ALTERNATING

CURRENT
Objective�Problems
[ Level�1 ]
Resistance, Impedance, Phase 8. The capacity of a pure capacitor is 1 F. In DC circuits, its
Difference and Resonance effective resistance will be
(a) zero (b) infinite
1. Voltage and current in an AC circuit are given by (c) 1 W (d) 1/ 2 W
æ pö æ pö
V = 5 sin ç100pt - ÷ and I = 4 sin ç100pt + ÷ , 9. An alternating emf is applied across a parallel
è 6ø è 6ø combination of a resistance R, capacitance C and an
then inductance L. If I R , I L and I C are the currents through R,
(a) voltage leads the current by 30° L and C respectively, then the diagram which correctly
(b) current leads the voltage by 30° represents, the phase relationship among I R , I L , I C and
(c) current leads the voltage by 60° source emf E, is given by
(d) voltage leads the current by 60° IL IR
2. An inductance of 1 mH, a condenser of 10 mF and a
resistance of 50 W are connected in series. The reactances (a) E (b) E
IR IL
of inductor and condensers are same. The reactance of
IC IC
either of them will be
(a) 100 W (b) 30 W (c) 3.2 W (d) 10 W
IC IR
3. In L-C-R circuit, the capacitance is changed from C to
4C. For the same resonant frequency, the inductance (c) E (d) E
IR IC
should be changed from L to
(a) 2L (b) L/2 (c) L/4 (d) 4L IL IL

4. A 10 W resistance, 5 mH coil and 10 mF capacitor are 10. In an AC circuit containing only capacitance, the current
joined in series. When a suitable frequency alternating (a) leads the voltage by 180°
current source is joined to this combination, the circuit (b) remains in phase with the voltage
resonates. If the resistance is halved, the resonance (c) leads the voltage by 90°
(d) lags the voltage by 90°
frequency
(a) is halved (b) is doubled 11. An L-C-R series circuit is connected to a source of
(c) remains unchanged (d) in quadrupled alternating current. At resonance the applied voltage and
current flowing through the circuit will have a phase
5. The reactance of a 25 mF capacitor at the AC frequency of difference of
4000 Hz is (a) zero (b) p /4 (c) p /2 (d) p
5 5 12. An inductance and a resistance are connected in series
(a) W (b) W
p p with an AC potential. In this circuit
(c) 10 W (d) 10 W (a) the current and the potential difference across the resistance
lead the potential difference across the inductance by phase
6. The frequency for which a 5 mF capacitor has a reactance angle p /2
1 (b) the current and the potential difference across the resistance
of W is given by lag behind potential difference across the inductance by an
1000
p
100 1000 angle
(a) MHz (b) Hz 2
p p
1 (c) the current and the potential difference across the resistance
(c) Hz (d) 1000�Hz lag behind the potential difference across the inductance by
1000
an�angle p .
7. The resonant frequency of a circuit is f. If the capacitance (d) the potential difference across the resistance lags behind the
p
is made 4 times the initial value, then the resonant potential difference across the inductance by an angle but
2
frequency will become the current in the resistance leads the potential difference
(a) f /2 (b) 2f p
(c) f (d) f /4 across�inductance�by
2
Alternating�Current 371

13. The resistance of a coil for DC is 5 W. In case of AC, the 23. In a circuit containing R and L, as the frequency of the
resistance will impressed AC increases, the impedance of the circuit
(a) remain 5 W (b) decrease (a) decreases
(c) increase (d) be zero (b) increases
(c) remains unchanged
14. What will be the approximate resistance offered by a (d) first increases and then decreases
capacitor of 10 mF and frequency 100 Hz?
(a) 160 W (b) 1600 W 24. With increase in frequency of an AC supply, the
(c) 16 W (d) None of these impedance of an L-C-R series circuit
15. In L-R circuit, resistance is 8 W and inductive reactance is (a) remains constant
6 W, then impedance is (b) increases
(a) 2 W (b) 14 W (c) 4 W (d) 10 W (c) decreases
p (d) decreases at first, becomes minimum and then increases
16. In an AC circuit, the current lags behind the voltage by .
3 25. Which of the shown graphs may represent the reactance
The components in the circuit may be of a series L-C combination?
(a) R and L (b) L and C (c) R and C (d) only R Reactance Reactance
17. The reactance of a coil when used in the domestic AC
power supply (220 V, 50 cycles per second) is 50 W. The
inductance of the coil is nearly (a) (b)
Frequency Frequency
(a) 2.2�H (b) 1.6�H (c) 0.22�H (d) 0.16�H
18. Which of the following curves correctly represent the
variation of capacitive reactance ( XC ) with frequency Reactance Reactance
( f )?
(c) (d)
(a) XC (b) XC Frequency Frequency

