Question

A coil of inductance $300mH$ and resistance $2\Omega$ is connected to a source of voltage $2V$. The current reaches half of its steady state value in:

• A. $0.05s$
• B. $0.1s$
• C. $0.15s$
• D. $0.3s$

Answer 1

Answer: (B)

The current at any instant is given by
$I=I_0\left(1-e^{-Rt/L}\right)$
$\frac{I_0}{2}=I_0\left(1-e^{-Rt/L}\right)$
$\frac{1}{2}=\left(1-e^{-Rt/L}\right)$
$e^{-Rt/L}=1/2$
$\frac{Rt}{L}=In2$
$\therefore t=\frac{L}{R}In2=\frac{300\times 10^{-3}}{2}\times 0.693$
$=150\times 0.693\times 10^{-3}$
$=0.10395s=0.1s$