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Conventional current

In an inducto...

Question

In an inductor of self- inductance L= 2mH, current changes with time according to relation i= t2(e)-t (-t is power of e). T what time emf is zero ?

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Solution

L = 2mH, $i = t^{2} e^{- t} E = - L \frac{d i}{d t} = - L [2 t e^{- t} + (- t^{2} e^{- t}] w h e n E = 0 - e^{- t} t^{2} + 2 t e^{- t} = 0 - e^{- t} (t^{2} - 2 t) = 0 (t^{2} - 2 t) = 0 t (t - 2) = 0 t = 2 s e c o n d$

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