyeconnected load with impedances of , . Find the total power. A. 1,553 W C. 1,883 W B. 2,589 W D. 2,104 W 903. A 100 V, balanced three-phase source has two single-phase loads. The first load has an impedance of (5 + jX) ohms and connected across lines A and B. The second load is connected across B and C and has an impedance of (R – j2) ohms. Determine the values of R and X, if the current in line B is A and the ratio of X to R is 1.5. A. 2 Ω, 3 Ω C. 4 Ω, 6 Ω B. 3 Ω, 4.5 Ω D. 5 Ω, 7.5 Ω 904. Three – single phase loads are connected between lines of a 280 V, balanced three phase source. The currents measured in lines B and C are:
A, component of the currents? A. A B. A
A. What is the negative sequence C. D.
A A
905. Two of the three unbalanced currents are given for an unbalanced, threephase system. Find the positive sequence of phase B current of the neutral current is A. A. A C. B. A D. A 906. The phase b voltage and the phase b current of a balanced 3-phase system are: V = 220 sin (t + 210°) and I = 10 sin (t – 180°). What is the power of the system? A. 3300 W C. 1905 W B. 5716 W D. 3810 W 907. Two voltage generators are in series. The voltage being generated are V ab = 50 sin(t - 30°) and Vbc = 100 sin(t + 60°). What is the output voltage Vac? A. 111.83 cis 33.5° C. 145.5 cis 50.1° B. 50 cis 30° D. 150 cis 30°
The two-port network is A. Non reciprocal & passive B. Non-reciprocal & active C. Reciprocal & passive D. reciprocal & active 913. If the two port network is reciprocal, then A. Z12 / Y12 = Z122 – Z11 Z12 B. Z12 = 1/Y22 C. h12 = -h21 D. AD-BC = 0 914. Two networks are cascaded through an ideal buffer. If tr1 & tr2 are the rise times of two networks, then the over-all rise time of the two networks together will be A. √ tr1 tr2 C. tr1 + tr2 B. √ (tr12 +tr22) D. (tr1 + tr2 )/ 2 915. Which one of the following combinations of open circuit voltage and Thevenin’s equivalent resistance represents the Thevenin’s equivalent of the circuit shown in the given figure?
TWO PORT NETWORKS
908. As the poles of a network shift away from the axis, the response A. remain constant C. becomes more oscillating B. becomes less oscillating D. none of these 909. The response of a network is decided by the location of A. Its zeros C. both zeros & poles B. Its poles D. neither zeros nor poles 910. The pole-zero configuration of a network function is shown. The magnitude of the transfer function will A. B. C. D.
Decrease with frequency increase with frequency Initially increase and then decreases with frequency Be independent of frequency
911. Given I1 = 2V1 + V2 and I2 = V1 + V2 the Z-parameters are given by A. 2, 1, 1, 1 C. 1, 1, 1, 2 B. 1, -1, -1, 2 D. 2, -1, 1, 1 912. The short – circuit admittance matrix of a two-port network is as shown
A. B.
1 V, 10 Ω 1 V, 1 kΩ
C. D.
1 mV, 1 kΩ 1 mV, 10 Ω
D. Symmetrical Components 916. REE Board Exam October 1998 If the loads of a wye-connected transformer are: Ia = 10 cis (-30°) Ib = 12 cis 215° Ic = 15 cis 82° What is the phase b positive sequence component? A. 13.4 cis (-32.2°) C. 12.27 cis 208.4° B. 10.2 cis 240° D. 12.27 cis (-31.6°) 917. REE Board Exam March 1998, September 2001 The three unbalanced currents are: Ia = 10 cis (-30°)
Ib = 0 Ic = 10 cis 150° Find the negative sequence current of phase a. A. 8.66 cis 30° C. -5.77 B. 5.77 cis (-60°) D. 5.77
Positive sequence current = 18.4 cis (-31.6°) Negative sequence current = 3.23 cis 168.2° Determine the phase b current. A. 18 cis 215° C. 19 cis 220° B. 15 cis 240° D. 20 cis 225°
918. EE Board Exam October 1984 Given the following currents: Ia = 60 + j0 A Ib = -36 – j48 A Ic = -48 + j36 A Solve for the negative sequence component Ia. A. 8.641 – j1.543 C. 9.751 – j1.464 B. 9.436 + j1.346 D. 8.354 + j1.034
923. REE Board Exam March 1998 The sequence components of phase a current are: Zero sequence current = 0.47 + j1.49 Positive sequence current = 18.4 cis (-31.6°) Negative sequence current = 3.23 cis 168.2° Determine the phase c current. A. 17.5 cis 91° C. 22.5 cis 82° B. 18 cis 215° D. 15 cis 100°
