Question

Please solve this question​

Answer 1

Given,

→ Inductance L = 2mH

$\sf \: current \: \: i = {t}^{2} {e}^{ - t}$

We know that,

$\sf \: \: emf( \epsilon) = L \frac{di}{dt}$

Now,

According to the question,

emf = 0

so,

$\sf \: \frac{di}{dt} = 0 \\ \\ = > \frac{d}{dt} ( {t}^{2} {e}^{ - t} ) = 0 \\ \\ = > {e}^{ - t} \frac{d}{dt} {t}^{2} + {t}^{2} \frac{d}{dt} {e}^{ - t} = 0 \\ \\ = > 2t {e}^{ - t} - {t}^{2} {e}^{ - t} = 0 \\ \\ = > 2t {e}^{ - t} = {t}^{2} {e}^{ - t} \\ \\ = > t {e}^{ - t} (t - 2) = 0 \\ \\ \therefore \: t - 2 = 0 \\ \\ = > t = 2 \: s$

So option (C) 2 s is the correct answer