The current through a coil of self inductance L = 2 mH is given by I = t2 e-t at time t. How long it will take to make the e.m.f. zero ?

Question

The current through a coil of self inductance L = 2 mH is given by I = t2 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

Tardigrade Admin · Accepted Answer

The current is given by the relation i=t2 e-t. Hence the emf would be equal to e=-L (d i/d t)=-2 × 10-3 ×(2 t e-t-t2 e-t) If the emf is zero, e=0, hence 2 t e-t=t2 e-t ⇒ t=2 s

Q. The current through a coil of self inductance $L = 2 m H$ is given by $I = t^{2} e^{- t}$ at time $t$ . How long it will take to make the e.m.f. zero ?

1 s

2 s

3 s

4 s

The current is given by the relation $i = t^{2} e^{- t}$ .
Hence the emf would be equal to
$e = - L \frac{d i}{d t} = - 2 \times 1 0^{- 3} \times (2 t e^{- t} - t^{2} e^{- t})$
If the emf is zero, $e = 0$ , hence
$2 t e^{- t} = t^{2} e^{- t}$
$\Rightarrow t = 2 s$

Q. The current through a coil of self inductance L=2mH is given by I=t2e−t at time t. How long it will take to make the e.m.f. zero ?

1 s

2 s

3 s

4 s

The current is given by the relation i=t2e−t. Hence the emf would be equal to e=−Ldtdi​=−2×10−3×(2te−t−t2e−t) If the emf is zero, e=0, hence 2te−t=t2e−t ⇒t=2s

Q. The current through a coil of self inductance $L = 2 m H$ is given by $I = t^{2} e^{- t}$ at time $t$ . How long it will take to make the e.m.f. zero ?

The current is given by the relation $i = t^{2} e^{- t}$ .
Hence the emf would be equal to
$e = - L \frac{d i}{d t} = - 2 \times 1 0^{- 3} \times (2 t e^{- t} - t^{2} e^{- t})$
If the emf is zero, $e = 0$ , hence
$2 t e^{- t} = t^{2} e^{- t}$
$\Rightarrow t = 2 s$