PhysicsCBSE Class 12 · Board exam 2024, set 55/1/1 · 2 marks · Very short answer

CBSE Class 12 Physics 2024: question 17

Set in the CBSE Class 12 board exam of 2024, paper 55/1/1, section B, question 17, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q17 · 2 marks · Very short answerCurrent Electricity

Find the temperature at which the resistance of a wire made of silver will be twice its resistance at 20°C. Take 20°C as the reference temperature and temperature coefficient of resistance of silver at 20°C = $4.0 \times 1 0^{- 3} K^{- 1}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 55/1/1.

Hints

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

Hint 1

Recall how resistance depends on temperature through the temperature coefficient α.

Hint 2

Write $R_{T} = R_{0} [1 + α (T - T_{0})]$ and put $R_{T} = 2 R_{0}$ .

Hint 3

The bracket must equal 2, so $α (T - 20) = 1$ . Solve for T.

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.

The resistance varies with temperature as $R_{T} = R_{0} [1 + α (T - T_{0})]$ , where $T_{0} = 2 0^{\circ}$ C is the reference temperature. We need the temperature at which $R_{T} = 2 R_{0}$ .
½ mark
Substituting: $2 R_{0} = R_{0} [1 + 4.0 \times 1 0^{- 3} (T - 20)]$ , so $4.0 \times 1 0^{- 3} (T - 20) = 1$ .
½ mark
Hence $T - 20 = \frac{1}{4.0 \times 1 0 ^{- 3}} = 250$ , which gives $T = 27 0^{\circ} C$ (about 543 K).
1 mark

Answer: $T = 27 0^{\circ}$ C (≈ 543 K)

Where the marks are

Writes $R_{T} = R_{0} [1 + α (T - T_{0})]$ (½ mark)
Substitutes $R_{T} = 2 R_{0}$ and $α = 4 \times 1 0^{- 3}$ K $^{- 1}$ (½ mark)
Obtains $T = 27 0^{\circ}$ C or 543 K (1 mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Current Electricity, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2024: question 17

Hints

Step-by-step solution

Revise the chapter

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