Course: Alternating Current

Presented by Kailash Sharma

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 EXERCISE-I
Part-I
(Single Correct type Questions)
1. r.m.s. value of current i = 3 + 4 sin (ωt + π/3) is:
5 7
(A) 5A (B) 17 A (C) A (D) A
2 2
2. The voltage of an AC source varies with time according to the equation,
V = 100 sin 100 πt cos 100π t.
Where t is in second and V is in volt. Then :
(A) the peak voltage of the source is 100 volt
(B) the peak voltage of the source is (100/ 2 ) volt
(C) the peak voltage of the source is 50 volt
(D) the frequency of the source is 50 Hz

3. An alternating voltage is given by: e = e1 sinωt + e2 cosωt. Then the root mean square value of
voltage is given by :
e1e2 e12 + e22
(A) e12 + e 22 (B) e1e 2 (C) (D)
2 2
2t
4. An AC voltage is given by : E = E0 sin
T
Then the mean value of voltage calculated over time interval of T/2 seconds:
(A) is always zero (B) is never zero (C) is (2E0/ π) always (D) may be zero


5. An AC voltage of V = 220 2 sin 100t +  is applied across a DC voltmeter, its reading will be:
 2
(A) 220 2 V (B) 2V (C) 220 V (D) zero

6. In AC circuit when ac 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 :
i
(A) (B) 2i (C) 0.637 i (D) zero
2

7. An AC current is given by I = I0 + I1 sin ωt then its rms value will be

I0
(A) I0 2 + 0.5 I12 (B) I0 2 + 0.5 I0 2 (C) 0 (D)
2

8. The phase difference between current and voltage in an AC circuit is π/4 radian. If the frequency of
AC is 50 Hz, then the phase difference is equivalent to the time difference:
(A) 0.78 s (B) 15.7 ms (C) 0.25 s (D) 2.5 ms

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 9. The effective value of current i = 2sin 10 πt + 2 sin (100 πt + 30°) is:
(A) 2A (B) 2 2 + 3 (C) 4 (D) None of these

10. If I1, I2, I3 and I4 are the respective r.m.s value of the time varying currents as shown in the four
cases I, II, III and IV. Then identify the correct relations.

(A) I1 = I2 = I3 = I4 (B) I3 > I1 = I2 > I4 (C) I3 > I4 > I2 = I1 (D) I3 > I2 > I1 > I4

11. In series LR circuit XL = 3R. Now a capacitor with XC = R is added in series. Ratio of new to old
power factor is
1
(A) 1 (B) 2 (C) (D) 2
2

12. A direct current of 2 A and an alternating current having a maximum value of 2 A flow through two
identical resistances. The ratio of heat produced in the two resistances in the same time interval will
be:
(A) 1 : 1 (B) 1 : 2 (C) 2 : 1 (D) 4 : 1

13. A resistor and a capacitor are connected to an AC supply of 200 volt, 50 Hz in series. The current in
the circuit is 2 ampere. If the power consumed in the circuit is 100 watt, then the resistance in the
circuit is:
(A) 100 Ω (B) 25 Ω (C) 125  75  (D) 400 Ω

14. A coil of inductance 5.0 mH and negligible resistance is connected to an alternating voltage
V = 10 sin (100 t). The peak current in the circuit will be :
(A) 2 amp (B) 1 amp (C) 10 amp (D) 20 amp

15. By what percentage the impedance in an AC series circuit should be increased so that the power
factor changes from (1/2) to (1/4) (when R is constant) ?
(A) 200% (B) 100% (C) 50% (D) 400%

16. If the frequency of the source e.m.f. in an AC circuit is n, the power varies with a frequency :
(A) n (B) 2 n (C) n/2 (D) zero

17. The power in ac circuit is given by P = ErmsIrmscosϕ. The value of cosϕ in series LCR circuit at
resonance is:
1
(A) zero (B) 1 (C) 1/2 (D)
2

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18. The current I, potential difference VL across the inductor and potential difference VC across the
capacitor in circuit as shown in the figure are best represented vectorially as

(A) (B) (C) (D)

19. A 0.21-H inductor and a 88-Ω resistor are connected in series to a 220-V, 50-Hz AC source. The
current in the circuit and the phase angle between the current and the source voltage are
respectively. (Use π = 22/7)
(A) 2 A, tan–1 3/4 (B) 14.4 A, tan–1 7/8
–1
(C) 14.4 A, tan 8/7 (D) 3.28 A, tan–1 2/11

