PhysicsCBSE Class 12 · Board exam 2023, set 55/1/1 · 1 mark · MCQ

CBSE Class 12 Physics 2023: question 4

Set in the CBSE Class 12 board exam of 2023, paper 55/1/1, section A, question 4, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q4 · 1 mark · MCQCurrent Electricity

A steady current flows through a metallic wire whose area of cross-section (A) increases continuously from one end of the wire to the other. The magnitude of drift velocity ( $v_{d}$ ) of the free electrons as a function of 'A' can be shown by :

(A)Graph: $v_{d}$ vs A, decreasing hyperbola-like curve
(B)Graph: $v_{d}$ vs A, straight line decreasing
(C)Graph: $v_{d}$ vs A, horizontal line (constant)
(D)Graph: $v_{d}$ vs A, straight line increasing

Figure in the paper: Four graphs of drift velocity $v_{d}$ against area A as described in the options. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 55/1/1.

Hints

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

Hint 1

The current is the same through every cross-section.

Hint 2

Write $I = n e A v_{d}$ and see how $v_{d}$ depends on $A$ .

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.

For a steady current, $I = n e A v_{d}$ is the same at every cross-section, so $v_{d} = \frac{I}{n e A} \propto \frac{1}{A}$ .
½ mark
A $1/ A$ dependence gives a hyperbola-like decreasing curve, which is option (A).
½ mark

Answer: Option (A)

Where the marks are

Uses $v_{d} \propto 1/ A$ to pick the hyperbola (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 paper2023 board paper, set 55/1/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 12 Physics 2023: question 4

Hints

Step-by-step solution

Revise the chapter

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