alternating current scholars empire

Average 1. The emf of an AC source is given by 220 2 sin(100 t ) . Find the RMS

voltage and average voltage for one cycle. (A) 220V, 220V (B) 220V, 0V (C) 2202V, 0V (D) none

2. An AC current is given by 1 sinoi i i t then its RMS value will be

(A) 2 20 10.5I I (B) 2 2

0 00.5I I

(C) 0 (D) 0 2I

3. The effective value of current i = 2 sin 100 (t) + 2 sin(100 t + 30°) is:

(A) 2A (B) 2 2 3 (C) 4 (D) None

4. The RMS value of alternating current i = i1 cos(t) + i2 sin(t) will be

(A) 2

1 2

1

2i i (B) 1 2

1

2i i (C) 1 22 2

1 2

1

2i i (D) 1 22 2

1 2

1

2i i

5. Current flowing in a wire is mixture of a DC & AC. The DC component is 10 A and RMS of AC component is 5A. Find the effective current flowing in the circuit. (A) 15A (B) 152A (C) 55A (D) none

6. Average value of alternating current i = I0 sin t for half cycle in terms of is

(A) 0I

(B) 02I

(C) 0

2

I (D) zero

7. From the following graph find Vavg and VRMS values of the wave for one cycle.

(A) ,2

m mRMS

V VV V

(B)

2,

2m m

RMS

V VV V

(C) ,2

m mRMS

V VV V

(D)

2,

2m m

RMS

V VV V

8. Find the root mean square (RMS) voltage for the variation of voltage as shown in the adjacent figure.

(A) 0

7

12V (B) 0

1

3V (C) 03

4

V (D) 0

7

24V

t

V

0

Vm

t (s)

V

0

Vo

Vo/2

PHYSICS/PRAVIN PANDEY/SCHOLARS EMPIRE

ALTERNATING CURRENTSCHOLARS EMPIRE

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PHYSICS

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SCHOLARS EMPIRE

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9. For a square wave having peak value Vo find the average value of voltage for half cycle and RMS value for complete cycle of voltage.

(A) Vavg = Vrms = 2Vo (B) Vavg = Vrms = Vo (C) Vavg = Vrms > Vo (D) Vavg = 0, Vrms = Vo

10. The current in a certain circuit varies with time as shown in figure. Find the average current and the RMS current in in one cycle.

(A) /2, / 3avg o RMS oI I I I (B) /2, / 2avg o RMS oI I I I

(C) 0, / 3avg RMS oI I I (D) 0, / 2avg RMS oI I I

Transformer 11. A step-up transformer increases

(A) current (B) voltage (C) frequency (D) power

12. A transformer connected to 220 V line shows an output of 2 A at 11000 V. The efficiency of the transformer is 100%. The current drawn from the line is (A) 200 A (B) 100 A (C) 500 A (D) 600 A

13. If the ratio of number of turns in the primary and secondary coils of a transformer is 1:25 and input voltage 220 V, then ratio of input power and output will be (A) 2:1 (B) 1:1 (C) 1:2 (D) 1:4

14. A generator produces 100 A of current at 4 KV. The voltage is stepped up to 240 KV by a transformer before being sent on a high-voltage transmission line across a rural area to a city. Assume that the effective resistance of the power line is 30.0 and that the transformers are ideal. (A) The current in the secondary circuit is 5/3 A. (B) The current in the secondary circuit is 6000 A. (C) The power delivered by the source is 400 KW. (D) The power lost in the transmission line is 250/3 W.

t

V

0

Vo

Vo

_

t

i

0

Io

_ Io


SCHOLARS EMPIRE

15. A transformer on a utility pole operates at VP = 8.4 kV on the primary side and supplies electrical energy to a number of nearby houses at VS = 120 V, both quantities being RMS values. The average rate of energy consumption (or dissipation) in the houses served by the transformer is 84 kW. Assume an ideal step-down transformer, a purely resistive load, and a power factor of unity. (A) The turns ratio NP/NS of the transformer is 70. (B) The current in primary and secondary coils are IP = 10 A, IS = 700 A. (C) Resistance in primary and secondary coils are RP = 840, RS = 0.17 (D) None