20. A 100 volt AC source of angular frequency 500 rad/s is connected to a LCR circuit with L = 0.8 H,
C = 5µF and R = 10Ω , all connected in series. The potential difference across the resistance is
100
(A) volt (B) 100 volt (C) 50 volt (D) 50 3
2

21. A pure resistive circuit element X when connected to an AC supply of peak voltage 200 V gives a
peak current of 5 A which is in phase with the voltage. A second circuit element Y, when connected
to the same AC supply also gives the same value of peak current but the current lags behind by 90°.
If the series combination of X and Y is connected to the same supply, what will be the rms value of
current ?
10 5 5
(A) amp (B) amp (C) amp (D) 5 amp
2 2 2

22. In an AC circuit, a resistance of R ohm is connected in series with an inductance L. If phase angle
between voltage and current be 45°, the value of inductive reactance will be.
(A) R/4 (B) R/2
(C) R (D) cannot be found with the given data

23. In an AC circuit the potential differences across an inductor and resistor joined in series are
respectively 16 V and 20 V. The total potential difference across the circuit is
(A) 20 V (B) 25.6 V (C) 31.9 V (D) 53.5 V

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24. An AC voltage source V = 200 2 sin 100t is connected across a circuit containing an AC ammeter
(it reads rms value) and capacitor of capacity 1µF. The reading of ammeter is :
(A) 10 mA (B) 20 mA (C) 40 mA (D) 80 mA

25. When 100 V DC is applied across a solenoid, a steady current of 1 A flows in it. When 100 V AC is
applied across the same solenoid, the current drops to 0.5 A. If the frequency of the AC source is
150 3 /π Hz, the impedance and inductance of the solenoid are
(A) 200 Ω and 1/3 H (B) 100 Ω and 1/16 H
(C) 200 Ω and 1.0 H (D) 1100 Ω and 3/117 H

26. If in a series LCR AC circuit, the rms voltage across L, C and R are V 1, V2 and V3 respectively,
then the voltage of the source is always :
(A) equal to V1 + V2 + V3 (B) equal to V1 – V2 + V3
(C) more than V1 + V2 + V3 (D) none of these is true

27. In the series LCR circuit as shown in figure, the voltmeter and ammeter readings are :

(A) V = 100 volt, I = 2 amp (B) V = 100 volt, I = 5 amp

(C) V = 1000 volt, I = 2 amp (D) V = 300 volt, I = 1 amp

28. A series LCR circuit containing a resistance of 120 ohm has angular resonance frequency
4 × 103 rad s–1. At resonance, the voltage across resistance and inductance are 60V and 40 V
respectively. The values of L and C are respectively :
(A) 20 mH, 25/8 µF (B) 2mH, 1/35 µF (C) 20 mH, 1/40µ F (D) 2mH, 25/8 nF

29. In an LCR circuit, the capacitance is made one-fourth, when in resonance. Then what should be the
change in inductance, so that the circuit remains in resonance ?
(A) 4 times (B) 1/4 times (C) 8 times (D) 2 times

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30. A resistor R, an inductor L, a capacitor C and voltmeters V1, V2 and V3 are connected to an
oscillator in the circuit as shown in the adjoining diagram. When the frequency of the oscillator is
increased, upto resonance frequency, the voltmeter reading (at resonance frequency) is zero in the
case of :

(A) voltmeter V1 (B) voltmeter V2

(C) voltmeter V3 (D) all the three voltmeters

1
31. The power factor of the circuit is . The capacitance of the circuit is equal to
2

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

32. When a resistance R is connected in series with an element A, the electric current is found to be
lagging behind the voltage by angle θ1. When the same resistance is connected in series with
element B, current leads voltage by θ2. When R, A, B are connected in series, the current now leads
voltage by θ. Assume same AC source is used in all cases, then :
(A) θ = θ2 – θ1 (B) tan θ = tan θ2 – tan θ1
1 + 2
(C)  = (D) None of these
2

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33. In the circuit, as shown in the figure, If the value of R.M. S current is 2.2 ampere, the power factor
of the box is

1 3 1
(A) (B) 1 (C) (D)
2 2 2

34. When 100 V DC is applied across a solenoid a current of 1A flows in it. When 100 V AC is applied
across the same coil, the current drops to 0.5 A. If the frequency of the AC source is 50 Hz, the
impedance and inductance of the solenoid are:
(A) 100 Ω, 0.93 H (B) 200 Ω, 1.0 H (C) 10 Ω, 0.86 H (D) 200 Ω, 0.55 H

