01/03/2024 23123

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MM : 240 Alternating Current RT-1 Time : 60 Min.

Topics Covered :
Section A:
Alternating Current

Section A

1. The primary and secondary coils of an ideal 4. A pure inductor of 50.0 mH is connected to
transformer have 100 and 500 turns an ac source of 220 V. If the frequency of the
respectively. The magnetic flux linking the source is 50 Hz. Then r.m.s current in the
primary coil is given by ϕ = 40t + 5. The circuit is nearly
output voltage across the secondary coil is (A) 28 A
(all the quantities are in SI units)
(B) 14 A
(A) 2000 V
(C) 12 A
(B) 400 V
(D) 24 A
(C) 200 V
(D) 100 V
5. In a series L-C-R circuit, voltage across
resistor, capacitor and inductor is 20 V each.
2. The average value of the current in given I-t If capacitor is short circuited the voltage
graph, between 0 to T, is across inductor is
(A) 10√– 2V
–
(B) 20√2V
–
(C) 5√2V

(D) 5
V
√2

(A) I0 6. The electric field energy in a capacitor

(B) I0 changes from maximum value to minimum
2 value in 2.0 ms when connected to an AC
(C) I0 source. The frequency of the source is
√2 (A) 125 Hz
(D) I0
(B) 250 Hz
4

(C) 500 Hz

3. In RLC series circuit, assume R = 500 Ω, L = (D) 50 Hz

60 mH, f = 60 Hz and V0 = 30 V. The values
of capacitance, for which average power 7. A series LCR circuit with L = 0.2 H, C = 500
dissipation through resistance R is μF and R = 20 Ω are connected to ac source
maximum and minimum will be respectively of voltage 220 V. Then the Q-factor of the
(A) 100 μF, 100 μF circuit is
(B) 0, 100 μF (A) 0.3
(C) 117 μF, 0 (B) 0.6
(D) 0, 117 μF (C) 1
(D) 0.8
8. The power factor of an R – L circuit is 1
. If 13. Transformers are used in
√3
(A) D.C. circuits only
the frequency of AC is doubled. Then new
power factor of the R – L circuit will be (B) A.C. circuits only
(A) 1 (C) Both D.C. and A.C. circuits
√3
(D) Integrated circuits
(B) 1

(C) 1 14. An AC supply has RMS voltage 30 V which

2 is fed in a pure resistance of 10 Ω. The
(D) 1
average power dissipated in this is
√2
(A) 99 watt
(B) 45 watt
9. In an AC circuit, a resistance of R is (C) 180 watt
connected in series with an inductance L. If
phase angle between voltage and current is (D) 90 watt
π

6
, then the value of inductive reactance will
be 15. The power factor of the circuit shown in
(A) R figure is
2

(B) R

(C) 2R

(D) R

√3

π
10. In series AC circuit, if V = V0 sin(ωt + ) and
6
2π
I = I0 sin(ωt + ) then (A) 0.2
3

(A) Voltage leads current by 2π

radian (B) 0.6
3
(C) 0.8
(B) Voltage lags current by 2π
radian
3 (D) 0.4
π
(C) Voltage leads current by radian
2

(D) Voltage lags current by

π
radian 16. In an AC circuit V and I are given by V = 50
2
sin(100 πt) volt,
π
I = 100 sin[100πt + ]mA.
11. A capacitor of capacitance 10 μF is 3

connected to an a.c. source of 220 V,

10
Hz. The power dissipated in the circuit is
2π

The capacitive reactance is (A) 2.5 W

(A) 104 Ω (B) 5 W
(C) 0.5 W
(B) 10–2 Ω
(D) 1.25 W
(C) 10–4 Ω
(D) 102 Ω 17. An ideal transformer increases the input
current 4 A to 24 A at the secondary. If the
12. In series R-L-C circuit at resonance, which of number of turns in the primary coil is 330,
the number of turns in the secondary coil is
the following is correct?
(A) 60
(B) 65
(C) 55
(D) 45