f f

Current, Voltage, RMS and

(c) XC (d) XC Average Values
f f 26. An alternating voltage is connected in series with a
resistance R and an inductance L. If the potential drop
19. A series L-C-R circuit is operated at resonance. Then
across the resistance is 200 V and across the inductance is
(a) voltage across R is minimum
(b) impedance is minimum 150 V, then the applied voltage is
(c) impedance is maximum (a) 350�V (b) 250�V
(d) current amplitude is minimum (c) 500�V (d) 300�V
27. An alternating voltage E = 200 2 sin (100t ) is connected
20. The value of current at resonance in a series L-C-R circuit
to a 1 mF capacitor through an AC ammeter. The reading
is affected by the value of
of the ammeter shall be
(a) R only (b) C only (c) L only (d) L,C and R
(a) 10�mA (b) 20�mA
21. A coil having an inductance of 1/x H is connected in (c) 40�mA (d) 80�mA
series with a resistance of 300 W. If 20 V and a 200 Hz
28. In the circuit shown, the AC source has voltage
source are impressed across the combination, the value of
V = 20cos (wt ) volt with w = 2000 rad/s, the amplitude of
the tangent of the phase angle between the voltage and
the current will be nearest to
the current is
5 4 3 4
(a) (b) (c) (d) 6W
4 5 4 3
22. In an AC circuit, a resistance of R W is connected in series
with an inductance L. If phase angle between voltage and 5 mH , 4 W 50 mF
current be 45°, the value of inductive reactance will be
(a) R /4 (a) 2�A
(b) R /2 (b) 3.3�A
(c) R (c) 2 / 5A
(d) cannot be found with the given data (d) 5A
372 Objective Physics�Vol.�2

29. The rms voltage of the waveform shown is 36. The voltage across a pure inductor is represented in
Y
figure. Which one of the following curves in the figure
will represent the current?
+ 10 V

0 t
t
– 10

(a) 10�V (b) 7�V

Reactance Reactance
(c) 6.37�V (d) None�of�these

30. The output sinusoidal current versus time curve of a

(a) (b)
rectifier is shown in the figure. The average value of Frequency Frequency
output current in this case is
Reactance Reactance
Current

(c) (d)
Frequency Frequency
I0

Time
37. In the circuit shown rms current is 11 A. The potential
I
(a) zero (b) 0 difference across the inductor is
2
2I 0 200 V
(c) (d) I 0 V
p L R�= 20 W
31. The instantaneous current in an AC circuit is C
i = 2 sin ( 50t + p /4 ). The rms value of current is
(a) 2 A (b) 50�A
(c) 90�A (d) 1�A 220 V, 50 Hz
32. A 20V AC is applied to a circuit consisting of a resistance (a) 220�V (b) 0�V (c) 300�V (d) 200�V
and a coil with a negligible resistance. If the voltage
38. An alternating voltage E (in volt) = 200 2 sin (100t ) is
across the resistance is 12 V, the voltage across the coil is
connected to a 1 mF capacitor through an AC ammeter.
(a) 16�V (b) 10�V
(c) 8�V (d) 6�V
The reading of the ammeter shall be
(a) 10�mA (b) 20�mA (c) 40�mA (d) 80�mA
33. An L-R circuit has R = 10 W and L = 2 H. If 120 V, 60 Hz
39. The peak value of an alternating emf E given by
AC voltage is applied, then current in the circuit will be
(a) 0.32�A (b) 0.16�A E = E 0 cos wt
(c) 0.48�A (d) 0.80�A is 10 V and frequency is 50 Hz. At time t = (1/ 600) s, the
instantaneous value of emf is
34. In a series L-C-R circuit, the voltage across resistance,
capacitance and inductance is 10 V each. If the (a) 10�V (b) 5 3 V (c) 5�V (d) 1�V
capacitance is short circuited, the voltage across the 40. An alternating voltage is given by
inductance will be
10 e = e1 sin wt + e2 cos wt
(a) V
2 Then, the root mean square value of voltage is given by
(b) 10�V e1 e2 e12 + e22
(c) 10 2 V (a) e12 + e22 (b) e1 e2 (c) (d)
2 2
(d) 20�V
35. In an L-C-R series circuit, the AC voltage across R, L and 41. An AC voltage is given by
C come out as 10 V, 10 V and 20 V respectively. The 2pt
E = E 0 sin
voltage across the entire combination will be T
(a) 30�V Then the mean value of voltage calculated over any time
(b) 10 3 V interval of T/2 second
(c) 20�V (a) is always zero (b) is never zero
(d) 10 2 V (c) is always (2E0 /p ) (d) may be zero
Alternating�Current 373

