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According to Faraday’s law of induction, Induced e.m.f. ε = -dϕ/dt = -(100t). Induced current i at t = 2 sec.

1. i = ε/R = 100 × 2 / 4000 = +0.5 A
2. i = ε/R = 100 × 2 / 2000 = +1 A
3. i = ε/R = 100 × 2 / 1000 = +2 A
4. i = ε/R = 100 × 2 / 5000 = +0.4 A

Correct answer: i = ε/R = 100 × 2 / 2000 = +1 A

Solution

According to Faraday's law, the induced emf is given as ε = -dϕ/dt = -(100t). At t = 2 s, ε = -100 × 2 = -200 V (magnitude is 200 V). Using Ohm's law, i = ε/R. Substituting R = 2000 Ω, i = 200/2000 = 1 A. Hence, the correct answer is B.

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