16. The overall efficiency of a transformer is 90%. The transformer is rated for an output of 9000 watts. The primary voltage is 1000 V. The ratio of turns in the primary to the secondary coil is 5: 1. The iron losses at full load are 700 watts. The primary coil has a resistance of 1 . (A) The voltage in the secondary coil is 200 V (B) the current in the primary coil is 10 A (C) the Joule’s heating loss in the secondary coil is 200 W (D) the resistance of the secondary coil is nearly 0.1

17. In order that eddy current is not developed in the core of a transformer, (A) one must increase the number of turns in the secondary coil (B) one must take a laminated transformer (C) one must make a step-down transformer (D) one must use a weak AC at high potential

18. If the primary coil of a transformer is connected to a battery, then an alternating current is produced in the secondary coil. (A) Yes (B) No (C) Depends on the type of transformers (D) Cannot say

19. When current flows in coil of a transformer, then its core become hot due to (A) eddy current (B) currents in the coil (C) alternating nature of current (D) cannot say

Fundamental 20. In a region of uniform magnetic induction B = 102 tesla, a circular coil of radius

30cm and resistance 2 is rotated about an axis which is perpendicular to the direction of B

and which forms a diameter of the coil. If the coil rotates at 200

rpm the amplitude of the alternating current induced in the coil is (A) 42mA (B) 30mA (C) 6mA (D) 200mA

21. If v1 = 10 sin( t + 30o) and v2 = 20 sin( t + 60o), which of these statements are true? (A) v1 leads v2 (B) v2 leads v1 (C) v1 & v2 are in phase (D) none

22. The phase difference between the alternating current and voltage represented by the equations sin & cos( /3)o oi I t v V t will be

(A) 4 /3 (B) /2 (C) 5 /6 (D) /3


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23. Two AC sources v1 & v2 are connected in series. Find v = v1 + v2, where

1 210cos(50 30 ) & 10cos(50 30 ).v t v t

(A) 10cos(50 )v t (B) 10 3 cos(50 )v t

(C) 10sin(50 )v t (D) 10 3 sin(50 )v t

24. In an AC circuit when a hotwire ammeter is connected, it reads i current if a student uses DC ammeter in place of AC ammeter the reading in the DC ammeter will be: (A) i/2 (B) 2i (C) 0.637 i (D) zero

25. A moving coil voltmeter is connected in parallel to an AC source cos .m t The reading of voltmeter will be:

(A) m (B) m/2 (C) zero (D) none

26. The current in a circuit is given by 10sini t A. Find the minimum time

taken for the current to change from 5A to zero. (A) 1/6 s (B) 1/3 s (C) 1/2 s (D) 1/12 s

27. The variation of the instantaneous current (I) and the instantaneous emf (V) in a circuit is shown in the adjacent figure. Which of the following statement is correct?

(A) The voltage lags behind the current by /3. (B) The voltage leads the current by /3. (C) The voltage and the current are in phase. (D) The voltage leads the current by

28. The phase difference between the current and the electromotive force in an AC circuit is /4 radian. If the frequency is 50 Hz, then the time difference corresponding to this phase difference will be (A) 0.02 sec (B) 2.5 sec (C) 3.5 ms (D) 2.5 ms

Capacitive circuit 29. The correct phasor diagram when an AC source is connected to a capacitor is

(A)

(B)

(C)

(D)

30. In an AC circuit, a capacitor of 1 F is connected to an AC source of angular frequency 1000 rad/sec. The value of capacitive reactance will be (A) 100 (B) 10 (C) 10,000 (D) 1000

t

VI

V , C m

Im

V , C mI

mV , C m

Im

VC

Im,m


SCHOLARS EMPIRE

31. Let f = 50 Hz, and C = 100 µF in an AC circuit containing a capacitor only. If the peak value of the current in the circuit is 1.57 A at t = 0. The expression for the instantaneous voltage across the capacitor will be (A) v = 50 sin (100 t – /2) (B) v = 100 sin (50 t) (C) v = 50 sin 100 t (D) v = 50 sin (100 t + /2)