Power Consumption and 51. The impedance of a circuit consists of 3 W resistance and
4 W reactance. The power factor of the circuit is
Heat Generation (a) 0.4 (b) 0.6 (c) 0.8 (d) 1.0
42. An AC supply gives 30 V rms which passes through a 52. In an AC circuit V0 , I 0 and cos q are voltage amplitude,
10W resistance. The power dissipated in it is current amplitude and power factor respectively, the
(a) 90 2 W (b) 90 W power consumption is
(c) 45 2 W (d) 45 W 1 æ 1ö
(a) V0 I 0 cos q (b) ç ÷ V0 I 0 cos q
2 è 2ø
43. The average power dissipated in a pure inductor of
inductance L when an AC current is passing through it, is æ 1ö
(c) V0 I 0 cos q (d) ç ÷ V0 I 0 cos q
1 1 2 è 2ø
(a) LI 2 (b) LI
2 4
53. Power factor is one for
(c) 2Li 2 (d) zero
(a) pure inductor
44. In an AC circuit, the power factor (b) pure capacitor
(a) is zero when the circuit contains an ideal resistance only (c) pure resistor
(b) is unity when the circuit contains an ideal resistance only (d) Either an inductor or a capacitor
(c) is zero when the circuit contains an ideal inductance only
54. A direct current of 2 A and an alternating current having a
(d) is unity when the circuit contains an ideal inductance only
maximum value of 2 A flow through two identical
45. Two identical electric heaters each marked 1000 W, resistances. The ratio of heat produced in the two
220 V are connected in series. This combination is resistances will be
connected to an AC supply of 220 V. What will be their (a) 1�:�1 (b) 1�:�2 (c) 2�:�1 (d) 4�:�1
combined rate of heating? (Assume that resistance of 55. The power factor of a circuit is
each heater remains constant) (a) Z/R (b) R/Z
(a) 2000�W (b) 1000�W (c) 500�W (d) 250�W (c) R/X (d) X/R
46. An alternating potential V = V0 sin wt is applied across a
æ pö
Miscellaneous Problems
circuit. As a result the current I = I 0 sin çwt – ÷ flows
è 2ø 56. The process by which AC is converted into DC is known as
in it. The power consumed in the circuit per cycle is (a) purification (b) amplification
(c) rectification (d) current amplification
(a) zero (b) 0.5 V0 I 0
(c) 0.707 V0 I 0 (d) 1.414 V0 I 0 57. A choke coil has
(a) high inductance and low resistance
47. In a heating arrangement an alternating current having a (b) low inductance and high resistance
peak value of 28 A is used. To produce the same heat (c) high inductance and high resistance
energy, if the constant current is used, its magnitude (d) low inductance and low resistance
must be
58. L, C and R denote�inductance,�capacitance�and�resistance
(a) about 14 A (b) about 28 A
(c) about 20 A (d) Cannot say respectively. Pick out the combination which does not
have the dimensions of frequency
48. 110 V (rms) is applied across a series circuit having 1 R 1 C
(a) (b) (c) (d)
resistance 11 W and impedance 22 W. The power RC L LC L
consumed is
(a) 275�W (b) 366�W (c) 550�W (d) 1100�W 59. For the series L-C-R circuit shown in the figure, what is
the resonance frequency and the current at the resonating
49. An R-L-C circuit containing a 52 W resistor, a 230 mH frequency?
inductor and a 8.8 mF capacitor is driven by an AC 8 mH
voltage source that has an amplitude of 150 V and
frequency f = 80 Hz. How much average power is
220 V 20 mF
dissipated by this circuit?
(a) 78.6�W (b) Zero (c) 19.6�W (d) 24.8�W 44 W

