Question

For a coil having $L=2mH$, current flow through it is $I=t^2{e}^{-t}$ then the time at which emf becomes zero:

• A. $2sec$
• B. $1sec$
• C. $4sec$
• D. $3sec$

Answer 1

The correct option is A $2sec$

Given,

Inductance, $L=2mH$

Change in current, $i=t^2{e}^{-t}$

$emf=-L\frac{di}{dt}=-L\frac{d\left(t^2{e}^{-t}\right)}{dt}=-L(2t{e}^{-t}-t^2{e}^{-1})$

$0=-L(2t{e}^{-t}-t^2{e}^{-1})$

$t(t-2)=0$

$t=0,2$

At $2\sec$emf become zero.