35. Power factor of an L-R series circuit is 0.6 and that of C-R series circuit is 0.5. It 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 C-R circuit is
4 3 3
(A) 6/5 (B) 5/6 (C) (D)
3 3 4

36. In the shown AC circuit phase different between currents I1 and I2 is

 x xL − xC  xL xL − xC 
(A) − tan −1 L (B) tan −1 (C) + tan −1 (D) tan −1 +
2 R R 2 R R 2

37. In a series R-L-C circuit, the frequency of the source is half of the resonance frequency. The nature
of the circuit will be
(A) capacitive (B) inductive (C) purely resistive (D) data insufficient

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38. In a transformer, number of turns in the primary are 140 and that in the secondary arte 280. If
current in primary is 4A, then that in the secondary is-
(A) 4A (B) 2A (C) 6A (D) 10 A

39. The primary of a 3 : 1 step-up transformer is connected to a source and the secondary is connected
to resistor R. The power dissipated by R in this situation is P. If R is connected directly to the
source it will dissipate a power of :
(A) P/9 (B) P/3 (C) P (D) 3P

40. An ideal efficient transformer has a primary power input of 10 kW. The secondary current when the
transformer is on load is 25 A. If the primary : secondary turns ratio is 8 : 1, then the potential
difference applied to the primary coil is
104  82 104  8 104 104
(A) V (B) V (C) V (D) V
25 25 25  8 25  82

41. The core of any transformer is laminated so as to -

(A) Make it light weight
(B) Make it robust and strong
(C) Increase the secondary voltage
(D) Reduce the energy loss due to eddy current

42. For an oscillator subjected to a damping force proportional to its velocity:

(A) the displacement is a sinusoidal function of time
(B) the velocity is a sinusoidal function of time.
(C) the frequency is a decreasing function of time
(D) none of above is true.

43. A bob of simple pendulum is oscillating in a viscous medium. The bob can be assumed to be a
small ball. If we replace the bob with another small ball of same density, but of larger radius
(A) the oscillation die out slowly and have lesser time period.
(B) the oscillation die out faster and have lesser time period.
(C) the oscillation die out slowly and have higher time period.
(D) the oscillation die out faster and have higher time period.

44. A sinusoidal force with a given amplitude is applied to an oscillator. To Maintain the largest
amplitude oscillation the frequency of the applied force should be:
(A) half the natural frequency of the oscillator
(B) the same as the natural frequency of the oscillator
(C) twice the natural frequency of the oscillator
(D) unrelated to the natural frequency of the oscillator

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45. The table below gives the value of the spring constant k, damping constant b, and mass m for a
particle in damped harmonic motion. Which of these takes the longest time for its mechanical
energy to decreases to one-fourth of its initial value ?
k b m k b m
(A) k0 b0 m0 (B) 3k0 2b0 m0
(C) k0/2 6b0 2m0 (D) k0 b0 10m0

46. An RLC circuit has a capacitance of 12 µF, an inductance of 25 mH, and a resistance of 60Ω. The
current oscillates with an angular frequency of:
(A) 1.2 × 103 rad/s (B) 1.4 × 103 rad/s (C) 1.8 × 103 rad/s (D) 2.2 × 103 rad/s

47. An RLC circuit has an inductance of 25 mH and a capacitance of 5.0 µF. The charge on the
capacitor does NOT oscillates but rather decays exponentially to zero. The resistance in the circuit
must be:
(A) greater than or equal to 100 2 Ω
(B) less than 100 2 Ω but greater than 50 2 Ω
(C) less than 50 2 Ω but greater than 25 2 Ω
(D) less than 25 2 Ω but greater than 0

48. Two underdamped oscillators are known to have the same natural frequency ω0. The mass and
damping coefficient of the first oscillator are m1 and b1, and the mass and damping coefficient of
the second oscillator are m2 and b2, respectively. A sinusoidal driving force of Fext = F0 cosωt is
applied to each oscillator. Starting with ω far from ω0, the driving force is tuned in order to observer
resonant behavior. If m1 = 4 m2 and b1 = 2b2, then which one of the following statements
concerning the driven oscillations is correct ?
(A) The resonant peak of the first driven oscillator is higher and narrower than that of the second
oscillator.
(B) The resonant peak of the first driven oscillator is higher and wider than that of the second
oscillator.
(C) The resonant peak of the first driven oscillator is lower and wider than that of the second
oscillator.
(D) The resonant peak of the first driven oscillator is lower and narrower than that of the second
oscillator.

