Physics · Electromagnetic induction and AC · chapter 6 of 14

Class 12 Physics Chapter 6: Electromagnetic Induction case study question with answers

One case-based question of the kind the board asks: a passage, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks
A small hydro-electric unit on a hill stream in Uttarakhand drives a simple ac generator. Water from a channel turns a turbine coupled to the armature, a rectangular coil of 120 turns, each of area 0.050 m², which rotates at a steady 25 revolutions per second about an axis perpendicular to a uniform field of 0.25 T. The ends of the coil are joined to slip rings, and brushes carry the current to the village supply. Take t = 0 at an instant when the plane of the coil is perpendicular to the field.
Part 1 · 1 mark
The peak emf of the generator is about
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Answer: (c) 236 V

ε₀ = NBAω = 120 × 0.25 × 0.050 × 2π × 25 = 236 V. 37.5 V leaves out 2π; 471 V doubles it; 1.96 V leaves out N.

Part 2 · 1 mark
The emf is at its maximum when the plane of the coil is
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Answer: (d) parallel to the field

ε = ε₀ sin ωt is greatest at θ = 90° and 270°, when the plane of the coil is parallel to B: the flux is zero but changing fastest.

Part 3 · 2 marks
Find the emf at t = 1/300 s, and the time between two successive instants at which the emf is zero.
Answer and marking scheme

ωt = 2π × 25 × (1/300) = π/6, so ε = ε₀ sin 30° = 236 × 0.5 = 118 V. The emf is zero twice in each revolution, so successive zeros are half a period apart: T/2 = 1/(2 × 25) = 0.020 s.

  • ε = ε₀ sin(π/6) = 118 V (1)
  • T/2 = 0.020 s (1)
Or
In the dry season the stream slows and the coil turns at only 12.5 revolutions per second. Find the new peak emf and frequency, and state the energy conversion taking place in the unit.
Answer and marking scheme

ε₀ = NBAω is proportional to ω, so it halves to about 118 V; the frequency equals the rate of revolution, 12.5 Hz. The kinetic energy of the flowing water, through the turbine's mechanical energy, is converted into electrical energy.

  • peak emf about 118 V and frequency 12.5 Hz (1)
  • mechanical (water) energy to electrical energy (1)
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