32. What is the instantaneous voltage across a 2mF capacitor when the current through it is 4sin(200 t /4) A.i

(A) 4sin(200 t /4)Cv (B) 10sin(200 t /4)Cv

(C) 10sin(200 t /4)Cv (D) 10cos(200 t /4)Cv

33. An alternating voltage v = 1002sin(100 t) V is connected to a 1F capacitor through an AC ammeter. What will be the reading of the ammeter? (A) 102mA (B) 10mA (C) 20mA (D) 202mA

Inductive circuit 34. An inductance of negligible resistance whose reactance is 22 at 200Hz is

connected to 200Volt, 50Hz power line. The value of inductance is (A) 0.0175 H (B) 0.175 H (C) 1.75 H. (D) 17.5 H

35. Find the maximum value of current when inductance of 2H is connected to 150V, 50 rad/s supply? (A) 1.5A (B) 1.52 A (C) 3A (D) 32 A

36. In a pure inductive circuit with AC; the curve between frequency & XL is

(A)

(B)

(C)

(D)

37. In a pure inductive circuit with AC ; the curve between frequency &1

LX is

(A)

(B)

(C)

(D)

Resistive circuit 38. In a pure resistance AC circuit, the phase difference between current and

voltage is (A) zero (B) /2 (C) /2 (D) /4

39. An alternating current circuit consists of ohmic resistance only. If the frequency of source is increased, then peak current flowing in the circuit will: (A) increase (B) decrease (C) remain same (D) none

40. A 100 Ω resistor is connected to an AC source 112 sin 250V s t . Find

the energy dissipated as heat during t = 0 at t = 8 ms. (A) 11.52 mJ (B) 5.76 mJ (C) 8.14 mJ (D) 6.02 mJ

XL

XL

XL

XL

1/XL

1/XL

1/XL

1/XL


SCHOLARS EMPIRE

41. A 100 Ω resistor is connected to an AC source 112 sin 250V s t . Find

the energy dissipated as heat during t = 0 at t = 9 ms (A) 11.52 mJ (B) 5.76 mJ (C) 8.14 mJ (D) 6.02 mJ

42. What is the peak voltage across R in the given circuit?

(A) 5V (B) 52 V (C) 3V (D) 32 V

43. In the circuit shown in figure = 100 rad/sec. The switch s is closed at time t = 0 and is opened at t = 14 min. Find the amount of heat produced in resistor.

(A) 60000 J (B) 36000 J (C) 63000 J (D) none

LR circuit 44. For a sine wave in the AC circuit with XL and R is series, the:

(A) voltage across R and XL are in phase. (B) Voltage across R and XL are 180o out of phase. (C) voltage across R leads the voltage across XL by 90o (D) voltage across R lags the voltage across XL by 90o

45. A series LR circuit is connected to an AC source. If at some instance the voltage across the AC source is 130 V and across resistor is 50 V, find the voltage across the inductor at that instance. (A) 120 V (B) 80 V (C) 50 V (D) 130 V

46. An LR circuit has a voltage input of 80cos(100 t) V.v The resulting

current is 20cos(100 t 37 ) Ai . Find the impedance of the circuit.