49. A simple pendulum has a time period T if there is no air resistance. If a small air resistance is acting
on the bob as it oscillates,
(A) The time period will be initially more than T and decreases with time.
(B) The time period will be less than T initially and increases with time.
(C) The time period will be less than T and remains constant.
(D) The time period will be more than T and remains constant.

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50. A block is executing damped harmonic oscillation with time period T. Choose correct statement
T
(1) Time taken to go from extreme to mean position is
4
T
(2) Time taken to go from one extreme to another is
2
T
(3) Time taken to go from one extreme to another is less
2
T
(4) Time taken to go from one extreme to another is more than
2

(A) 1, 2 only (B) 1, 2, 3 only (C) 2 only (D) 1, 2, 4 only

2.2
51. A coil has an inductance of H and is joined in series with a resistance of 220Ω. When an

alternating e.m.f. of 220 V at 50 c.p.s. is applied to it, then the wattless component of the rms
current in the circuit is
(A) 5 ampere (B) 0.5 ampere (C) 0.7 ampere (D) 7 ampere

52. An AC voltage source V = V0 sin ω t is connected across resistance R and capacitance C as shown
1
in figure. It is given that R = . The peak current is I0. If the angular frequency of the voltage
C

source is changed to keeping R and C fixed, then the new peak current in the circuit is :
3

I0 I0 I0 I0
(A) (B) (C) (D)
2 2 3 3

53. An LCR series circuit with 100 Ω resistance is connected to an AC source of 200 V and angular
frequency 300 radians per second. When only the capacitance is removed, the current lags the
voltage by 60°. When only the inductance is removed, the current leads the voltage by 60º. Then the
current and power dissipated in LCR circuit are respectively
(A) 1A, 200 watt. (B) 1A, 400 watt. (C) 2A, 200 watt. (D) 2A, 400 watt.

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 Part-II
Previous Year’s JEE Main Questions (2005-2020)
1. A circuit has a resistance of 12 ohm and an impedance of 15 ohm. The power factor of the circuit
will be :
(A) 0.8 (B) 0.4 (C) 1.25 (D) 0.125
[AIEEE-2005]

2. The phase difference between the alternating current and emf is π/2. Which of the following cannot
be the constituent of the circuit?
(A) C alone (B) R, L (C) L, C (D) L alone
[AIEEE-2005]

3. In a series LCR circuit R = 200Ω and the voltage and the frequency of the main supply is 220 V and
50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the
voltage by 30º. On taking out the inductor from the circuit the current leads the voltage by 30º. The
power dissipated in the LCR circuit is
(A) 305 W (B) 210 W (C) W (D) 242 W
[AIEEE-2010]

4. An arc lamp requires a direct current of 10 A at 80 V to function. if it is connected to a 220 V(rms),

50 Hz AC supply, the series inductor needed for it to work is close to :
(A) 0.08 H (B) 0.044 H (C) 0.065 H (D) 80 H
[JEE Main 2016]

5. A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR
circuit. Given that R = 5Ω, L = 25 mH and C = 1000 μF. The total impedance, and phase difference
between the voltage across the source and the current will respectively be:

(A) 10  and tan −1   (B) 10  and tan −1   (C) 7  and tan −1  

5 8 5
(D) 7Ω and 45°
3 3 3
[JEE Main Online 2017]


6. In an a.c circuit, the instantaneous e.m.f and current are given by e = 100sin30t; i = 20sin  30 t − 
 4 
In one cycle of a.c. the average power consumed by the circuit and the wattles current are,
respectively
100 50
(A) 50, 10 (B) ,10 (C) ,0 (D) 50, 0
2 2
[JEE Main-2018]

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 1
7. For an RLC circuit driven with voltage of amplitude vm and frequency 0 = the current
LC
exhibits resonance. The quality factor Q, is given by
0 L 0 R R CR
(A) (B) (C) (D)
R L (0C) 0
[JEE Main-2018]

8. A power transmission line feeds input power at 2300 V to a step down transformer with its primary
windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the
current in the primary of the transformer is 5A and its efficiency is 90%, the output current would
be :
(A) 25 A (B) 50 A (C) 35 A (D) 45 A
[JEE Main-2018]

