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An inductor has self-inductance L = 2 mH. The current through it varies with time as i = t² e^-t. At what instant is the induced emf zero?

1. 4 s
2. 3 s
3. 2 s
4. 1 s

Correct answer: 2 s

Solution

di/dt = d/dt(t^2 e^-t) = e^-t (2t - t^2) = t e^-t (2 - t). This is zero (for t > 0) when 2 - t = 0, i.e. t = 2 s.

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