PhysicsCBSE Class 12 · Sample paper, session 2024-25 · 2 marks · Very short answer

CBSE Class 12 Physics sample paper 2024-25: question 21

From the official CBSE sample question paper for 2024-25, section B, question 21, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21 · 2 marks · Very short answerCurrent Electricity

A cylindrical conductor of length l and cross-section area A is connected to a DC source. Under the influence of electric field set up due to source, the free electrons begin to drift in the opposite direction of the electric field.
(I) Draw the curve showing the dependency of drift velocity on relaxation time.
(II) If the DC source is replaced by a source whose current changes its magnitude with time such that $I = I_{o} sin 2 π ν t$ , where $ν$ is the frequency of variation of current, then determine the average drift velocity of the free electrons over one complete cycle.

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

Write the expression for drift velocity in terms of E and τ.

Hint 2

Drift velocity is proportional to current, $I = n e A v_{d}$ .

Hint 3

What is the average of a sine function over one full period?

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.

(I) Drift speed: $v_{d} = \frac{e E}{m} τ$ . For a given field E, $v_{d} \propto τ$ .
½ mark
So the graph of $v_{d}$ (y-axis) against $τ$ (x-axis) is a straight line through the origin with slope $e E / m$ .
½ mark
(II) $I = n e A v_{d}$ , so $v_{d} = \frac{I}{n e A} = \frac{I _{0}}{n e A} sin 2 π ν t$ . The drift velocity varies sinusoidally and reverses direction every half cycle.
½ mark
Average over one cycle: $⟨ v_{d} ⟩ = \frac{I _{0}}{n e A} \cdot \frac{1}{T} \int_{0}^{T} sin 2 π ν t d t = 0$ . The average drift velocity over a complete cycle is zero.
½ mark

Answer: (I) Straight line through the origin ( $v_{d} \propto τ$ ); (II) average drift velocity = 0

Where the marks are

States $v_{d} = e E τ / m$ (½ mark)
Graph: straight line through the origin (½ mark)
Relates $v_{d}$ to I: $v_{d} = I / n e A$ , sinusoidal (½ mark)
Average over a cycle = 0 (½ mark)

Revise the chapter

Chapter: Current Electricity (notes, formulas, where marks are lost and every past question)
Topic: Drift Velocity, Mobility and Resistivity

Practise this chapterBoard-style questions from Current Electricity, 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 21

Hints

Step-by-step solution

Revise the chapter

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