Question

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

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

Answer 1

Answer: (A)

$I=t^2{e}^{-t}$
$|\in |=L\frac{dI}{dt}$ here emf is zero when $\frac{dI}{dt}=0$
$\frac{dI}{dt}=2t{e}^{-t}-t^2{e}^{-t}=0;2t{e}^{-t}=t^2{e}^{-t}$
i.e. $t{e}^{-t}(t-2)=0\Rightarrow t\ne \infty t\ne 0,t=2$ sec.