Q. A coil of inductance $300\, mH$ and resistance $2\, \Omega$ is connected to a source of voltage $2V$. The current reaches half of its steady state value in:
AIEEEAIEEE 2005Alternating Current
Solution:
The current at any instant is given by
$I=I_{0}\left(1-e^{-Rt/L}\right)$
$\frac{I_{0}}{2}=I_{0}\left(1-e^{-Rt/L}\right)$
$\frac{1}{2}=\left(1-e^{-Rt/L}\right)$
$e^{-Rt/L}=1/2$
$\frac{Rt}{L}=In\,2$
$\therefore t=\frac{L}{R} In\,2=\frac{300\times10^{-3}}{2}\times0.693$
$=150\times0.693\times10^{-3}$
$= 0.10395\, s= 0.1\,s$
