JEE Physics Alternating Current MCQs Set 21

Practice MCQs for JEE Physics Alternating Current

Access targeted multiple-choice questions for Alternating Current designed to align with the latest JEE academic syllabus for JEE Physics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

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Multiple Choice Questions

Question 1: The power factor is one for a
(a) pure inductor
(b) pure capacitor
(c) pure resistor
(d) either an inductor or a capacitor
Show Answer & Explanation

Answer: (c) pure resistor

Explanation:
1. In a pure resistor the phase difference is zero, so cos φ = 1.

Teacher's Note:
1. Recall the basic relation.

Question 2: In a series combination of R, L and C with an a.c. source at resonance, if R = 20 ohm, then the impedance Z of the combination is
(a) 20 ohm
(b) zero
(c) 10 ohm
(d) 400 ohm
Show Answer & Explanation

Answer: (a) 20 ohm

Explanation:
1. At resonance Z = R = 20 ohm.

Teacher's Note:
1. Recall the basic relation.

Question 3: The heat produced in a given resistance in a given time by the sinusoidal current I0 sin ωt will be the same as that of a steady current of magnitude nearly
(a) 0.71 I0
(b) 1.412 I0
(c) I0
(d) \( \sqrt{I_0} \)
Show Answer & Explanation

Answer: (a) 0.71 I0

Explanation:
1. The equivalent steady (rms) current is I0/√2 = 0.707 I0.

Teacher's Note:
1. Recall the basic relation.

Question 4: An inductive circuit contains a resistance of 10 ohm and an inductance of 2 henry. If an a.c. voltage of 120 V and frequency 60 Hz is applied to this circuit, the current would be nearly
(a) 0.32 A
(b) 0.16 A
(c) 0.48 A
(d) 0.80 A
Show Answer & Explanation

Answer: (b) 0.16 A

Explanation:
1. X_L = 2π × 60 × 2 = 754 ohm.
2. Z ≈ 754 ohm and I = 120/754 = 0.16 A.

Teacher's Note:
1. Recall the basic relation.

Question 5: A step down transformer reduces 220 V to 110 V. The primary draws 5 ampere of current and the secondary supplies 9 ampere. The efficiency of the transformer is
(a) 20%
(b) 44%
(c) 90%
(d) 100%
Show Answer & Explanation

Answer: (c) 90%

Explanation:
1. Input power = 220 × 5 = 1100 W.
2. Output power = 110 × 9 = 990 W.
3. Efficiency = 990/1100 = 90%.

Teacher's Note:
1. Recall the basic relation.

Question 6: In a series LCR circuit R = 200 ohm and the voltage and the frequency of the main supply are 220 V and 50 Hz respectively. On taking out the capacitance from the circuit, the current lags behind the voltage by 30°. On taking out the inductor from the circuit, the current leads the voltage by 30°. The power dissipated in the LCR circuit is
(a) 305 W
(b) 210 W
(c) zero
(d) 242 W
Show Answer & Explanation

Answer: (d) 242 W

Explanation:
1. Both removals give a 30° phase, so X_L = X_C and the circuit is at resonance.
2. P = V²/R = 220²/200 = 242 W.

Teacher's Note:
1. Recall the basic relation.

Question 7: The alternating current of equivalent value of I0/√2 is
(a) peak current
(b) r.m.s. current
(c) D.C. current
(d) all of these
Show Answer & Explanation

Answer: (b) r.m.s. current

Explanation:
1. The rms value is I0/√2.

Teacher's Note:
1. Recall the basic relation.

Question 8: With an increase in the frequency of an a.c. supply, the inductive reactance
(a) decreases
(b) increases directly with frequency
(c) increases as the square of frequency
(d) decreases inversely with frequency
Show Answer & Explanation

Answer: (b) increases directly with frequency

Explanation:
1. X_L = ωL = 2πfL is directly proportional to f.

Teacher's Note:
1. Recall the basic relation.

