In an inductor of self-inductance L = 2 mH, current changes

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In an inductor of self-inductance L = 2 mH, current changes with time according to relation i = t²e^–t. At what time emf is zero?

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

Correct Option: C

L = 2mH, i = t²e^–t

E = - L	di	= - L[-t²e^–t + 2te^-t]
	dt

when E = 0,
- e^-te^–t + 2te^-t = 0
or, 2t e^-t = e^-t t²
⇒ t = 2 sec.