(A) 1 (B) 2 (C) 22 (D) 4

47. An inductive circuit contains resistance of 10 and an inductance of 2.0 H. If an AC voltage of 120 V and frequency 60 Hz is applied to this circuit, the current would be nearly: (A) 0.8 A (B) 0.48 A (C) 0.16 A (D) 0.32 A

48. A 1/10 H inductor and a 12-ohm resistance are connected in series to a 220 V, 50 Hz AC source. Calculate the phase angle between the current and the source voltage. (A) tan1 (6/5) (B) tan1 (11/5) (C) tan1 (5/6) (D) tan1 (5/11)

49. A circuit consisting of 1 ohm resistance and 0.01 H inductance is connected to a 200 V line of frequency 50 cycles/sec. (A) XL = (B) Z = 3.3 (C) cos = 10/33 (D) none

1.2V 5.8V R

12V

RMS va lues a regiven in the figure

25 3V

50

25 sin t

S


SCHOLARS EMPIRE

50. Find the voltage across the inductor as a function of time.

(A) 6cos(10 )Lv t (B) 6cos(10 53 )Lv t

(C) 6cos(10 106 )Lv t (D) 6cos(10 90 )Lv t

51. An AC-circuit having supply voltage v consists of a resistor of resistance 3 and an inductor of reactance 4 as shown in the figure. The voltage across the inductor at t = T/2 is

(A) 2 V (B) 10 V (C) zero (D) 4.8 V

52. A 200 resistor is connected in series with a 0.2 H inductor. The voltage across the resistor as a function of time is vR = 5cos(1000t) V where t is in seconds. Write the expression for circuit current as a function of time ‘t’. (A) iR = 5cos(1000t) mA (B) iR = 25cos(1000t) mA (C) iR = 5sin(1000t) mA (D) iR = 25sin(1000t) mA

53. In the previous problem, find the voltage across the AC source. (A) = 5cos(1000t) V (B) = 52cos(1000t) V (C) = 5sin(1000t) V (D) = 52sin(1000t) V

54. An AC source of voltage V and of frequency 50 Hz is connected to an inductor of 2H and negligible resistance. A current of RMS value I flows in the coil. When the frequency of the voltage is changed to 400 Hz keeping the magnitude of V the same, the current is now (A) 8I in phase with V (B) 4I and leading by 90° from V (C) I/4 and lagging by 90° from V (D) I/8 and lagging by 90° from V

55. A coil has an inductance of 0.7 H and is joined in series with a resistance of 220 . When an alternating voltage of 220 V, 50 Hz is applied to it. Find the power factor. (A) 1/2 (B) 1/2 (C) 3/2 (D) none

56. A current of 4A flows in a coil when connected to a 12 V DC source. If the same coils is connected to a 12 V, 50 rad/s, AC source, a current of 2.4 A flows in the circuit. Determine the inductance of coil. (A) 0.02 H (B) 0.04 H (C) 0.08 H (D) 0.1 H

57. An iron choke and an electric bulb are connected in series with the AC mains. On introducing a soft iron bar in the coil, the intensity of the light bulb will (A) decrease (B) increase (C) remains same (D) none

58. A choke coil is preferred to a rheostat in an AC circuit as (A) it increases current (B) it increases voltage (C) it increases power (D) it consumes almost zero power

0.3H4

10cos( 53 ) V t o

R XL

v = t10sinI


SCHOLARS EMPIRE

59. When an AC source of emf = o sin(100t) is connected across a circuit, the phase difference between the emf and the current i in the circuit is /4 as shown in figure. If the circuit consists of RC or RL or LC in series, the relationship between the two elements is

(A) R = 1 k, C = 1 F (B) R = 1 k, L = 10 H (C) R = 1 k, C = 10 F (D) R = 1 k, L = 1 H

CR circuit 60. A series RC circuit has VR = 4V and VC = 3V. The RMS value of the applied

voltage is: (A) 52V (B) 4V (C) 3V (D) 5V

61. A series combination of a resistor of resistance R and a capacitor of capacitance C are connected across a source of emf = osin t. The phase angle between emf and current is

