PhysicsCBSE Class 12 · Board exam 2025, set 55/1/1 · 3 marks · Short answer

CBSE Class 12 Physics 2025: question 22(b)

Set in the CBSE Class 12 board exam of 2025, paper 55/1/1, section C, question 22(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q22(b) · 3 marks · Short answerCurrent Electricity

(i) A conductor of length $l$ is connected across an ideal cell of emf E. Keeping the cell connected, the length of the conductor is increased to $2 l$ by gradually stretching it. If R and R′ are initial and final values of resistance and $v_{d}$ and $v_{d}^{'}$ are initial and final values of drift velocity, find the relation between (i) R′ and R and (ii) $v_{d}^{'}$ and $v_{d}$ .
(ii) When electrons drift in a conductor from lower to higher potential, does it mean that all the 'free electrons' of the conductor are moving in the same direction ?

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 55/1/1.

Hints

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

Hint 1

When a wire is stretched its volume is unchanged, so its area changes. Also, V across it is fixed by the ideal cell.

Hint 2

Write $v_{d} = e E τ / m$ with $E = V / l$ and see what doubling l does.

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)(i) Stretching does not change the volume: $A l = A^{'} (2 l) \Rightarrow A^{'} = \frac{A}{2}$ .
½ mark
$R^{'} = \frac{ρ ( 2 l )}{A /2} = 4 \frac{ρl}{A} = 4 R$ .
½ mark
(i)(ii) Drift velocity: $v_{d} = \frac{e E τ}{m} = \frac{e V τ}{m l}$ , since the field is $E = V / l$ .
½ mark
The cell's emf V stays the same while the length doubles, so $v_{d}^{'} = \frac{e V τ}{m ( 2 l )} = \frac{v _{d}}{2}$ .
½ mark
(ii) No. Free electrons keep moving randomly in all directions. The field only superimposes a small average drift towards higher potential, so they do not all move in the same direction.
1 mark

Answer: (i) R′ = 4R; v_d′ = v_d/2. (ii) No; electrons move randomly with only a small net drift.

Where the marks are

Uses constant volume to get $R^{'} = 4 R$ (1 mark)
Uses $v_{d} = e V τ / (m l)$ with V constant to get $v_{d}^{'} = v_{d} /2$ (1 mark)
Answers 'No' with the random-motion reason (1 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 paper2025 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2025: question 22(b)

Hints

Step-by-step solution

Revise the chapter

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