919. REE Board Exam October 1998 The three unbalanced currents are: Ia = 10 cis (-30°) Ib = 0 Ic = 10 cis 150° Find the zero sequence current. A. 3.33 cis 30° C. 5.77 B. 0 D. 3.33
924. EE Board Exam April 1992 Determine the symmetrical components of the line current in line ‘a’ if one of the in-phase impedance of its delta connected load connected across lines ‘ca’ is removed. The delta load with impedance of ohms per phase is supplied from a 220 volts, 60 cycle, 3-phase source. Assume a phase sequence of a-b-c. A. Ia1 = 11 A, Ia2 = 11 A, Ia0 = 0 A B. Ia1 = 7.33 A, Ia2 = 7.33 A, Ia0 = 7.33 A C. Ia1 = 22 A, Ia2 = 22 A, Ia0 = 22 A D. Ia1 = 25.4 A, Ia2 = 12.7 A, Ia0 = 0 A
920. EE Board Exam October 1984 Given the following currents: Ia = 60 + j0 A Ib = -36 – j48 A Ic = -48 + j36 A Solve for the zero component of Ia. A. 10 + j4 C. -8 – j4 B. 8 – j6 D. 12 – j6 921. REE Board Exam October 1997 The sequence currents of phase a current are as follows: Zero sequence current = Positive sequence current = Negative sequence current = Determine the phase a current. A. C. B. D. 922. REE Board Exam October 1998 The sequence components of phase a current are: Zero sequence current = 0.47 + j1.49
925. EE Board Exam April 1991 A star-connected balanced load takes 75 A from a balanced 3-phase, 4-wire supply. If the two supply lines of the fuses are removed determine the symmetrical components of the lines after the fuses are removed. A. I1 = 25 A, I2 = 25 A, I3 = 25 A B. I1 = 25 A, I2 = 50 A, I3 = 0 A C. I1 = 75 A, I2 = 75 A, I3 = 75 A D. I1 = 75 A, I2 = 0 A, I3 = 0 A 926. REE Board Exam September 2000 If the loads of a wye-connected transformer are: Ia = 10 cis (-30°) Ib = 12 cis 215° Ic = 15 cis 82° Find the positive sequence component of phase a current. A. 13.4 cis (-32.2°) C. 12.27 cis 208.4° B. 10.2 cis 240° D. 12.27 cis (-31.6°) 927. The method of symmetrical components is very useful for
A. B. C. D.
solving unbalanced polyphase circuits analyzing the performance of 3-phase electrical machinery calculating currents resulting from unbalanced faults all of the above
928. An unbalanced system of 3-phase voltages having RYB sequence actually consists of A. a positive-sequence component B. a negative-sequence component C. a zero-sequence component D. all of the above 929. The zero-sequence component of the unbalanced 3-phase system of vectors VA, VB and VC is of their vector sum. A. one-third C. two-third B. one-half D. one-fourth 930. In the case of an unbalanced star-connected load supplied from an unbalanced 3-, 3 wire system, load currents will consists of A. positive-sequence components B. negative-sequence components C. zero-sequence components D. only A and B 2
931. In symmetrical components, what is the vector sum of 1 + a + a ? A. 1 C. -1 B. 0 D. infinity 932. REE Board Exam October 1997 The sequence currents of a three phase current are: Zero sequence current = 14.13 cis 17.34° Positive sequence current = 708.26 cis (-31°) Negative sequence current = 2.98 cis 10.06° Determine the phase a current. A. 720 cis (-30°) C. 710 cis 88° B. 730 cis (-15.2°) D. 695 cis 15.2° 933. REE Board Exam April 2001 The three unbalanced currents are: Ia = 10 cis (-30°) Ib = 0 Ic = 10 cis 150° Find the phase B positive sequence current. A. 8.66 A C. 5.77 A B. 5.77 cis 240° A D. 8.66 cis 120° A
934. REE Board Exam September 2002 The phase currents of a three-phase system are: Ia = 100 cis 0° Ib = 80 cis 240° Ic = 91.8 cis 130.9° Find the zero sequence current. A. 90.23 cis 3.68° A B. 270.7 cis 3.68° A C. 34.68 cis (-30.24°) A D. none of the above 935. Given three unbalanced three-phase voltages: Va = 150 + j0 V Vb = -90 – j120 V Vc = -120 + j90 V Determine Va1 A. 142.43 + j12.35 B. 135.32 – j 1.34 C. 145.62 + j13.66 D. 140.23 – j9.32 936.
A. B.
C. D.