(A) tan-1 1

cR (B) tan-1

R

c (C) tan-1 (cR) (D) tan-1

c

R

62. Find v(t) and i(t) across capacitor in the circuit shown in Fig.

(A) 5 2 cos(2 t /4) V (B) 5 2 cos(2 t /4) V

(C) 5 2 sin(2 t /4) V (D) 5 2 sin(2 t /4) V

63. An AC source of emf = 110sin(t /6) V is connected to a CR circuit. The resulting current in the circuit is i = 5sin(t + /6) A. (A) impedance of circuit is 22. (B) the potential difference across capacitor is vC = 553sin(t /3) V. (C) Resistance in the circuit is 11 (D) Average power dissipated in circuit is 137.5 W

64. In a CR circuit connected with AC, if the potential difference of source at an instant is 5 V, the potential difference across capacitor at the same instant is 4 V. The potential difference across R at that instant can be (A) 3V (B) 9V (C) 1V (D) none

65. An AC source of angular frequency is fed across a resistor R and a capacitor C in series. The current registered is I. If now the frequency of source is

t

i

1/8F4

10cos(2 )t


SCHOLARS EMPIRE

changed to /3 (but maintaining the same voltage), the current in the circuit is found to be halved. The ratio of reactance to resistance at the original frequency will be.

(A) 3/5 (B) 5/3 (C) 3/5 (D) 5/3

66. In circuit power factor of box is given 0.5 and power factor of circuit is given3/2 (voltage leading the current through it in both cases). Find the resistance in the box.

(A) 5/3 (B) 53 (C) 5 (D) 15

LC circuit 67. A 10F capacitor is connected with 1H inductance in series with a 50Hz

source of alternating current. Calculate the impedance of the combination. (A) 2.47 (B) 3.47 (C) 4.47 (D) 5.47

68. For the circuit shown in the figure, the RMS current through the inductor is 0.9 A while the RMS current through the condenser is 0.4 A. Hence, the current drawn from the generator is

(A) I = 1.3 A (B) I = 0.9 A (C) I = 0.5 A (D) I = 0.6 A

69. Which of the following may represent the impedance of series LC combination connected to an AC source cosm t .

(A)

(B)

(C)

(D)

LCR circuit 70. In a series LCR circuit an AC source of emf cosm t is applied. Let

, , &L C R mV V V be peak values of voltages across inductor, capacitor,

resistor and the AC source. Also, , , &L C Rv v v be the instantaneous values of voltages across inductor, capacitor, resistor and the AC source. Which among the following is/are correct? (A) L C R mV V V

(B) L C Rv v v

(C) 2 2L C R mV V V

(D) 2 2_ _ _L RMS C RMS R RMS RMSV V V

71. When the frequency of AC is doubled, the impedance of an LCR series circuit (A) is halved (B) is doubled (C) increases (D) none

Box1

Z

Z

Z

Z


SCHOLARS EMPIRE

72. An AC circuit has R = 100, XL = 300 and XC = 200, all in series. The phase difference between current and applied voltage is (A) 0o (B) 37o (C) 45o (D) 90o

73. In the series circuit shown in the adjacent figure, the voltmeter reading will be

(A) 300 V (B) 800 V (C) 8002 V (D) 200 V

74. A series RCL circuit has R = 30, XC = 50, and XL = 90 . The impedance of the circuit is: (A) 30 140j (B) 30 40j (C) 30 40j (D) 30 140j

75. Find the current through AC source for the circuit shown below.

(A) 10cos(200 t 37 ) A (B) 10cos(200 t 37 ) A

(C) 10cos(200 t 53 ) A (D) 10cos(200 t 53 ) A

76. An LCR series circuit with 100 resistance is connected to an AC source of 200 V and angular frequency 300 rad/s. When only the capacitance is removed, the current lags behind the voltage by 60°. When only the inductance is removed, the current leads the voltage by 60°. Calculate the current and the power dissipated in the LCR circuit. (A) 2A, 200W (B) 2A, 100W (C) 4A, 400W (D) 2A, 400W

77. In a series LCR circuit connected to an AC source of emf v = 100 sin(100t) volt, the current is given by i = 100 sin[100t + (/3)] mA. The power dissipated in the circuit is (A) 104 W (B) 2.5 W (C) 10 W (D) 5 W

78. A 300 resistor is in series with a 0.6 H inductor and 1 µF capacitor. Circuit carries an RMS current of 0.2 A with an angular frequency 103 rad/s. (A) The power factor of the circuit is 0.6 (B) Average power consumed by the circuit is 12W (C) Average power dissipated in the resistor is 12 W (D) none

79. A two element series circuit has average power of 200W and power factor 1/2 with current leading the applied voltage. Determine the circuit elements, if the applied voltage is 200cos 800 /6 Vt where t is in s.