50. In an L-R circuit, the inductive reactance is equal to the (a) 2500 rad s-1 and 5 2 A
resistance R of the circuit. An emf E = E 0 cos (wt ) is (b) 2500 rad s-1 and 5 A
applied to the circuit. The power consumed in the circuit is 5
(c) 2500 rad s-1 and A
E02 E02 E02 E02 2
(a) (b) (c) (d)
2R 4R 2R 8R (d) 25 rad s-1 and 5 2 A
374 Objective Physics�Vol.�2

60. The figure shows variation of R, X L and X C with 63. Current and voltage in AC are
frequency f in a series L, C, R circuit. Then for what i = i0 sin (wt - p / 4)
frequency point, the circuit is inductive?
and V = V0 sin (wt + p / 4),
XC XL
Then,
(a) X L > XC
(b) R=0
R (c) Both are correct
(d) Both are wrong
f 64. For the circuit shown in the figure, the current through
A B C
(a) A the inductor is 1.6 A, while the current through the
(b) B condenser is 0.4 A. Then,
(c) C C
(d) All�points

61. An AC source of variable frequency f is connected to an

L
L-C-R series circuit. Which one of the graphs in figure
represents the variation of current I in the circuit with
frequency f ?
I I
(a) the current drawn from the source is I = 2 2A
(a) (b) (b) I = 1.65 A
(c) I = 1.2 A
(d) I = 2.0 A
f f
I I 65. In the circuit shown in figure, the supply has a constant
rms value V but variable frequency f. The frequency at
which the voltage drop across R is maximum is
(c) (d)
C L
R
f f 1 mF 1
p p H
62. A constant voltage at different frequencies is applied
across a capacitance C as shown in the figure. Which of ~
200 V
the following graphs correctly depicts the variation of (a) 100 Hz
current with frequency? (b) 500 Hz
(c) 300 Hz
(d) None of the above
Signal 66. Alternating current is transmitted to distant places at
generator V
(a) high voltage and low current
(b) high voltage and high current
A (c) low voltage and low current
(d) low voltage and high current
I I
67. The frequency of a sinusoidal wave
(a) (b) E = 0.40cos [ 2000t + 0.80] would be
(a) 1000 p Hz
(b) 2000 Hz
w w (c) 20 Hz
(d) 1000/p Hz
I I
68. A 220 V AC is more dangerous than 220 V DC, because
(c) (d) (a) the AC attracts
(b) the DC repels
(c) the body offers less resistance to AC
w w (d) peak voltage for AC is much larger than 220 V
Alternating�Current 375

69. In the given figure, a series L-C-R circuit is connected to a 75. Ohm’s law expressed as, E = IR
variable frequency source of 230 V. The impedance and (a) can never be applied to AC
amplitude of the current at the resonating frequency will be (b) applies to AC in the same manner as to DC
(c) always applies to AC circuits when Z is substituted for R
L = 0.5 H C�= 80 mF R�= 40 W (d) tells us that Eeff = 0.707 (Emax ) for AC

