In an inductor of self-inductance L = 2 mH, current changes with time according to relation, I=t2e-t At what time emf is zero?

Question

In an inductor of self-inductance L = 2 mH, current changes with time according to relation, I=t2e-t At what time emf is zero? (A) 4 s (B) 3 s (C) 2 s (D) 1 s

Tardigrade Admin · Accepted Answer

L=2 mH=2×10-3 H I=t2e-t (dI/dt)=t2e-1(-1)+e-t(2t)=te-t(-t+2) Emf =L(dI/dt)=2×10-3 t e-t(-t+2) Now, emf = 0, when (-t+2)=0 or t=2 s

Q. In an inductor of self-inductance $L = 2 m H$ , current changes with time according to relation, $I = t^{2} e^{- t}$ At what time emf is zero?

$4 s$

$3 s$

$2 s$

$1 s$

$L = 2 m H = 2 \times 1 0^{- 3} H$
$I = t^{2} e^{- t}$
$\frac{d I}{d t} = t^{2} e^{- 1} (- 1) + e^{- t} (2 t) = t e^{- t} (- t + 2)$
Emf $= L \frac{d I}{d t} = 2 \times 1 0^{- 3} t e^{- t} (- t + 2)$
Now, emf = $0$ , when $(- t + 2) = 0$
or $t = 2 s$

Q. In an inductor of self-inductance L=2mH, current changes with time according to relation, I=t2e−t At what time emf is zero?

4s

3s

2s

1s