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  4. For a coil having L = 2 mH, current flow through it is I= t2e-l then, the time at which emf become zero

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

AIPMTAIPMT 2001

Solution:

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