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Two coils C_1 and C_2 are… (Class 12 Physics 2023, Q25)

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PhysicsCBSE Class 12 · Board exam 2023, set 55/5/1 · 2 marks · Very short answer

CBSE Class 12 Physics 2023: question 25

Set in the CBSE Class 12 board exam of 2023, paper 55/5/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerElectromagnetic Induction

Two coils and are placed close to each other. The magnetic flux linked with the coil varies with the current flowing in coil , as shown in the figure. Find
(i) the mutual inductance of the arrangement, and
(ii) the rate of change of current that will induce an emf of 100 V in coil .

Figure in the paper: Graph of (wb) on vertical axis (marks 5, 10, 15) versus (A) on horizontal axis (marks 2, 4, 6): a straight line through the origin rising to about 15 wb at = 6 A. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 55/5/1.

Hints

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

Hint 1

The relation between the flux in C₂ and the current in C₁ is linear. What does its slope represent?

Hint 2

Use Faraday's law in the form ε = M dI₁/dt.

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.

  1. (i) Flux linkage is related to current by , so the mutual inductance is the slope of the – graph.

    ½ mark

  2. From the graph, H.

    ½ mark

  3. (ii) The induced emf is .

    ½ mark

  4. So .

    ½ mark

Answer: (i) M = 2.5 H; (ii) dI₁/dt = 40 A/s

Where the marks are

  • Uses φ₂ = MI₁ / slope (½ mark)
  • M = 2.5 H (½ mark)
  • Uses ε = M dI₁/dt (½ mark)
  • dI₁/dt = 40 A s⁻¹ (½ mark)

Revise the chapter

Practise this chapterBoard-style questions from Electromagnetic Induction, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 55/5/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.