9. A series AC circuit containing an inductor (20 mH), a capacitor (120 F) and a resistor (60) is
driven by an AC source of 24 V/50 Hz. The energy dissipated in the circuit in 60 s is :
(A) 2.26 × 103 J (B) 3.39 × 103 J (C) 5.65 × 102 J (D) 5.17 × 102 J
[JEE Main-2019]

10. In the following circuit, C = 3/2 µF, R = 20, L = 3/10 H and R1 = 10. Current in L.R1 path is
I1 and C-R2 path I2. The voltage of AC source is given by, V = 2002 sin (100t) volts. The phase
difference between I1 and I2 is:

(A) 60o (B) 30o (C) 90o (D) 0o

[JEE Main-2019]

11. An alternating voltage (t) 220sin100 t volt is applied to a purely resistive load of 50. The time
taken for the current to rise from half of the peak value to the peak value is:
(A) 7.2 ms (B) 5 ms (C) 2.2 ms (D) 3.3 ms
[JEE Main-2019]

12. A circuit connected to an ac source of emf e = e0 sin(100t) with t in seconds, gives a phase
difference of /4 between the emf e and current i. Which of the following circuits will exhibit this ?
(A) RC circuit with R=1 k and C=10F (B) RL circuit with R=1 k  and L=10 mH
(C) RC circuit with R= 1 k  and C = 1F (D) RL circuit with R=1 k  and L=1mH
[JEE Main-2019]

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13. A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output
power of 2.2 kw. If the current in the secondary coil is 10A, then the input voltage and current in
the primary Coil are:
(i) 440 V and 5A (ii) 440 V and 20 A (iii) 220 V and 10A (iv) 220 V and 20A
(A) 748J (B) 700J (C) 374J (D) 350J
[JEE Main-2019]

14. In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the
choke current changes uniformly from 0.25 A to 0 in duration of 0.025 ms. The self–inductance of
the choke (in mH) is estimated to be ………
[JEE Main-2020]

15. In LC circuit the inductance L = 40 mH and capacitance C = 100 F. If a voltage V(t) = 10sin(314t)
is applied to the circuit, the current in the circuit is given as:
(A) 0.52 cos 314 t (B) 10 cos 314 t (C) 5.2 cos 314 t (D) 0.52 sin 314 t
[JEE Main-2020]

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 EXERCISE-II
Part-I
Section-A
(Multiple Correct type Questions)
1. Average power consumed in an A.C. series circuit is given by (symbols have their usual meaning) :
E max 2 R Imax 2 | z | cos 
(A) Erms Irms cos ϕ 2
(B) (Irms) R (C) (D)
2(| z |) 2 2

2. An AC source supplies a current of 10 A (rms) to a circuit, rms voltage of source is 100 V. The
average power delivered by the source :
(A) must be 1000 W (B) may be less than 1000 W
(C) may be greater than 1000 W (D) may be 1000 W

3. In a series LCR circuit with an AC source (Erms = 50 V and v = 50/π Hz), R = 300 Ω , C = 0.02 mF,
L = 1.0 H, Which of the following is correct
(A) the rms current in the circuit is 0.1 A
(B) the rms potential difference across the capacitor is 50 V
(C) the rms potential difference across the capacitor is 14.1 V
(D) the rms current in the circuit is 0.14 A

4. A coil of inductance 5.0 mH and negligible resistance is connected to an oscillator giving an output
voltage E = (10V) sinω t Which of the following is correct
(A) for ω = 100 s–1 peak current is 20 A (B) for ω= 500 s–1 peak current is 4 A
(C) for ω = 1000 s–1 peak current is 2 A (D) for ω = 1000 s–1 peak current is 4 A

5. A pure inductance of 1 henry is connected across a 110 V, 70Hz source. Then correct option are
(Use π = 22/7):
(A) reactance of the circuit is 440 Ω (B) current of the circuit is 0.25 A
(C) reactance of the circuit is 880 Ω (D) current of the circuit is 0.5 A

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6. In the circuit shown in figure, if both the bulbs B1 and B2 are identical :

(A) their brightness will be the same

(B) B2 will be brighter than B1
(C) as frequency of supply voltage is increased the brightness of bulb B1 will increase and that of
B2 will decrease.
(D) only B2 will glow because the capacitor has infinite impedance

7. A circuit is set up by connecting L = 100 mH, C = 5 µF and R =100 Ω in series. An alternating emf
500
of (150 2)vol, Hz is applied across this series combination. Which of the following is correct

(A) the impedance of the circuit is 141.4 Ω
(B) the average power dissipated across resistance 225 W
(C) the average power dissipated across inductor is zero.
(D) the average power dissipated across capacitor is zero.