18. In alternating current circuit, the a.c. meters

(A) 4f2 LC = 0.5
measure
(B) XL – XC = 0 (A) R.M.S. value
(C) Minimum power dissipation occurs at (B) Peak value
resonance
(C) Mean value
(D) Both (1) & (2) are correct
(D) Mean square value
19. The average value of the given current 23. A : Direct current is less dangerous than
waveform from t = 0 to t = 2 T is alternating current.
R : For same voltage rating, direct current
have more peak value than alternating
current.
(A) Both Assertion & Reason are true and
the reason is the correct explanation of
the assertion.
(B) Both Assertion & Reason are true but
the reason is not the correct
explanation of the assertion.
(C) Assertion is true statement but Reason
is false.
(A) I0 (D) Both Assertion and Reason are false
statements.
(B) 0
(C) I 0

T
24. A transformer is used on a 2000 V input line
to deliver 20 A at 120 V at the secondary
(D) I0

2T
coil. If the power efficiency of the transformer
is 80% then the current drawn from the input
line is
20. In pure inductive circuit, current (a.c. circuit) (A) 3 A
(A) Lags behind emf by π rad
2 (B) 2 A
(B) Leads the emf by π
rad (C) 1.5 A
2

(C) Lags behind emf by π

rad (D) 1.25 A
6

(D) Is in phase with applied emf

25. An ac source rated 50 V (rms) supplies a
current of 10 A (rms) to a circuit. The
21. In the circuit shown in figure, what will be the average power delivered by the source
readings of voltmeter V and ammeter A? (A) Must be 500 W
(B) Must be less than 500 W
(C) May be greater than 500 W
(D) May be less than 500 W

26. The phase difference between potential

difference across inductor and potential
difference across capacitor in a series RLC
circuit is
(A) 800 V, 2 A
(A) π
(B) 220 V, 2.2 A
(B) Zero
(C) 300 V, 2 A π
(C)
(D) 100 V, 2 A 2
π
(D)
4

22. If Alternating Current in a circuit is given I =

I0 sin(100πt), then time taken by the current 27. Reactance of a series LCR AC circuit is
to change from zero to peak value will (Here equal to the resistance. The power factor of
I is in ampere and t is in second) the circuit is equal to
(A) 1 s (A) √3
200
2

(B) 1
s (B) –
√2
50

(C) 1
s
(C) 1

100 √2

(D) 1
s (D) 1

600 2

28. The core of a transformer is laminated to

reduce energy losses due to
(A) Resistance in winding
(B) Hysteresis
(C) Eddy currents
(D) None of these
29. A resistor of resistance 100 Ω is connected 34. The r.m.s. value of potential difference V
to an a.c source E = 12 sin (250π s–1 )t volt. shown in the figure between 0 and T is
2
The average power consumed by bulb is
(A) 70 W
(B) 7.2 W
(C) 0.72 W
(D) 72 W

30. Energy dissipates in LCR circuits in: (A) V0

(A) Inductor only (B) V0

(B) Resistor only 2

(C) Capacitor only (C) V0

√2
(D) All of these
(D) V0

31. An alternating voltage V = 60 sin 50t + 80

cos 50t is applied to a resistor of resistance 35. At a frequency ω0 , the reactance of a certain
10 Ω. The r.m.s value of current through the capacitor equal that of certain inductor. If
resistor is frequency changed to 2ω0 , the ratio of
(A) 5√– 2A reactance of inductor to that of the capacitor
(B) 10 A is
(C) 5 A (A) 4 : 1
√2
(B) √– 2 : 1
–
(D) 10√2 A (C) –
1 : 2√2

(D) 1 : 2
32. The rms value of current is 1 A. The rms
value of potential difference between P and
Q is 36. 200
An inductance of (
π
) mH , a
−3
10
capacitance of (
π
)F and a resistance
of 10 Ω are connected in series with an ac
source 220 V, 50 Hz, The phase angle of the
circuit is
(A) π
(A) 5V 6

