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

Options

A. 2 s
B. 3 s
C. 4 s
D. 1 s

Answer

A

Explanation

`I=t^(2)e^(-t)`
`:. (dI)/(dt) = 2 te^(-t)-t^(2)e^(-t)=te^(-t)(2-t)`
The induced e.m.f. `e = -L(dI)/(dt)`
For e to be = 0, `(dI)/(dt) =0` as L cannot be zero.
`:'` Either t=0 or t=2 [this is option (a)]