Question

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

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

Answer 1

The correct option is A $2$ sec.

$emf=L\frac{dI}{dt}$

$0=2\times {10}^{-3}\frac{d\left(t^2{e}^{-t}\right)}{dt}$

differentiate by product rule

$t^2\left({-e}^t\right)+2t{e}^t=0$

$2t{e}^t=t^2{e}^{-t}$

$2t=t^2$

$t=2sec$