76. A choke coil and capacitor are connected in series and the
current through the combination is maximum for AC of
frequency n. If they are connected in parallel, at what
frequency is the current through the combination
(a) 20 W and 4.2 A (b) 30 W and 6.9 A minimum?
(c) 25 W and 5.8 A (d) 40 W and 5.75 A (a) n (b) n/2
(c) 2n (d) None of these
70. Using an AC voltmeter, the potential difference in the
electrical line in a house is read to be 234 V. If the line 77. The rms value of an AC of 50 Hz is 10 A. The time taken
frequency is known to be 50 cycles per sec, the equation by an alternating current in reaching from zero to
for the line voltage is maximum value and the peak value of current will be
(a) 165 sin (200pt ) (b) 234 sin (100pt ) (a) 2 ´ 10–2 s and 14.14 A (b) 1 ´ 10–2 s and 7.07 A
(c) 331 sin (100pt ) (d) 440 sin (200pt ) (c) 5 ´ 10–3 s and 7.07 A (d) 5 ´ 10–3 s and 14.14 A
71. The reciprocal of impedance is called
78. A capacitor is a perfect insulator for
(a) reactance (b) admittance
(c) inductance (d) conductance (a) direct current
(b) alternating current
72. In figure, which voltmeter reads zero, when w is equal to (c) direct as well as alternating current
the resonant frequency of series L-C-R circuit? (d) None of the above
V1 V2
79. In non-resonant circuit, what will be the nature of the
16 mF circuit for frequencies higher than the resonant
10 W 10 m W
frequency?
(a) Resistive
V3 (b) Capacitive
(c) Inductive
(d) None of the above
E = E0 sinw t 80. In the series L-C-R circuit, the voltmeter and ammeter
(a) V1 (b) V2
readings are
400 V 400 V
(c) V3 (d) None of these
V
73. An inductor of 10 mH and a capacitor of 16 mF are
connected in the circuit as shown in figure. The
frequency of the power supply is equal to the resonant R = 50 W L C
frequency of the circuit. Which ammeter will read zero A
ampere?
A1
10 mH
100 V, 50 Hz
16 mF A2 (a) V = 100 V, I = 2 A
(b) V = 100 V, I = 5 A
A3 (c) V = 1000 V, I = 2 A
(d) V = 300 V, I = 1 A
E = E0 sinw t 81. An AC source is connected to a capacitor. The current in
the circuit is I. Now, a dielectric slab is inserted into the
(a) A1 (b) A2
(c) A3 (d) None of these
capacitor, then the new current is
(a) equal to I
74. Frequency of AC mains in India is (b) more than I
(a) 30 cps (b) 50 cps (c) less than I
(c) 60 cps (d) 120 cps (d) may be more than or less than I
 [ Level�2 ]
Only�One�Correct�Option 6. An ideal choke takes a current of 8 A when connected to
an AC source of 100 V and 50 Hz. A pure resistor under
1. Which of the following options is correct?
100 V
the same conditions takes a current of 10 A. If two are
connected in series to an AC supply of 100 V and 40 Hz,
0.2 A then the current in the series combination of above
resistor and inductor is
(a) 10�A (b) 5�A (c) 5 2 A (d) 10 2 A

R 2H C 7. An AC source is connected with a resistance (R) and an

uncharged capacitance (C), in series. The potential
400 V 400 V difference across the resistor is in phase with the initial
(a) R = 400 W, C = 0.5 mF (b) R = 500 W, C = 0.5 mF potential difference across the capacitor for the first time
(c) R = 500 W, C = 1 mF (d) R = 400 W, C = 0.1 mF at the instant (assume that at t = 0, emf is zero).
p 2p p 3p
2. For series L-C-R AC circuit shown in figure, the readings (a) (b) (c) (d)
4w w 2w 2w
of V1 and V3 are same and each equal to 100 V. Then,
where, w is the angular frequency.
V1 V2 V3 8. Current through an AC series L-C-R circuit is 2 A, if
operated at resonant frequency and 1 A if operated at
50% less than resonant frequency. The current (in A) if
the frequency is 100% more than the resonant
frequency, is
200 V, 50 Hz (a) 2 (b) 1
(a) the reading V2 is 200 V (c) 3 (d) Data insufficient
(b) the reading of V2 is 0
(c) the circuit is in resonant mode and resonant frequency is 9. For an AC circuit containing capacitor only, the applied
50�Hz AC voltage waveform is shown in figure.
(d) The inductive and capacitive reactance are equal V

3. When an AC voltage, of variable frequency is applied to b

series L-C-R circuit, the current in the circuit is the same a e t
at 4 kHz and 9 kHz. The current in the circuit is c
maximum at d
(a) 5�kHz (b) 6.5�kHz (c) 4.2�kHz (d) 6�kHz
4. When 100 V DC is applied across a solenoid, a current of For this situation mark the correct statement(s).
1 A flows in it. When 100 V AC is applied across the (a) As V increases from a to b, the charging of capacitor takes
same solenoid the current drops to 0.5 A. If the frequency place
of the AC source is 50 Hz, the impedance and inductance (b) As V increases from a to b, the current in circuit decreases
of the solenoid are from�maximum�to�zero�value
(a) 200 W and 0.55 H (b) 100 W and 0.86 H (c) As V decreases�from b to c,�the�capacitor�discharges
(c) 200 W and 1.0 H (d) 1100 W and 0.93 H (d) As V decreases from b to c charging of capacitor takes place

5. An inductor L and a capacitor C are connected in the 10. In the given figure, which voltmeter will read zero
circuit as shown in the figure. Which ammeter will read voltage at resonant frequency?
zero ampere? V1 V2 V3
L
A1
R L C
C V4
A2

A3
E = E0 sin wt
E = E0 sin wt
(a) A1 (b) A2
(c) A3 (d) None of these (a) V1 (b) V2 (c) V3 (d) V4
Alternating�Current 377

