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

Answer

C

Explanation

`L = 2mH = 2 xx 10^(-3) H`
`I = t^2 e^(-t) , (dI)/(dt) = t^2 e^(-t) (-1) + e^(-t) (2t) = te^(-t) (-t + 2)`
emf ` = L (dI)/(dt) = 2 xx 10^(-3) te^(-1) (-t+2)`
Now , emf = 0, when (-t+ 2) = 0 or t = 2s