Chapter Exam

Chapter-7 Alternating Current — Online MCQ Test

Q: What is the RMS (root mean square) value of an alternating current with peak value I₀?

Answer: B. I₀/√2 — The RMS value of an AC current is defined as I₀/√2, where I₀ is the peak (maximum) value of the current.

Q: Which of the following is the SI unit of reactance?

Answer: B. Ohm — Reactance (inductive or capacitive) is measured in Ohms (Ω), the same unit as resistance.

Q: In an AC circuit, the impedance Z is related to resistance R, inductive reactance Xₗ, and capacitive reactance Xc by which expression?

Answer: B. Z = √[R² + (Xₗ - Xc)²] — Impedance is the vector sum of resistance and net reactance: Z = √[R² + (Xₗ - Xc)²].

Q: What is the inductive reactance of a pure inductor with inductance L in an AC circuit of frequency f?

Answer: A. Xₗ = 2πfL — Inductive reactance is directly proportional to frequency and inductance: Xₗ = 2πfL or ωL, where ω = 2πf.

Q: A sinusoidal AC voltage is given by V(t) = 230sin(ωt) V. What is its RMS voltage?

Answer: B. 230/√2 V ≈ 163 V — The peak voltage is 230 V, so RMS voltage = 230/√2 ≈ 163 V. The value 230 V used in India is already the RMS value.

Q: In a purely inductive circuit, what is the phase difference between voltage and current?

Answer: B. 90° (voltage leads) — In a pure inductor, voltage leads current by 90° because the inductor opposes changes in current.

Q: In a series RLC circuit, if the inductance is decreased while keeping resistance and capacitance constant, the resonant frequency will:

Answer: B. Increase — Resonant frequency f₀ = 1/(2π√LC) is inversely proportional to √L. Decreasing L increases the resonant frequency.

Q: An AC circuit contains only a capacitor (C = 20 μF) and an AC voltage source (V = 100 V, f = 100 Hz). What is the current in the circuit?

Answer: A. 1.26 A — Xc = 1/(2πfC) = 1/(2π × 100 × 20 × 10⁻⁶) ≈ 79.6 Ω. Current I = V/Xc = 100/79.6 ≈ 1.26 A.

Q: A resonant LCR circuit has R = 5 Ω, L = 10 mH, and the resonant frequency is 1000 Hz. What is the capacitance?

Answer: A. 2.53 μF — At resonance, f₀ = 1/(2π√LC), so C = 1/(4π²f₀²L) = 1/(4π² × 10⁶ × 0.01) ≈ 2.53 × 10⁻⁶ F = 2.53 μF.

Q: In an LCR series circuit, at a frequency below resonance, which type of circuit behavior is exhibited?

Answer: B. Capacitive (current leads voltage) — Below resonance, Xc > Xₗ, so the net reactance is capacitive, making the circuit capacitive in nature. Current leads voltage in a capacitive circuit.

PHYSICS · Grade 12 · CBSE(NCERT)

Practice Chapter-7 Alternating Current with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 12 PHYSICS. This chapter covers: AC circuits - RMS value - reactance - impedance - LCR circuit - resonance - transformer - AC generator. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-7 Alternating Current — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 12 PHYSICS — Chapter-7 Alternating Current, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the RMS (root mean square) value of an alternating current with peak value I₀?

A. I₀/2
B. I₀/√2 ✓
C. I₀√2
D. 2I₀

Answer: B. I₀/√2
The RMS value of an AC current is defined as I₀/√2, where I₀ is the peak (maximum) value of the current.

Which of the following is the SI unit of reactance?

A. Ampere
B. Ohm ✓
C. Henry
D. Farad

Answer: B. Ohm
Reactance (inductive or capacitive) is measured in Ohms (Ω), the same unit as resistance.

In an AC circuit, the impedance Z is related to resistance R, inductive reactance Xₗ, and capacitive reactance Xc by which expression?

A. Z = R + Xₗ + Xc
B. Z = √[R² + (Xₗ - Xc)²] ✓
C. Z = R² + (Xₗ - Xc)²
D. Z = R + (Xₗ - Xc)

Answer: B. Z = √[R² + (Xₗ - Xc)²]
Impedance is the vector sum of resistance and net reactance: Z = √[R² + (Xₗ - Xc)²].

What is the inductive reactance of a pure inductor with inductance L in an AC circuit of frequency f?

A. Xₗ = 2πfL ✓
B. Xₗ = L/(2πf)
C. Xₗ = 2πfL²
D. Xₗ = 1/(2πfL)

Answer: A. Xₗ = 2πfL
Inductive reactance is directly proportional to frequency and inductance: Xₗ = 2πfL or ωL, where ω = 2πf.

A sinusoidal AC voltage is given by V(t) = 230sin(ωt) V. What is its RMS voltage?

A. 230 V
B. 230/√2 V ≈ 163 V ✓
C. 230√2 V ≈ 325 V
D. 115 V

Answer: B. 230/√2 V ≈ 163 V
The peak voltage is 230 V, so RMS voltage = 230/√2 ≈ 163 V. The value 230 V used in India is already the RMS value.

In a purely inductive circuit, what is the phase difference between voltage and current?

A. 0°
B. 90° (voltage leads) ✓
C. 45°
D. 180°

Answer: B. 90° (voltage leads)
In a pure inductor, voltage leads current by 90° because the inductor opposes changes in current.

In a series RLC circuit, if the inductance is decreased while keeping resistance and capacitance constant, the resonant frequency will:

A. Decrease
B. Increase ✓
C. Remain unchanged
D. Become zero

Answer: B. Increase
Resonant frequency f₀ = 1/(2π√LC) is inversely proportional to √L. Decreasing L increases the resonant frequency.

An AC circuit contains only a capacitor (C = 20 μF) and an AC voltage source (V = 100 V, f = 100 Hz). What is the current in the circuit?

A. 1.26 A ✓
B. 0.126 A
C. 12.6 A
D. 0.0126 A

Answer: A. 1.26 A
Xc = 1/(2πfC) = 1/(2π × 100 × 20 × 10⁻⁶) ≈ 79.6 Ω. Current I = V/Xc = 100/79.6 ≈ 1.26 A.

A resonant LCR circuit has R = 5 Ω, L = 10 mH, and the resonant frequency is 1000 Hz. What is the capacitance?

A. 2.53 μF ✓
B. 25.3 μF
C. 0.253 μF
D. 253 μF

Answer: A. 2.53 μF
At resonance, f₀ = 1/(2π√LC), so C = 1/(4π²f₀²L) = 1/(4π² × 10⁶ × 0.01) ≈ 2.53 × 10⁻⁶ F = 2.53 μF.

In an LCR series circuit, at a frequency below resonance, which type of circuit behavior is exhibited?

A. Inductive (current lags voltage)
B. Capacitive (current leads voltage) ✓
C. Purely resistive
D. Behavior depends only on R

Answer: B. Capacitive (current leads voltage)
Below resonance, Xc > Xₗ, so the net reactance is capacitive, making the circuit capacitive in nature. Current leads voltage in a capacitive circuit.

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