8. In a series RC circuit with an AC source (peak voltage E0 = 50 V and f = 50 π/ Hz), R = 300Ω,

C = 25µ F. Then :
(A) the peak current is 0.1 A (B) the peak current is 0.7 A
(C) the average power dissipated is 1.5 W (D) the average power dissipated is 3 W

9. In the AC circuit shown below, the supply voltage has constant rms value V but variable frequency
f. At resonance, the circuit :

V
(A) has a current I given by I =
R
(B) has a resonance frequency 500 Hz
(C) has a voltage across the capacitor which is 180° out of phase with that across the inductor
V
(D) has a current given by I =
2
1 1
R + + 
2
 

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10. The overall efficiency of a transformer is 90%. The transformer is rated for an output of 9000 watt.
The primary voltage is 1000 volt. The ratio of turns in the primary to the secondary coil is 5 : 1. The
iron losses at full load are 700 watt. The primary coil has a resistance of 1 ohm.

(i) The voltage in secondary coil is:

(A) 1000 volt (B) 5000 volt (C) 200 volt (D) zero volt

(ii) In the above, the current in the primary coil is :

(A) 9 amp (B) 10 amp (C) 1 amp (D) 4.5 amp

(iii) In the above, the copper loss in the primary coil is:
(A) 100 watt (B) 700 watt (C) 200 watt (D) 1000 watt

(iv) In the above, the copper loss in the secondary coil is:
(A) 100 watt (B) 700 watt (C) 200 watt (D) 1000 watt

(v) In the above, the current in the secondary coil is:

(A) 45 amp (B) 46 amp (C) 10 amp (D) 50 amp

(vi) In the above, the resistance of the secondary coil is approximately:

(A) 0.01 (B) 0.1 (C) 0.2 (D) 0.4

Section-B
(Comprehension type Questions)
Paragraph for Qus 1 to 3
In a series L-R circuit, connected with a sinusoidal ac source, the maximum potential difference
across L and R are respectively 3 volts and 4 volts.
1. At an instant the potential difference across resistor is 2 volts. The potential difference in volt,
across the inductor at the same instant will be:
(A) 3 cos 30° (B) 3 cos 60° (C) 3 cos 45° (D) None of these

2. At the same instant, the magnitude of the potential difference in volt, across the ac source may be
4+3 3 3 3
(A) 4 + 3 3 (B) (C) 1 + (D) 2 +
2 2 2

3. If the current at this instant is decreasing the magnitude of potential difference at that instant across
the ac source is
(A) Increasing (B) Decreasing (C) constant (D) Cannot be said

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 Paragraph for Qus 4 to 6
A current of I = 20 sin (100 πt) ( in amp.) flows through the AC source. The current flows through

two branches. In first branch, current I1 ahead of I.
3


In second branch, current I2 is behind I. The voltage of network is 220 2 sin (100πt)
6

4. Choose the correct circuit diagram.

(A) (B)

(C) (D)

5. At t = 0.01 sec, comment on instantaneous magnitude of I1 and I2

(A) I1 = 5 3 A, I2 = 5 3 A (B) I1 = 5 3 A, I 2 = 5A
(C) I1 = 5 A, I 2 = 5 3 A (D) I1 = 0A, I2 = 20A

6. Impedance of 1st Branch is Z1 and impedance of second branch is Z2.

2 22
(A) Z1 = 22 , Z2 = 22  (B) Z1 = , Z2 = 22 3 
3 6
2
(C) Z1 = 22 2 , Z2 = 22  (D) Z1 = 22 3 , Z2 = 22 2 
3

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 PART-II
(Subjective type Questions)
1. Find the value of an inductance which should be connected in series with a capacitor of 5µF, a
resistance of 10Ω and an ac source of 50 Hz so that the power factor of the circuit is unity.

2. In an L-R series A.C circuit the peak potential difference across an inductance and resistance joined
in series are respectively 12 V and 16V. Find the total potential difference across the circuit.

