PhysicsCBSE Class 12 · Sample paper, session 2023-24 · 3 marks · Short answer

CBSE Class 12 Physics sample paper 2023-24: question 25

From the official CBSE sample question paper for 2023-24, section C, question 25, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 3 marks · Short answerCurrent Electricity

A wire of uniform cross-section and resistance 4 ohm is bent in the shape of square ABCD. Point A is connected to a point P on DC by a wire AP of resistance 1 ohm. When a potential difference is applied between A and C, the points B and P are seen to be at the same potential. What is the resistance of the part DP?

Figure in the paper: Square ABCD with A top-left, B top-right, C bottom-right, D bottom-left; point P on side DC; a wire AP drawn diagonally from A to P. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Each side of the square has resistance 1 Ω. Equal potential at B and P means a balanced Wheatstone bridge.

Hint 2

Between A and P, the wire AP is in parallel with the path A→D→P.

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.

Total resistance 4 Ω is shared equally by the four sides, so each side has 1 Ω. Let resistance of DP = $x$ , then PC = $(1 - x)$ .
Between A and P there are two parallel paths: wire AP (1 Ω) and AD + DP $(1 + x)$ Ω, so $R_{A P} = \frac{1 \cdot ( 1 + x )}{2 + x}$ .
Since B and P are at the same potential, the bridge ABCP is balanced: $\frac{R _{A B}}{R _{B C}} = \frac{R _{A P}}{R _{P C}}$ .
1½ marks
$\frac{1}{1} = \frac{( 1 + x ) / ( 2 + x )}{1 - x} \Rightarrow 1 + x = (2 + x) (1 - x) = 2 - x - x^{2}$
$\Rightarrow x^{2} + 2 x - 1 = 0 \Rightarrow x = - 1 + 2$ (positive root)
Resistance of DP $= (2 - 1) Ω \approx 0.414 Ω$
1½ marks

Answer: $R_{D P} = (2 - 1) Ω \approx 0.41 Ω$

Where the marks are

Each side 1 Ω, sets DP = x, PC = 1 − x, combines AP with AD+DP in parallel and writes balanced bridge condition (1½ marks)
Solves $x^{2} + 2 x - 1 = 0$ to get $x = (2 - 1)$ Ω (1½ marks)

Revise the chapter

Chapter: Current Electricity (notes, formulas, where marks are lost and every past question)
Topic: Kirchhoff's Rules and Wheatstone Bridge

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 2023-24: every question, by section.

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CBSE Class 12 Physics sample paper 2023-24: question 25

Hints

Step-by-step solution

Revise the chapter

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