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=2xx10^(-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)=2xx10^(-3)te^(-1)(-t+2)`
Now, emf=0, when `(-t+2)=0` or `t=2s`