3. A 50W, 100 V lamp is to be connected to an ac mains of 200 V, 50 Hz. What capacitance is

essential to be put in series with the lamp.

4. An LCR series circuit with 100Ω 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 inductance is removed, the current leads the voltage by 60°. Calculate the current
and the power dissipated in the LCR circuit.

5. A box P and a coil Q are connected in series with an ac source of variable frequency. The emf of
source at 10 V. Box P contains a capacitance of 1µF in series with a resistance of 32 Ω coil Q has a
self-inductance 4.9 mH and a resistance of 68Ω series. The frequency is adjusted so that the
maximum current flows in P and Q. Find the impedance of P and Q at this frequency. Also find the
voltage across P and Q respectively.

6. A series LCR circuit containing a resistance of 120 Ω has angular resonance frequency
4 × 105 rad s–1. At resonance the voltage across resistance and inductance are 60V and 40 V,
respectively. Find the values of L and C. At what frequency the current in the circuit lags the
voltages by 45° ?

7. An inductor (xL = 2Ω) a capacitor (xC = 8Ω) and a resistance (8Ω) is connected in series with an ac
source. The voltage output of A.C source is given by v = 10 cos 100π t.

The instantaneous p.d. between A and B is equal to x × 10–1 volt, when it is half of the voltage
output from source at that instant Find out value of x.

8. A 2000 Hz, 20 volt source is connected to a resistance of 20 ohm, an inductance of 0.125/π H and a
capacitance of 500/ π nF all in series. Calculate the time (in seconds) in which the resistance
(thermal capacity = 100 joule/ºC) will get heated by 10º C. (Assume no loss of heat)

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 9. A series LCR circuit containing a resistance of 120 ohm has angular resonance frequency
4 × 105 rad s–1. At resonance, the voltage across resistance and inductance are 60V and 40 V
respectively. At frequency the current in the circuit lags the voltage by 45º is equal to
x × 105 rad/sec. Find value of x.

10. An LCR circuit has L = 10 mH, R = 150 Ω and C = 1µF connected in series to a source of
150 2 cosω t volt. At a frequency that is 50% of the resonant frequency, calculate the average
power (in watt) dissipated per cycle

11. In the figure shown an ideal alternative current (A.C.) source of 10 Volt is connected. Find half of
the total average power (in watts) given by the cell to the circuit.

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 EXERCISE-III
JEE ADVANCED Previous Year’s Questions
1. An AC voltage source of variable angular frequency ω and fixed amplitude V connected in series
with a capacitance C and an electric bulb of resistance R (inductance zero). When ω is increased :
(A) the bulb glows dimmer (B) the bulb glows brighter
(C) total impedence of the circuit is unchanged (D) total impedence of the circuit increases
[JEE 2010]

2. You are given many resistances, capacitors and inductors. These are connected to a variable DC
voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three
circuits) in different ways as shown in Column II. When a current (steady state for DC or rms for
AC) flows through the circuit, the corresponding voltage V1 and V2. (indicated in circuits) are
related as shown in Column I . Match the two column.
[JEE 2010]
Column-I Column-II
(A) I ≠ 0, V1 is proportional to I (p)

(B) I ≠ 0, V2 > V1 (q)

(C) V1 = 0, V2 = V (r)

(D) I ≠ 0, V2 is proportional to I (s)

(t)

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3. A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without
a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through
the resistor and voltage VC across the capacitor are compared in the two cases. Which of the
following is/are true?
(A) I AR  I BR (B) I AR  I RB (C) VCA  VCB (D) VCA  VCB
[JEE 2011]

4. A series R-C combination is connected to an AC voltage of angular frequency ω = 500 radian/s. If

the impedance of the R-C circuit is R 1.25 , the time constant (in millisecond) of the circuit is
[JEE 2011]

5. In the given circuit, the AC source has ω = 100 rad/s. Considering the inductor and capacitor to be
ideal, the correct choice (s) is(are)

[JEE-2012]
(A) The current through the circuit, I is approximately 0.3 A
(B) The current through the circuit, I is 0.3 2 A.
(C) The voltage across 100 Ω resistor = 10 2 V
(D) The voltage across 50 Ω resistor = 10V

Paragraph for Questions 6 and 7

A thermal power plant produces electric power of 600 kW at 4000 V, which is to be transported to a
place 20 km away from the power plant for consumers' usage. It can be transported either directly
with a cable of large current carrying capacity or by using a combination of step-up and step-down
transformers at the two ends. The drawback of the direct transmission is the large energy
dissipation. In the method using transformers, the dissipation is much smaller. In this method, a
step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the
consumers' end, a step-down transformer is used to supply power to the consumers at the specified
lower voltage. It is reasonable to assume that the power cable is purely resistive and the
transformers are ideal with a power factor unity. All the currents and voltages mentioned are rms
values.

