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
A) 0.05 s
B) 0.1 s
C) 0.15 s
D) 0.3 s
Explanation
(b) The current at any instant is given by
$\ \ \ \ \ \ \ \ \ \ \ I = I_{0}(1 - e^{- Rt/L})$
$\ \ \ \ \ \ \ \ \ \frac{I_{0}}{2} = I_{0}(1 - e^{- Rt/L})$
$\ \ \ \ \ \ \ \ \ \ \frac{1}{2} = (1 - e^{- Rt/L})$
$e^{- Rt/L} = \frac{1}{2}$
$\ \ \ \ \ \ \ \ \ \frac{Rt}{L} = 1\ $n$\ 2$
$\therefore\ \ \ \ \ \ \ t = \frac{L}{2}\ 1\ n\ 2 = \frac{3\ \ 00 \times 1\ \ 0^{- 3}}{2} \times 0.6\ \ 93$
$= 1\ 50 \times 0.6\ \ 93 \times 1\ \ 0^{- 3}$
$= 0.10395s = 0.1\ s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.