PhysicsCBSE Class 12 · Sample paper, session 2024-25 · 5 marks · Long answer

CBSE Class 12 Physics sample paper 2024-25: question 32(I)

From the official CBSE sample question paper for 2024-25, section E, question 32(I), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(I) · 5 marks · Long answerAlternating Current

Explain briefly, with the help of a labelled diagram, the basic principle of the working of an a.c. generator. In an a.c. generator, coil of N turns and area A is rotated at an angular velocity ω in a uniform magnetic field B. Derive an expression for the instantaneous value of the emf induced in coil. What is the source of energy generation in this device?

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

Open one hint at a time and try again before the next.

Hint 1

Think about what happens to the flux through a coil as the angle between its normal and $B$ changes.

Hint 2

Write the flux as a function of $θ = ω t$ , then apply Faraday's law $e = - d ϕ / d t$ .

Hint 3

Ask yourself what does work to keep the coil turning against Lenz's law.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Principle: An a.c. generator works on electromagnetic induction. When a coil is rotated in a uniform magnetic field, the magnetic flux linked with it changes continuously. This induces an emf (and a current in a closed circuit) that keeps reversing direction.
1 mark
Labelled diagram (described):
- A rectangular armature coil ABCD of many turns of insulated copper wire is wound on a soft-iron core.
- It is placed between the concave pole pieces N and S of a strong field magnet.
- It rotates about an axis perpendicular to $B$ .
- The coil ends are joined to two slip rings $R_{1}, R_{2}$ that rotate with the coil.
- Two stationary carbon brushes $B_{1}, B_{2}$ press on the slip rings and connect to the external load.
1 mark
Flux at time t: Let the normal to the coil be along $B$ at $t = 0$ , and let the coil rotate with angular velocity $ω$ , so $θ = ω t$ .
Flux linkage: $ϕ = N B A cos ω t$
1 mark
Instantaneous emf: By Faraday's law,
$e = - \frac{d ϕ}{d t} = - N B A \frac{d}{d t} (cos ω t) = N B A ω sin ω t$
Hence $e = e_{0} sin ω t$ , where $e_{0} = N B A ω$ is the peak emf.
The current through a load $R$ is $i = \frac{e _{0}}{R} sin ω t = i_{0} sin ω t$ , which varies sinusoidally.
1 mark
Source of energy: The electrical energy comes from the mechanical energy spent in rotating the armature coil against the opposing (Lenz's law) torque, for example by a turbine.
1 mark

Answer: $e = N B A ω sin ω t$ (peak $e_{0} = N B A ω$ ); source of energy is the mechanical work done in rotating the coil.

Where the marks are

States the principle of electromagnetic induction with changing flux through a rotating coil (1 mark)
Labelled diagram/construction: armature, field magnet, slip rings, brushes (1 mark)
Writes flux $ϕ = N B A cos ω t$ (1 mark)
Derives $e = N B A ω sin ω t$ with $e_{0} = N B A ω$ (1 mark)
Identifies mechanical energy as the source (1 mark)

Revise the chapter

Chapter: Alternating Current (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Alternating Current, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2024-25: every question, by section.

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CBSE Class 12 Physics sample paper 2024-25: question 32(I)

Hints

Step-by-step solution

Revise the chapter

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