(A) R = 50, C = 25µF (B) R = 25, C = 25µF (C) R = 25, C = 50 (D) R = 50, C = 50µF

V300V 300V

800 2cos t

5mF 20mH

50cos(200 ) Vt


SCHOLARS EMPIRE

80. In the circuit, as shown in the figure, if the maximum value of RMS current is 2.2 A, the power factor of the box is

(A) 1

2 (B) 1 (C)

3

2 (D)

1

2

81. The magnitude of impedance of a series LCR circuit is best represented as

(A)

(B)

(C)

(D)

82. The power factor of the circuit is 1/2. The capacitance of circuit can be:

(A) 400 µF (B) 300 µF (C) 500 µF (D) 200 µF

Resonance in LCR Series 83. For highly inductive LCR circuit, what should be done to maximize power

loss? (A) Add C in series (B) Add C in parallel (C) Add L in series (D) none

84. Current leads the emf in sinusoidally driven LCR circuit. What should be done

to increase the power loss in the resistor? By doing so what’ll happen to resonant frequency? (A) Add C in series (B) Add C in parallel (C) Add L in series (D) none

85. A series LCR circuit containing a resistance of 120 has angular resonance frequency 4×105 rad/s. At resonance, the voltages across resistance and inductance are 60 V and 40 V respectively. Find the values of L and C. (A) 0.2 µF (B) 1/32µF (C) 1/32 mH (D)0.2mH,

86. For what value of , vo will be zero.

(A) 10 rad/sec (B) 50 rad/sec (C) 100 rad/sec (D) 150 rad/sec

C (1/ H

220 2cos( ) V t

Z

Z

Z Z

C 0.1H2sin( ) Vt

5mF 20mH

50cos( ) Vt

vo


SCHOLARS EMPIRE

87. A coil, a capacitor and an AC source of RMS voltage 24 V are connected in series. By varying the frequency of the source, RMS current of 6A is observed. If coil is connected to a battery of emf 12 V and internal resistance 4, then current through it in steady state is (A) 2.4 A (B) 1.8 A (C) 1.5 A (D) 1.2 A

88. Power factor of an L-R series circuit is 0.6 and that of a C–R series circuit is 0.5. If the element (L, C, and R) of the two circuits are joined in series the power factor of this circuit is found to be 1. The ratio of the resistance in the L-R circuit to the resistance in the CR circuit is (A) 6/5 (B) 5/6 (C) 4/33 (D) 33/4

89. At what frequency, the input and output voltage vo will be in phase.

(A) 0 (B) 1 Hz (C) 100 Hz (D)

Calculating Impedance of Circuits 90. In the given circuit, the circuit impedance is

(A) 8 (B) 16 (C) 24 (D) 30

91. Determine the input impedance of the circuit.

(A) 0 (B) 3 (C) 8 (D) 82

92. Determine the input impedance of the circuit in figure at = 10 rad/s.

(A) 10 (B) 10 (C) 20 (D) 20


(A) 200 (B) 1002 (C) 2002 (D) 100

0.3H4

30 8j10j

_

7j_

15j8

4 j

F0.5H

18H140

5mF1mF 60


SCHOLARS EMPIRE


(A) 102 (B) 105 (C) 103 (D) 20

95. In figure shown below, the impedance of the circuit is

(A) 5.3 k (B) 7.5 k (C) 10 k (D) 6 k

Miscellaneous 96. A voltage 100cos(50 30 )v t V is applied to a parallel combination of 30

resistor and a 0.5mF capacitor. Find the steady state current through the AC source.

