PhysicsCBSE Class 12 · Sample paper, session 2025-26 · 5 marks · Long answer

CBSE Class 12 Physics sample paper 2025-26: question 31(I)

From the official CBSE sample question paper for 2025-26, section E, question 31(I), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q31(I) · 5 marks · Long answerElectrostatic Potential and Capacitance

(A) A dielectric slab of thickness t, is introduced between the plates of parallel plate capacitor of area A and separation d (where t<d). Find an expression for the capacitance with the dielectric slab.
(B) A copper sphere of capacitor C is dropped in ocean. Will the capacitance of the sphere increase, decrease or remain same? Justify.
(C) A capacitor is connected across a source of potential difference V and then the separation ‘d’ between the plates is increased using insulating stick. Plot ‘V’ vs ‘d’ graph for the given capacitor.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

The field is $σ / ε_{0}$ in air and reduced by K inside the slab; add the potential drops.

Hint 2

For the sphere, use $C = 4 π ε_{0} ε_{r} R$ .

Hint 3

What fixes the voltage across a capacitor that stays connected to a source?

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.

(A) Charge $\pm q$ on plates, $σ = q / A$ . Field in the air gaps $E_{0} = σ / ε_{0}$ ; inside the slab, due to polarisation, $E = E_{0} / K$ .
½ mark
Potential difference: $V = E_{0} (d - t) + \frac{E _{0}}{K} t = \frac{q}{A ε _{0}} (d - t + \frac{t}{K})$
1 mark
$C = \frac{q}{V} = \frac{ε _{0} A}{d - t + \frac{t}{K}}$
½ mark
(B) The capacitance increases. Justification: $C = q / V$ ; in water the polar molecules get polarised and reduce the field around the sphere, so for the same charge its potential is lower. Since $C = 4 π ε_{0} ε_{r} R$ , it becomes about $ε_{r}$ (≈80) times larger.
2 marks
(C) The capacitor stays connected to the source, so V across it stays equal to the source voltage whatever d is (only C and q decrease). The V–d graph is a straight line parallel to the d-axis at height V.
1 mark

Answer: (A) $C = ε_{0} A / (d - t + t / K)$ ; (B) increases (≈80 times); (C) horizontal straight line (V constant)

Where the marks are

Fields in air and dielectric (½ mark)
Expression for potential difference (1 mark)
Capacitance $ε_{0} A / (d - t + t / K)$ (½ mark)
Capacitance increases, justified by reduced potential due to polarisation (2 marks)
V–d graph horizontal, V constant as battery stays connected (1 mark)

Revise the chapter

Chapter: Electrostatic Potential and Capacitance (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Electrostatic Potential and Capacitance, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2025-26: every question, by section.

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CBSE Class 12 Physics sample paper 2025-26: question 31(I)

Hints

Step-by-step solution

Revise the chapter

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