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A rectangular coil of 20 turns and area of cross-section 25 sq. cm has a resistance of 100Ω. If a magnetic field which is perpendicular to the plane of coil changes at a rate of 1000 tesla per second, the current in the coil is

1. 1 A
2. 50 A
3. 0.5 A
4. 5 A

Correct answer: 0.5 A

Solution

The induced emf is given by Faraday's law: E = -N * (dΦ/dt), where N is the number of turns and dΦ/dt is the rate of change of magnetic flux. Here, dΦ/dt = A * dB/dt = (25 × 10^-4 m²) * (1000 T/s) = 0.25 V. With N = 20, E = 20 * 0.25 = 5 V. Using Ohm's law, I = E/R = 5/100 = 0.05 A.

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