Question

for a coil having L= 2mH , current flowing through it is i=t2 e-t then the time at which emf become zero

1) 2s

3) 1s

3) 4s

4) 3s

Answer 1

The emf will be zero at t = 2 second.

Solution:

The coil which has current flow of I in an equation with time t is given by differentiating the given equation as follows,

Given: L = 2 mH

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

Emf e = 0

As we know that the emf of the coil is given by –

$\begin{array}{l}{\text {Emf } e=L\left(\frac{d I}{d t}\right)} \\ {0=2 \times 10^{-3}\left[\frac{d\left(t^{2} e^{-t}\right)}{d t}\right]} \\ {\frac{d\left(t^{2} e^{-t}\right)}{d t}=0}\end{array}$

Differentiating the equation we get  

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

2 = t

Time t = 2 sec.

Answer 2

Thus, time at which emf becomes zero is 2 s.