PhysicsCBSE Class 12 · Board exam 2024, set 55/1/1 · 5 marks · Long answer

CBSE Class 12 Physics 2024: question 32(b)

Set in the CBSE Class 12 board exam of 2024, paper 55/1/1, section E, question 32(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(b) · 5 marks · Long answerAlternating Current

(i) Draw a labelled diagram of a step-up transformer and describe its working principle. Explain any three causes for energy losses in a real transformer.
(ii) A step-up transformer converts a low voltage into high voltage. Does it violate the principle of conservation of energy? Explain.
(iii) A step-up transformer has 200 and 3000 turns in its primary and secondary coils respectively. The input voltage given to the primary coil is 90 V. Calculate :
(1) The output voltage across the secondary coil
(2) The current in the primary coil if the current in the secondary coil is 2.0 A.

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

Which phenomenon links the changing flux in one coil to an emf in another?

Hint 2

Think about what happens to current when voltage is stepped up, and compare input and output power.

Hint 3

Use $V_{s} / V_{p} = N_{s} / N_{p}$ and $V_{p} I_{p} = V_{s} I_{s}$ .

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) Diagram (described in words): A laminated soft-iron core carries two coils, either on separate limbs or wound one over the other.
- The primary coil has few turns ( $N_{p}$ ) and is connected to the ac input $V_{p}$ .
- The secondary coil has many turns ( $N_{s} > N_{p}$ ) and is connected across the load, giving output $V_{s}$ .
- Label: core, primary, secondary, input ac, output.
1 mark
Working principle – mutual induction. The alternating voltage applied to the primary drives an alternating current in it. This produces an alternating magnetic flux in the core, which links the secondary coil and induces an emf in it.
For an ideal transformer, $\frac{V _{s}}{V _{p}} = \frac{N _{s}}{N _{p}}$ . Since $N_{s} > N_{p}$ , the output voltage is stepped up.
½ mark
Causes of energy loss (any three):
1. Flux leakage – not all of the primary's flux links the secondary.
2. Resistance of the windings – $I^{2} R$ heating in the copper coils.
3. Eddy currents – currents induced in the iron core heat it. This is reduced by using a laminated core.
4. Hysteresis – energy is lost in repeatedly magnetising and demagnetising the core. This is reduced by using soft iron.
1½ marks
(ii) No. When the voltage is stepped up, the current is stepped down in the same ratio: $I_{s} / I_{p} = N_{p} / N_{s}$ .
So the output power $V_{s} I_{s}$ equals the input power $V_{p} I_{p}$ (ideal case). In practice it is slightly less, because of losses. No extra energy is created, so conservation of energy is not violated.
1 mark
(iii)(1) $V_{s} = V_{p} \frac{N _{s}}{N _{p}} = 90 \times \frac{3000}{200} = 1350 V$
½ mark
(2) $V_{p} I_{p} = V_{s} I_{s} \Rightarrow I_{p} = I_{s} \frac{N _{s}}{N _{p}} = 2.0 \times \frac{3000}{200} = 30 A$
½ mark

Answer: (i) works by mutual induction; losses: flux leakage, winding resistance, eddy currents, hysteresis; (ii) No – current is reduced in the same ratio, so power is conserved; (iii)(1) 1350 V, (2) 30 A

Where the marks are

Labelled diagram of a step-up transformer ( $N_{s} > N_{p}$ , core, both coils) (1 mark)
Working principle: mutual induction, with explanation (½ mark)
Any three causes of energy loss (½ × 3 = 1½ marks)
Explains no violation: current decreases as voltage increases, so power in = power out (1 mark)
$V_{s} = 1350$ V (½ mark)
$I_{p} = 30$ A (½ mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Alternating Current, 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.

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.

CBSE Class 12 Physics 2024: question 32(b)

Hints

Step-by-step solution

Revise the chapter

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