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Solutions

Overview

Step-by-step NCERT solutions for Alternating Current (Chapter 7, CBSE Class 12 Physics) — every question and answer worked out in full, not just the final result. You can also read the Alternating Current textbook chapter.

Solved

What these solutions cover

All 8 questions in Alternating Current are solved in the PDF. Here's what's inside, exercise by exercise:

Exercises

  1. A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply.
    • (a) What is the rms value of current in the circuit?
    • (b) What is the net power consumed over a full cycle?
  2. The peak voltage of an ac supply is 300 V. What is the rms voltage? (b) The rms value of current in an ac circuit is 10 A. What is the peak current?
  3. A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.
  4. A 60 µF capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.
  5. In Exercises 7.3 and 7.4, what is the net power absorbed by each circuit over a complete cycle. Explain your answer.
  6. A charged 30 µF capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?
  7. A series LCR circuit with R = 20 Ω, L = 1.5 H and C = 35 µF is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?
  8. Figure 7.17 shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80 µF, R = 40 Ω.
    • (a) Determine the source frequency which drives the circuit in resonance.
    • (b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.
    • (c) Determine the rms potential drops across the three elements of the circuit. Show that the potential…
Sample

Worked examples

3 questions from Alternating Current, solved step by step.

Exercises

A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply. (a) What is the rms value of current in the circuit? (b) What is the net power consumed over a full cycle?

Given: R = 100 Ω, V_rms = 220 V, f = 50 Hz.

(a) rms current:

I = V_rms / R = 220 V / 100 Ω = 2.2 A

(b) Net power consumed over a full cycle:

For a purely resistive circuit, the power factor cos φ = 1.

P = V_rms × I_rms = 220 V × 2.2 A = 484 W

Equivalently, P = I² R = (2.2)² × 100 = 484 W.

Answer: (a) I = 2.2 A; (b) P = 484 W

Exercises

The peak voltage of an ac supply is 300 V. What is the rms voltage? (b) The rms value of current in an ac circuit is 10 A. What is the peak current?

(a) Given: vₘ = 300 V.

V_rms = vₘ / √2 = 300 / 1.414 = 212.1 V ≈ 212 V

(b) Given: I_rms = 10 A.

iₘ = √2 × I_rms = 1.414 × 10 A = 14.1 A

Answer: (a) V_rms ≈ 212 V; (b) iₘ ≈ 14.1 A

Exercises

A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.

Given: L = 44 mH = 44 × 10⁻³ H, V_rms = 220 V, f = 50 Hz.

Inductive reactance:

XL = 2π f L = 2 × 3.14159 × 50 × 44 × 10⁻³

XL = 13.82 Ω

rms current:

I = V_rms / XL = 220 / 13.82 = 15.92 A ≈ 15.9 A

Answer: I ≈ 15.9 A

All 8 questions in Alternating Current are solved step by step in the Solutions PDF above.

Keep solving

More solutions in Physics Part I

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More NCERT Solutions for Class 12

Read the Alternating Current textbook chapter / PDF, or browse all CBSE Class 12 Physics solutions.

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