# In an inductor of selfinductance l = 2mH, current changes with time according to the relation I = t^2e^-t. The time at which the emf becomes zero is (A) 4s (B) 2s (C) 1s (D) 0.5s

Given

L = 2mH and I = t2e-t

E = -L(dI/dt)

= -L [d/dt(t2e-t)] $$E = -L\left | 2te^{-t}-t^{2}e^{-t} \right |$$

If the emf is zero, E = 0

Hence,

⇒ 2te-t = t2e-t

We get,

t = 2s

Hence, the emf becomes zero at 2s

Therefore, the correct option is (B)