Question 9: The product e_rms I_rms is called
(a) true power
(b) apparent power
(c) power factor
(d) Q factor
Show Answer & Explanation

Answer: (b) apparent power

Explanation:
1. The product of rms voltage and rms current is the apparent power.

Teacher's Note:
1. Recall the basic relation.

Question 10: In an experiment, 200 V a.c. is applied at the ends of an LCR circuit. The circuit consists of an inductive reactance X_L = 50 ohm, a capacitive reactance X_C = 50 ohm and an ohmic resistance R = 10 ohm. The impedance of the circuit is
(a) 10 ohm
(b) 20 ohm
(c) 30 ohm
(d) 40 ohm
Show Answer & Explanation

Answer: (a) 10 ohm

Explanation:
1. X_L = X_C, so Z = R = 10 ohm.

Teacher's Note:
1. Recall the basic relation.

Question 11: The impedance of an LCR series circuit is
(a) \( \sqrt{R^2+(X_L-X_C)^2} \)
(b) \( \sqrt{R^2+(X_L+X_C)^2} \)
(c) \( \sqrt{R+(X_L+X_C)^2} \)
(d) \( \sqrt{X_L-X_C+R} \)
Show Answer & Explanation

Answer: (a) \( \sqrt{R^2+(X_L-X_C)^2} \)

Explanation:
1. Z = √[R² + (X_L - X_C)²].

Teacher's Note:
1. Recall the basic relation.

Question 12: The primary winding of a transformer has 100 turns and its secondary winding has 200 turns. The primary is connected to an a.c. supply of 120 V and the current flowing in it is 10 A. The voltage and the current in the secondary are
(a) 240 V, 5 A
(b) 240 V, 10 A
(c) 60 V, 20 A
(d) 120 V, 20 A
Show Answer & Explanation

Answer: (a) 240 V, 5 A

Explanation:
1. V_s = 120 × 200/100 = 240 V.
2. I_s = 10 × 100/200 = 5 A.

Teacher's Note:
1. Recall the basic relation.

Question 13: The graph between inductive reactance and frequency is
(a) a parabola
(b) a straight line
(c) a hyperbola
(d) an arc of a circle
Show Answer & Explanation

Answer: (b) a straight line

Explanation:
1. X_L = 2πfL is directly proportional to f.

Teacher's Note:
1. Recall the basic relation.

Question 14: A resistance of 100 ohm, an inductance of 0.5 henry and a capacitance of 10 × 10⁻⁶ farad are connected in series through a 50 Hz a.c. supply. The impedance is
(a) 1.8765 ohm
(b) 18.76 ohm
(c) 189.7 ohm
(d) 101.3 ohm
Show Answer & Explanation

Answer: (c) 189.7 ohm

Explanation:
1. X_L = 2π × 50 × 0.5 = 157.1 ohm and X_C = 1/(2π × 50 × 10⁻⁵) = 318.3 ohm.
2. Z = √(100² + 161.2²) = 189.7 ohm.

Teacher's Note:
1. Recall the basic relation.

Question 15:
Assertion (A): A capacitor blocks direct current in the steady state.
Reason (R): The capacitive reactance of a capacitor is inversely proportional to the frequency f of the source of emf.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. For d.c. f = 0, so X_C = 1/(2πfC) is infinite and no steady current flows.
2. The reason explains the assertion.

Teacher's Note:
1. X_C is infinite for d.c.

Question 16: The inductive reactance of an inductor of inductance L is
(a) \( \frac1{2\pi fC} \)
(b) \( \frac1{2\pi fL} \)
(c) \( 2\pi fC \)
(d) \( 2\pi fL \)
Show Answer & Explanation

Answer: (d) \( 2\pi fL \)

Explanation:
1. X_L = ωL = 2πfL.

Teacher's Note:
1. Recall the basic relation.

Question 17: The core of a transformer is laminated to reduce
(a) flux leakage
(b) hysteresis
(c) copper loss
(d) eddy current
Show Answer & Explanation

Answer: (d) eddy current

Explanation:
1. Laminations increase the resistance of eddy-current paths and so reduce eddy currents.

