PhysicsCBSE Class 12 · Board exam 2025, set 55/1/1 · 3 marks · Short answer

CBSE Class 12 Physics 2025: question 22(a)

Set in the CBSE Class 12 board exam of 2025, paper 55/1/1, section C, question 22(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q22(a) · 3 marks · Short answerCurrent Electricity

Two batteries of emf's 3V & 6V and internal resistances 0.2 Ω & 0.4 Ω are connected in parallel. This combination is connected to a 4 Ω resistor. Find :
(i) the equivalent emf of the combination
(ii) the equivalent internal resistance of the combination
(iii) the current drawn from the combination

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 55/1/1.

Hints

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

Hint 1

For cells in parallel, the equivalent emf is a weighted average: $E_{e q} = (E_{1} r_{2} + E_{2} r_{1}) / (r_{1} + r_{2})$ .

Hint 2

The internal resistances combine like resistors in parallel. Then use Ohm's law for the whole circuit.

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.

(i) For two cells in parallel: $E_{e q} = \frac{E _{1} r _{2} + E _{2} r _{1}}{r _{1} + r _{2}}$ .
½ mark
$E_{e q} = \frac{3 \times 0.4 + 6 \times 0.2}{0.2 + 0.4} = \frac{2.4}{0.6} = 4$ V.
½ mark
(ii) $r_{e q} = \frac{r _{1} r _{2}}{r _{1} + r _{2}}$ .
½ mark
$r_{e q} = \frac{0.2 \times 0.4}{0.6} = \frac{0.08}{0.6} \approx 0.133 Ω$ .
½ mark
(iii) $I = \frac{E _{e q}}{R + r _{e q}} = \frac{4}{4 + 0.133}$ .
½ mark
$I = \frac{4}{4.133} \approx 0.97$ A.
½ mark

Answer: (i) 4 V; (ii) ≈ 0.133 Ω (2/15 Ω); (iii) ≈ 0.97 A

Where the marks are

Formula and value $E_{e q} = 4$ V (1 mark)
Formula and value $r_{e q} = 0.133 Ω$ (1 mark)
Uses $I = E_{e q} / (R + r_{e q})$ and gets ≈ 0.97 A (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 paper2025 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2025: question 22(a)

Hints

Step-by-step solution

Revise the chapter

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