(A) 25

cos(50 67 ) A6

t (B) 25

cos(50 37 ) A6

t

(C) 25

cos(50 67 ) A6

t (D) 25

cos(50 37 ) A6

t

97. In the circuit diagram shown, XC = 100 , XL = 200 and R = 100 . The effective current through the source is

(A) 2 A (B) 2A (C) 0.5 A (D) 22A

98. Determine potential difference across capacitor as a function of time in the circuit shown below. [Emf of AC source is in volts]

(A) 5 2 cos 4 Vt (B) 5 2 sin 4 Vt (C) 5cos 4 Vt (D) 5sin 4 Vt

99. Determine potential difference across capacitor as a function of time in the circuit shown below. [Emf of AC source is in volts]

(A) 12.5cos 4 Vt (B) 12.5sin 4 Vt

(C) 12.5cos(4 82 ) Vt (D) 12.5sin(4 82 ) Vt

100100m

100

20

50 F

2A

2A 15V

RC

Lv = t20 V0sin

v= t10cos( 45 ) o

5H 10mF

v= t10cos( 45 ) o

1.8H

12.5mF


SCHOLARS EMPIRE

100. Determine the RMS value of potential difference across capacitor in the circuit shown below. [Emf of AC source is in volts]

(A) 2.5 V (B) 2.5/2 V (C) 7.5 V (D) 7.5/2 V

101. An AC circuit is shown in the figure. What is the RMS current I2?

(A) 1.4 A (B) 1 A (C) 2 A (D) 2.8 A

102. In the circuit shown, the emf of the AC source is in volts. Find the potential difference across the inductor as a function of time.

1

1

11F10cos( )t

(A) 12 5 cos tan (0.5)t (B) 12 5 cos tan (2)t

(C) 12 5 cos tan (0.5)t (D) 12 5 cos tan (2)t

103. Find the potential difference across the inductor as a function of time.

(A) 78cos(200 37 ) Vt (B) 78sin(200 53 ) Vt

(C) 78sin(200 37 ) Vt (D) 78cos(200 53 ) Vt

104. Find the current through AC in the circuit shown below.

(A) 4sin(10 37 ) Aot (B) 4sin(10 37 ) Aot

(C) 4cos(10 37 ) Aot (D) 4cos(10 ) At

105. In the circuit shown, find the current through AC source.

v= t10cos( 45 ) o 5H

5/144F

0.25H

8mF

v= t50sin( )

I2

100 F

F

60sin(200 ) Vt

F0.5H20sin(10 ) Vt


SCHOLARS EMPIRE

(A) 1sin(10 37 ) At (B) 1sin(10 37 ) At

(C) 1sin(10 53 ) At (D) 1sin(10 53 ) At

106. In the circuit shown, the current measured by ammeter does not depend on R. Then which among the following is/are correct.

(A) C = 1μF (B) C = 2μF (C) Impedence of circuit is 100 (D) Impedence of circuit is 1000

107. Find the resonant angular frequency of the circuit shown in the fig.

(A) 1

LC (B)

2221

1 L C R

LC L C R

(C) 2122

1 L C R

LC L C R

(D) none

108. A series circuit containing inductance L1 and capacitance C1 oscillates at angular frequency . A second series circuit, containing inductance L2 and capacitance C2, oscillates at the same angular frequency. In terms of , what is the angular frequency of oscillation of a series circuit containing all four of these elements? Neglect Resistance. (A) (B) 2 (C) 3 (D) none

18H180

1mF 60300sin(10 ) Vt

R

C

L=

10m

H

A

10 rad/s4

R1L

C

v= tV sin( )o

R2


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1. In the circuit shown, a current 20sin(100 ) Ai t flows through an AC source

of emf 220 2 sin(100 ) Vt . In the first branch, current i1 is π/3 ahead i. in the second branch, current i2 is π/6 behind i.