1 15. An AC voltage V = V0 sin 100 t is applied to the circuit,

11. A coil having an inductance of henry is connected in
p the phase difference between current and voltage is found
series with a resistance of 300 W. If 20 V 200 Hz AC p
source is applied across the combination, the phase angle to be , then
4
between the voltage and the current is V, I
5 V I
-1
(a) tan
4
4
(b) tan -1
5 t
-1 3
(c) tan
4
4 p/4
(d) tan -1
3
(a) R = 100 W, C = 1 mF (b) R = 1kW, C = 10 mF
12. In the circuit shown in figure, the AC source gives a (c) R = 10 kW, L = 1 H (d) R = 1 kW, L = 10 H
voltage V = 20 cos ( 2000t ). Neglecting source resistance,
the voltmeter and ammeter readings will be 16. When an alternating voltage of 220 V is applied across a
(approximately) device P, a current of 0.25 A flows through the circuit
and it leads the applied voltage by an angle p/ 2 radian.
10 W
A When the same voltage source is connected across
another device Q, the same current is observed in the
circuit but in phase with the applied voltage. What is the
5 mH 50 mF
current when the same source is connected across a series
combination of P and Q.
1 p
(a) A lagging in phase by with voltage
4 2 4
V 1 p
(b) A leading in phase by with voltage
(a) 4 V, 2.0 A 4 2 4
(b) 0 V, 2A 1 p
(c) A leading in phase by with voltage
(c) 0 V, 1.4 A 2 4
(d) 8 V, 2.0 A 1 p
(d) A leading in phase by with voltage
2 6
13. A signal generator supplies a sine wave of 20 V, 5 kHz to
the circuit shown in the figure. Then, choose the wrong 17. An inductor ( X L = 2W ) a capacitor ( X C = 8 W ) and a
statement. resistance ( R = 8 W ) are connected in series with an AC
source. The voltage output of AC source is given by
1/p mF V = 10 cos (100pt ).
XC = 8 W 8W
A
100 W B
XL = 2 W

20 V, 5 kHz

(a) The current in the resistive branch is 0.2 A

(b) The current in the capacitive branch is 0.126 A
The instantaneous potential difference between points A
(c) Total line current is » 0.283 A and B, when the applied voltage is 3/5th of the maximum
(d) Current in both the branches is same value of applied voltage is
(a) 0 V (b) 6 V
14. A complex current wave is given by (c) 8 V (d) None of these
i = ( 5 + 5 sin 100 pt ) A. Its average value over one time
period is given as 18. A group of electric lamps having a total power rating of
(a) 10 A 1000 W is supplied by an AC voltage
(b) 5 A E = 200 sin ( 310 t + 60° ) . Then, the rms value of the
(c) 50 A circuit current is
(d) zero (a) 10�A (b) 5 2 A (c) 20�A (d) 10 2 A
378 Objective Physics�Vol.�2

19. One 10 V, 60 W bulb is to be connected to 100 V line. 25. Which of the following statement is correct regarding the
The required self inductance of indication coil will be AC circuit shown in the adjacent figure?
( f = 50 Hz) XL = 4 W XC = 4 W R=2W
(a) 0.052�H (b) 2.42�H
(c) 16.2�H (d) 16.2�mH
20. An alternating voltage V = 30 sin 50t + 40 cos 50t is
applied to a resistor of resistance 10 W. The rms value of
current through resistor is
5 10
(a) A (b) A
2 2 V = 100 sin wt
(c) 5 A (d) None of these (a) The rms value of current through the circuit is irms = 5 2 A
21. An alternating voltage V = 140 sin 50t is applied to a (b) The phase difference between source emf and current is
resistor of 10 W. This voltage produces DH heat in the æ 1ö
f = cos-1 ç ÷
resistor in time Dt. To produce the same heat in the same è 3ø
time, required DC current is (c) Average�power�dissipated�in�the�circuit�is�500�W
(a) 14 A (d) None of the above
(b) about 20 A 26. In the given AC circuit, when switch S is at position 1,
(c) about 10 A
the source emf leads current by p/ 6. Now, if the switch is
(d) None of the above
at position 2, then
22. An AC circuit consists of a resistance and a choke coil in L = 3 mH
series. The resistance is of 220 W and choke coils is of 1
0.7 H. The power absorbed from 220 V and 50 Hz, source R
S
connected with the circuit, is
(a) 55�W 2
(b) 110�W C = 1000 mF
(c) 220�W 3
(d) 440�W
V = V0 sin1000t
23. In the series L-C-R circuit, the voltmeter and ammeter p
readings are respectively (a) current leads source emf by
4
V p
200 V 200 V (b) current leads source emf by
3
p
(c) source emf lead current by
R = 50 W L
4
C
p
A (d) source emf leads current by
3