Teacher's Note:
1. Recall the basic relation.

Question 18: The tuning circuit of a radio receiver has a resistance of 50 ohm, an inductor of 10 mH and a variable capacitor. A 1 MHz radio wave produces a potential difference of 0.1 mV. The value of the capacitor to produce resonance is (take π² = 10)
(a) 2.5 pF
(b) 5.0 pF
(c) 25 pF
(d) 50 pF
Show Answer & Explanation

Answer: (a) 2.5 pF

Explanation:
1. C = 1/(4π² f² L) = 1/(4 × 10 × 10¹² × 10⁻²) = 2.5 × 10⁻¹² F = 2.5 pF.

Teacher's Note:
1. Recall the basic relation.

Question 19: The instantaneous values of alternating current and voltage in a circuit are i = (1/√2) sin(100πt) A and e = (1/√2) sin(100πt + π/3) V. The average power in watts consumed in the circuit is
(a) 1/4
(b) \( \sqrt3/4 \)
(c) 1/2
(d) 1/8
Show Answer & Explanation

Answer: (d) 1/8

Explanation:
1. P = (1/2) e0 i0 cos φ = 0.5 × 0.5 × cos 60° = 1/8 W.

Teacher's Note:
1. Recall the basic relation.

Question 20: In an LCR series resonant circuit, the capacitance is changed from C to 4C. For the same resonant frequency, the inductance should be changed from L to
(a) 2L
(b) L/2
(c) 4L
(d) L/4
Show Answer & Explanation

Answer: (d) L/4

Explanation:
1. f = 1/(2π√(LC)) requires LC to stay constant.
2. So L must become L/4.

Teacher's Note:
1. Recall the basic relation.

Question 21: At resonance frequency the impedance in a series LCR circuit is
(a) maximum
(b) minimum
(c) zero
(d) infinite
Show Answer & Explanation

Answer: (b) minimum

Explanation:
1. At resonance X_L = X_C and Z = R, the minimum value.

Teacher's Note:
1. Recall the basic relation.

Question 22: Which of the following correctly describes the variation of capacitive reactance X_C with frequency?
(a) X_C first rises and then falls
(b) X_C increases without limit at one frequency
(c) X_C decreases hyperbolically with increasing frequency
(d) X_C rises to a peak and then falls linearly
Show Answer & Explanation

Answer: (c) X_C decreases hyperbolically with increasing frequency

Explanation:
1. X_C = 1/(2πfC) is inversely proportional to f, a hyperbola.

Teacher's Note:
1. Recall the basic relation.

Question 23:
Assertion (A): The voltage and current in a series a.c. circuit are given by V = V0 sin ωt and i = i0 cos ωt. The power dissipated in the circuit is zero.
Reason (R): Power in an a.c. circuit is given by P = (V0 i0/2) cos φ.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The phase difference is 90°, so cos φ = 0 and the average power is zero.
2. The reason gives the formula that leads to this.

Teacher's Note:
1. cos 90° = 0.

Question 24: In a pure inductor, the voltage
(a) lags the current by π/2
(b) leads the current by π/2
(c) leads the current by π/3
(d) leads the current by π/4
Show Answer & Explanation

Answer: (b) leads the current by π/2

Explanation:
1. In an inductor the voltage leads the current by 90°.

Teacher's Note:
1. Recall the basic relation.

Question 25: A resistance R draws power P when connected to an a.c. source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes Z, the power drawn will be
(a) \( P\sqrt{R/Z} \)
(b) \( P(R/Z) \)
(c) P
(d) \( P(R/Z)^2 \)
Show Answer & Explanation

Answer: (d) \( P(R/Z)^2 \)

Explanation:
1. P = V²/R at first.
2. With the inductor I = V/Z, so P' = I²R = V²R/Z² = P (R/Z)².

Teacher's Note:
1. Recall the basic relation.

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