(a) Find the impedance Z1 and Z2 of both branches. (b) At t = 0.01 s, find i1 & i2.

2. A 750 Hz, 20 volt source is connected to a resistance of 100 , an inductance of 0.1803 henry and a capacitance of 10 F (all in series). Calculate the time in which the resistance (thermal capacity = 2 J/C) will get heated by 10C.

3. Find the values of R1 and R2, if the network shown in figure is to be resonant

at all frequencies. Ans: 1 2

LR R

C

4. An LCR circuit has L = 10 mH, R = 3 and C = 1 F connected in series to a

source of 15 cos(t) volt. Calculate the current amplitude and the average power dissipated per cycle at a frequency that is 10% lower than the resonant frequency.

5. A 200 km long telegraph wire has a capacity of 0.014 F/km. If it carries an alternating current of 50 kCycles/s, what should be the value of an inductance required to be connected in series so that the impedance is minimum

6. Find the condition for potential difference between points a, b to be zero for all frequency in the circuit shown in the figure.

7. Deduce the balance condition for the bridge arrangement shown in figure. D

stands of detector. [Detector D could be AC ammeter or AC voltmeter or headphones].

i1

i2

i

R1L

C

v= tV sin( )o

R2

R1L

C

v= tV sin( )o

R2

ab

SUBJECTIVE


SCHOLARS EMPIRE

8. Two inductors of self inductances L1 and L2 and of resistances R1 and R2 (not

shown here) respectively, are connected in the circuit as shown in the figure. At the instant t = 0, key K is closed, obtain an expression for which the galvanometer will show zero deflection at all times after the key is closed.

9. Deduce the balance condition in the bridge circuit shown below.

10. Three identical inductors L and two identical capacitors C are connected in a

two-loop circuit as shown in figure.

For figure (a) find the a) current in middle inductor. b) angular oscillation frequency of current in other two inductors. For figure (b) find the c) current in middle inductor. d) angular oscillation frequency of current in other two inductors.

G

R1

R2

R3

R4

C

L

R1L1

R2L2

G

K

G

R1

C1

C2

R2

R3

R4

L L LC C

i iL L L

C C

i i

Figure ( )a Figure ( )b


SCHOLARS EMPIRE

1. B 2. A 3. D 4. C 5. C 6. B 7. C 8. D 9. D 10. C 11. B 12. C 13. B 14. ACD 15. ABC 16. ABCD 17. B 18. B 19. A 20. C 21. B 22. C

23. B 24. D 25. C 26. A 27. B 28. D 29. C 30. D 31. A 32. C 33. B 34. A 35. B 36. A 37. B 38. A 39. C 40. B 41. D 42. B 43. C 44. D

45. B 46. D 47. C 48. C 49. ABC 50. C 51. D 52. B 53. B 54. D 55. B 56. C 57. A 58. D 59. C 60. D 61. A 62. A 63. ABCD 64. BC 65. A 66. C

67. C 68. C 69. D 70. BCD 71. D 72. C 73. B 74. B 75. B 76. D 77. B 78. ABC 79. A 80. A 81. B 82. C 83. A 84. B 85. B 86. C 87. C 88. D

89. D 90. C 91. D 92. A 93. C 94. B 95. A 96. A 97. A 98. A 99. C 100. D 101. B 102. A 103. D 104. A 105. A 106. BC 107. C 108. A

1. (a) 1 2

222 2 , 22

3Z Z (b) 1 25 3 A, 5 3 Ai i

2. t = 384 sec

3. 1 2

LR R

C

4. 0.704 A, 0.744 W 5. 0.36 mH 6. R1R2 = L/C 7. 2

2 3 1 4 3 2/ &R R L C R R R LC R

8. 1 2 1 2/ /L L R R

9. R3/R4 = R1/R2 = C2/C1

10. (a) zero (b) 1 / LC (c) 1 / 3LC

OBJECTIVE ANSWERS

SUBJECTIVE ANSWERS


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