100 V, 50 Hz 27. In the given AC circuit

I1 Xc

(a) V = 200 V, I =4A

(b) V = 150 V, I =2A
(c) V = 100 V, I =5A I2
I R
(d) V = 100 V, I =2A

24. Current in resistance is 1 A, then

R L C
V = V0 sin wt
3V 8V 4V (a) current I 2 and V are is same phase
(b) current I 2 leads I 1 by 90°
(c) current I leads I 2 by q < 90°
Vs
(d) current I leads I 1 by q < 90°

(a) Vs = 5 V 28. Two coils have a mutual inductance 0.005 H. The current
(b) impedance of network is 5W changes in the first coil according to equation
(c) power factor of given circuit is (0.6) lagging (current is I = I 0 sin wt, where I 0 = 10 A and w = 100 p rad/s. The
lagging) maximum value of emf in the second coil is (in volt)
(d) All of the above (a) 2 p (b) 5 p (c) p (d) 4 p
Alternating�Current 379

29. In a certain circuit current changes with time according to 35. In the circuit shown in figure, the AC source gives a
i = 2 t . The root mean square value of current between voltageV = 20 cos ( 2000 t ). Neglecting source resistance,
t = 2 to t = 4s will be the voltmeter and ammeter readings will be
(a) 3 A (b) 3 3 A (c) 2 3 A (d) 3A 6W
A
30. An AC source of angular frequency w is fed across a
resistor r and a capacitor C in series. The current 5 mH, 4W 50 mF
registered is I. If now the frequency of source is changed
w
to (but maintaining the same voltage), the current in the
3 V
circuit is found to be halved. Calculate the ratio of
reactance to resistance at the original frequency w. (a) 1.68 V, 0.47 A (b) 0 V, 0.47 A
(c) 5.6 V, 1.4 A (d) 0 V, 1.4 A
3 2 1 4
(a) (b) (c) (d)
5 5 5 5 36. A pure resistive circuit element X , when connected to an
AC supply of peak voltage 200 V, gives a peak current of
31. An L-C-R series circuit with a resistance of 100 W is 5 A. A second circuit element Y , when connected to the
connected to an AC source of 200 V (rms) and angular same AC supply also gives the same value of peak
frequency 300 rad /s. When only the capacitor is current but the current lags behind by 90°. If the series
removed, the current lags behind the voltage by 60°. combination of X and Y is connected to the same supply,
When only the inductor is removed the current leads the what will be the rms value of current?
voltage by 60°. The average power dissipated in original 10
L-C-R circuit is (a) A
2
(a) 50�W (b) 100�W (c) 200�W (d) 400�W 5
(b) A
2
32. A virtual current of 4 A and 50 Hz flows in an AC circuit 5
containing a coil. The power consumed in the coil is (c) A
2
240 W. If the virtual voltage across the coil is 100 V. Its (d) 5�A
inductance will be
1 1 1 1 37. A 50 Hz, AC source of 20 V is connected across R and C
(a) H (b) H (c) H (d) H
3p 5p 7p 9p as shown in figure. The voltage across R is 12 V. The
voltage across C is
33. In the circuit shown below, what will be the reading of R C
the voltmeter and ammeter?
100 W

V
300 V 300 V
A (a)��8�V
(b)��16�V
(c)��10�V
220 V, 50 Hz (d) not possible to determine unless value of R andC are given
(a) 200 V, 1 A (b) 800 V, 2 A
(c) 220 V, 2 A (d) 220 V, 2.2 A
38. A coil, a capacitor and an AC source of rms voltage 24 V
are connected in series. By varying the frequency of the
34. A circuit contains resistance R and an inductance L in source, a maximum rms current of 6 A is observed. If this
series. An alternating voltage V = V0 sin wt is applied coil is connected to a battery of emf 12 V and internal
across it. The currents in R and L respectively will be resistance 4 W, the maximum current through it will be
R L (a) 2.4�A (b) 1.8�A
(c) 1.5�A (d) 1.2�A
39. In series L-C-R circuit voltage drop across resistance is
8 V and across inductor is 6 V and across capacitor is
12 V. Then,
AC (a) voltage of the source will be leading in the circuit
(a) I R = I 0 cos wt , I L = I 0 cos wt (b) voltage drop across each element will be less than the
(b) I R = - I 0 sin wt , I L = I 0 cos wt applied�voltage
(c) I R = I 0 sin wt , I L = - I 0 cos wt (c) power factor of the circuit will be 3/4
(d) None of the above (d) None of the above
380 Objective Physics�Vol.�2