(B) 7V (B) π

(C) 3V (C) π

3
(D) 4V
(D) π

33. A : An electric bulb is first connected to a DC

source and then to an AC source having the 37. A 12 ohm resistor and 0.038 henry inductor
same peak voltage. Bulb glows with same are connected in series to an ac source
brightness in both the cases. operating 100 V, 50 Hz. The phase angle
R : The peak value of voltage for an AC between the current and voltage source will
source is equal the root mean square be nearly
voltage. (A) 30°
(A) Both Assertion & Reason are true and (B) 60°
the reason is the correct explanation of (C) 90°
the assertion
(D) 45°
(B) Both Assertion & Reason are true but
the reason is not the correct
explanation of the assertion 38. In a series LCR circuit with R = 10 Ω, L = 1 H
(C) Assertion is true statement but Reason and C = 10.1 μF connected across a
is false variable frequency 220 V ac supply then the
resonant frequency and the corresponding
(D) Both Assertion and Reason are false average power transferred to the circuit in
statements one complete cycle at resonant frequency
will be
(A) 50 Hz, 4840 W
(B) 6 Hz, 4800 W
(C) 50 Hz, 2000 W
(D) 60 Hz, 4000 W
39. Which of the following curve best represents 42. If current in a circuit is given by I = a +
variation of impedance with angular bsinωt, then rms value of current will be
frequency of applied source in LCR series (A) −−−−
a +b
2 2

√
circuit? 2

(A) (B) a+b

√2

−−−−−−
(C) 2
b
√a2 +
2

(D) √a2 +b
2

(B)
2

43. Ratio of number of turns in secondary coil to

primary coil in an ideal transformer is 5 : 2. If
the primary voltage is 400 V, then secondary
(C) voltage is
(A) 160 V
(B) 400 V
(C) 1000 V
(D) Zero
(D)

44. A transformer is used to run an electrical

appliance rated 140 W, 24 V from a 240 V ac
mains. The current in the main cable is 0.7
A. The efficiency of transformer is given by
(A) 83.3%
40. The variation of reactance of capacitor with (B) 74.5%
frequency of source is best represented as
(C) 58%
(A)
(D) 65%

45. For a series RLC circuit, R = XL = 2XC. The

impedance of the circuit and phase
difference between V and I will be
(A) √5R –1
(B) 2
, tan (2)

(B) √5R
–1 1
, tan ( )
2 2

–
(C) √5XC , tan
–1
(2)

–
(D) √2R, tan
–1
(3)

(C)
46. If the power factor in an AC circuit changes
1 1
from 2
to 4
then by what percent
impedance will change (approximately) if
resistance remains constant?
(A) Increase by 200 %
(D) (B) Decrease by 200 %
(C) Increase by 100 %
(D) Decrease by 100 %

41. In an AC L-R series circuit, resistance is 6 Ω

and inductive reactance is 8 Ω. Select
correct statement.
(A) Current leads emf by 53°
(B) Current leads emf by 37°
(C) emf leads current by 53°
(D) emf leads current by 37°
47. A : A.C. cannot be measured by an ordinary 52. In an LR circuit discharging current is given
ammeter. by I = I0 e–t/τ , where τ is the time constant of
R : The average value of A.C. over a the circuit. The average current for the
complete cycle is zero. period t = 0 to t = 2τ is
(A) Both Assertion & Reason are true and (A) I [e−1 ]
0

