Q. The current through a coil of self inductance $L = 2\ mH$ is given by $I = t^{2}e^{- t}$ at time. $t$. How long it will take to make the e.m.f. zero
A) 1 s
B) 2 s
C) 3 s
D) 4 s
Explanation
(b) $I = t^{2}e^{- t} \Rightarrow \frac{dI}{dt} = 2te^{- t} - t^{2}e^{- t} = te^{- t}(2 - t)$
The induced emf is $\varepsilon = - L\frac{dI}{dt}$
According to given problem, $\varepsilon = 0 \Rightarrow \frac{dI}{dt} = 0$ [Since $L \neq 0$]
Or $e^{- t}t(2 - t) = 0$ either $t = 0$ or $t = 2\ s$
$t = 2s$ matches with the option (b)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.