40. In the L-C-R circuit shown in figure, 2. Current in an AC circuit is given by

XC = 20 W XL = 10 W i = 3 sin wt + 4 cos wt , then
(a) rms value of current is 5 A
R = 10 W (b) mean�value�of�this�current�in�positive�one-half�period
6
will�be
p
(c) if voltage applied is V = Vm sin wt, then the circuit must be
containing�resistance�and�capacitance
V = 400 sin wt
(d) if voltage applied is V = Vm cos wt, then the circuit may
(a) current�will�lead�the�voltage contain�resistance�and�inductance�only
(b) rms value�of�current�is�20�A
(c) power�factor�of�the�circuit�is 1/ 2 3. A tube light of 60 V, 60 W rating is connected across an
(d) voltage�drop�across�resistance�is�200�V AC source of 100 V and 50 Hz frequency. Then
2
(a) an inductance of H may be connected in series
41. If the rms current in a 50 Hz AC circuit is 5 A, the value 5p
of the current 1/300 s after its value becomes zero is 250
(b) a capacitor of mF may be connected in series to it
(a) 5 2 A (b) 5 3 / 2 A (c) 5 / 6 A (d) 5 / 2 A p
4
42. When a voltage measuring device is connected to AC (c) an inductor of H may be connected in series
5p
mains, the meter shows the steady input voltage of 220 V. (d) a resistance of 40 W may be connected in series
This means
(a) input�voltage�cannot�be�AC�voltage,�but�a�DC�voltage 4. In an AC circuit, the power factor
(b) maximum�input�voltage�is�220�V (a) is unity when the circuit contains an ideal resistance only
(c) the�meter�reads�not v but�< v 2>�and�is�calibrated�to�read (b) is unity when the circuit contains an ideal inductance only
(c) is zero when the circuit contains an ideal resistance only
< v2 >
(d) is zero when the circuit contains an ideal inductance only
(d) the�pointer�of�the�meter�is�stuck�by�some�mechanical�defect
5. In an AC series circuit given that, R = 10 W, X L = 20 W
43. To reduce the resonant frequency in an L-C-R series
and X C = 10 W. Then, choose the correct options.
circuit with a generator
(a) Voltage function will lead the current function
(a)�the�generator�frequency�should�be�reduced
(b) Total impedance of the circuit is 10 2 W
(b)�another�capacitor�should�be�added�in�parallel�to�the�first
(c)�the�iron�core�of�the�inductor�should�be�removed (c) Phase angle between voltage function and current function
(d)�dielectric�in�the�capacitor�should�be�removed is�45°
1
(d) Power factor of circuit is
44. An inductor of reactance 1W and a resistor of 2W are 2
connected in series to the terminals of a 6V (rms)
AC source. The power dissipated in the circuit is 6. In the above problem further choose the correct options.
(a)�8�W (b)�12�W (a) The given values are at frequency less than the resonance
(c)�14.4�W (d)�18�W frequency
(b) The given values are at frequency more than the resonance
More�than�One�Correct�Options frequency
(c) If frequency is increased from the given value, impedance of
1. In a R-L-C series circuit shown, the readings of the�circuit�will�increase
voltmeters V1 and V2 are 100 V and 120 V. Choose the (d) If frequency is decreased from the given value, current in the
correct statement(s). circuit may increase or decrease

V2 7. In the circuit shown in figure,

40 W XL = 20 W

2A 100 V
V1
V = 130 V V = V0 sin wt
(a) VR = 80 V (b) X C = 50 W (c) VL = 40 V (d) V0 = 100 V
(a) Voltage across resistor, inductor and capacitor are 50 V,
86.6�V�and�206.6�V,�respectively 8. In L-C-R series AC circuit
(b) Voltage across resistor, inductor and capacitor are 10 V, (a) If R is increased current will decrease
90�V�and�30�V,�respectively (b) If L is increased current will decrease
(c) Power factor of the circuit is 5/13 (c) If C is increased current will increase
(d) Circuit is capacitive in nature (d) If C is increased current will decrease