the reason is the correct explanation of e

the assertion (B) I0

2
[e − 1]
(B) Both Assertion & Reason are true but 2e
2

the reason is not the correct (C) I0

[e
2
− 1]
explanation of the assertion e
2

(C) Assertion is true statement but Reason (D) I0

[e − 1]
is false 2e

(D) Both Assertion and Reason are false

statements 53. Two identical bulbs B1 and B2 are
connected in circuit with a capacitor and an
inductor as shown in figure.
48. If the current in a wire changes with time,
−
−
4
according to i = √
3
1/6
(t ) . Mean square
value of current between t = 0 to t = 8 s will
be
(A) 2 A
(B) 4 A
(C) 6 A
(D) 8 A (A) Brightness of both bulbs are same
(B) B2 is brighter than B1
49. A fully charged capacitor of 50 μF with initial (C) B1 is brighter than B2
charge of 10 mC is connected to a coil of self
inductance 5 mH at t = 0. The time at which (D) B2 will not glow, because capacitor
the energy stored in inductor and capacitor offers infinite impedance
is equal, will be
(A) π ms 54. With increase in frequency of an a.c. supply,
(B) 3π
ms the impedance of an LCR series circuit
4

(C) π (A) Remains constant

ms
2
(B) Decreases
(D) π
ms (C) Increases
8

(D) Decreases at first, becomes minimum

and then increases
50. Which of the following statement is incorrect
about AC circuit?
(A) For resonance, the presence of both L 55. The quality factor of RLC ac circuit as shown
and C elements in the circuit is must in in the figure is (neglect mutual induction)
LCR series circuit
(B) The power factor in a LCR series circuit
is a measure of how close the circuit is
to expending the maximum power
(C) The quality factor is the measure of the
sharpness of resonance in series RLC
circuit
(D) In a step up transformer, voltage
changes from low to high and the
current is increased by the same
proportion
−
−−−
(A) 1 2
√
R 3LC
51. The rms value of the emf for the following
−−−
expression of emf is (B) R√LC
π
E = 8 sinωt + 6 sin(ωt+ 2 ) (C) 1
−
−−
6L
– √
(A) 5 √2 V R C

−
−−−
(B) 7 √–
2 V
(D) 1 2LC
√
R 3

(C) 10 V
(D) 10 √–2 V
56. A : Energy is produced when a transformer 59. The primary and secondary windings of a
steps up voltage. transformer have self inductances L1 = 6.0
R : A step-up transformer can be used as an H, L2 = 0.06 H respectively and a coefficient
amplifier. of coupling K = 0.8. If primary current
(A) Both Assertion & Reason are true and increases at the rate of 103 A/s then emf
the reason is the correct explanation of
induced in primary and secondary windings
the assertion
respectively are (there is no load connected
(B) Both Assertion & Reason are true but across the secondary)
the reason is not the correct (A) 6000 V, 60 V
explanation of the assertion
(B) 6000 V, 360 V
(C) Assertion is true statement but Reason
is false (C) 6000 V, 480 V
(D) Both Assertion and Reason are false (D) 6000 V, 48 V
statements
60. In a parallel L - C circuit as shown in the
57. A : Loads are generally inductive in AC figure
circuit in our home.
R : Capacitor can be used to improve power
factor in a circuit containing inductor and
resistor.
(A) Both Assertion & Reason are true and
the reason is the correct explanation of
the assertion
(B) Both Assertion & Reason are true but (A) Current through source i must be
the reason is not the correct greater than iL
explanation of the assertion
(B) Current through source i must be less
(C) Assertion is true statement but Reason
than iC
is false
(D) Both Assertion and Reason are false (C) iL may be greater than i
statements (D) iL must be equal to i

58. A : A resistance is connected to an AC

source. If a capacitor is included in the
series in circuit. The average power
dissipated in the resistance will increase.
R : If a resistance is connected to an AC
source with an inductor in series. The
average power dissipated in the resistance
will increase.
(A) Both Assertion & Reason are true and
the reason is the correct explanation of
the assertion
(B) Both Assertion & Reason are true but
the reason is not the correct
explanation of the assertion
(C) Assertion is true statement but Reason
is false
(D) Both Assertion and Reason are false
statements