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6. If the direct transmission method with a cable of resistance 0.4 Ω km–1 is used, the power
dissipation (in %) during transmission is :
(A) 20 (B) 30 (C) 40 (D) 60
[JEE ADVANCED_2013]

7. In the method using the transformers, assume that the ratio of the number of turns in the primary to
that in the secondary in the step-up transformer is 1 : 10. If the power to the consumers has to be
supplied at 200V, the ratio of the number of turns in the primary to that in the secondary in the step-
down transformer is :
(A) 200 : 1 (B) 150 : 1 (C) 100 : 1 (D) 50 : 1
[JEE ADVANCED_2013]

8. At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and
alternating current I(t) = I0 cos (ωt,), with I0 = 1A and ω = 500 rad s–1 starts flowing in it with the
initial direction shown in the figure.
7
At t = , the key is switched from B to D. Now onwards only A and D are connected. A total
6
charge Q flows from the battery to charge the capacitor fully. If C = 20µ, R = 10Ω and the battery is
ideal with emf of 50V, identify the correct statement (s)

7
(A) Magnitude of the maximum charge on the capacitor before t = is 110−3 C.
6
7
(B) The current in the left part of the circuit just before t = is clockwise.
6

(C) Immediately after A is connected to D. the current in R is 10A.

(D) Q = 2 × 10–3 C
[JEE (Advanced)-2014]

9. Two inductors L1 (inductance 1 mH, internal resistance 3Ω) and L2 (inductance 2mH, internal
resistance 4Ω), and a resistance R (resistance 12Ω) are all connected in parallel across a 5 V battery.
The circuit is switched on at time t = 0. The ratio of the maximum to the minimum current (Imax/Imin)
drawn from the battery is
[JEE (Advanced)-2016]

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10. In the circuit shown, L = 1µH, C = 1µF and R = 1kΩ. They are connected in series with an a.c.
source V = V0 sin ωt as shown. Which of the following option is/are correct ?

(A) At ω ∼ 0 the current flowing through the circuit becomes nearly zero
(B) The current will be in phase with the voltage if ω = 104 rad s–1.
(C) At ω >> 106 rad s–1, the circuit behaves like a capacitor
(D) The frequency at which the current will be in phase with the voltage is independent of R
[JEE (Advanced)-2017]

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 ANSWER KEY
EXERCISE-I
Part-I
1. B 2. C 3. D 4. D 5. D 6. D 7. A 8. D 9. D 10. B
11. D 12. C 13. B 14. D 15. B 16. B 17. B 18. D 19. A 20. B
21. C 22. C 23. B 24. B 25. A 26. D 27. A 28. A 29. A 30. B
31. C 32. B 33. A 34. D 35. D 36. C 37. A 38. B 39. A 40. B
41. D 42. D 43. A 44. B 45. D 46. B 47. A 48. D 49. D 50. C
51. B 52. B 53. D

Part-II
Previous Year’s Question (2005-2020)

1. A 2. B 3. D 4. C 5. D 6. B 7. A 8. D 9. D 10. C
11. D 12. A 13. A 14. 10 15. A

EXERCISE-II
PART-I
Section-A
1. ABCD 2. BD 3. AB 4. ABC 5. AB 6. BC 7. ABCD 8. AC 9. ABC
10. (i)-C; (ii)-B; (iii)-A; (iv)-C; (v)-B; (vi)-B

Section-B
1. A 2. B 3. A 4. B 5. A 6. C

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 PART-II
20
1.  2H 2. 20 V 3. C = 9.2µF 4. 2A, 400 W
2
1
5. 77Ω, 97.6 Ω, 7.7 V, 9.76 V 6. 0.2 mH, F 8 105 rad / s
32
7. 48 8. 50 9. 8 10. 75 11. 9

EXERCISE-III

1. B 2. (A) – r,s,t ; (B) – q,r,s,t ; (C) – p,q ; (D) – q,r,s,t 3. BC 4. 4

5. AC 6. D 7. A 8. CD 9. 8 10. AD

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