Question

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?

• A. $4\,s$
• B. $3\,s$
• C. $2\,s$
• D. $1\,s$

Answer 1

Answer: (C)

$L=2\,mH=2\times10^{-3}\,H$
$I=t^{2}e^{-t}$
$\frac{dI}{dt}=t^{2}e^{-1}(-1)+e^{-t}(2t)=te^{-t}(-t+2)$
Emf $=L\frac{dI}{dt}=2\times10^{-3}\,t\,e^{-t}(-t+2)$
Now, emf = $0$, when $(-t+2)=0$
or $t=2\,s$