PhysicsCBSE Class 12 · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 12 Physics sample paper 2023-24: question 20

From the official CBSE sample question paper for 2023-24, section B, question 20, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q20 · 2 marks · Very short answerCurrent Electricity

A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds to a steady value of 2.8 A. What is the steady temperature of the heating element if the room temperature is 27.0 °C and the temperature coefficient of resistance of nichrome is $1.70 \times 1 0^{- 4}$ °C $^{- 1}$ ?

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

The initial current is at room temperature; the steady current is at the hot temperature.

Hint 2

Find both resistances using $R = V / I$ and use $R = R_{0} (1 + α Δ T)$ .

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.

Resistance varies with temperature as $R = R_{0} (1 + α Δ T)$ , where $R_{0}$ is the resistance at room temperature 27.0 °C.
½ mark
$R_{0} = \frac{V}{I _{0}} = \frac{230}{3.2} = 71.9 Ω$ and $R = \frac{V}{I} = \frac{230}{2.8} = 82.1 Ω$ . So $\frac{R}{R _{0}} = \frac{I _{0}}{I} = 1 + α Δ T$ .
½ mark
$Δ T = \frac{I _{0} / I - 1}{α} = \frac{3.2/2.8 - 1}{1.70 \times 1 0 ^{- 4}} = \frac{0.1429}{1.70 \times 1 0 ^{- 4}} \approx 840^{\circ} C$ .
Steady temperature $T = 27 + 840 = 867^{\circ} C$ .
1 mark

Answer: Steady temperature ≈ 867 °C

Where the marks are

Writes $R = R_{0} (1 + α Δ T)$ (½ mark)
Expresses $R_{0} = V / I_{0}$ and $R = V / I$ (½ mark)
Obtains $Δ T \approx 840$ °C and $T \approx 867$ °C (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 paperSample paper 2023-24: every question, by section.

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CBSE Class 12 Physics sample paper 2023-24: question 20

Hints

Step-by-step solution

Revise the chapter

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