Q. An inductor of 2 H and a resistance of $10\ \Omega$ are connected in series with a battery of 5 V. the initial rate of change of current is
A) $0.5\ As^{- 1}$
B) $2.0\ As^{- 1}$
C) $2.5\ As^{- 1}$
D) $0.25\ As^{- 1}$
Explanation
(c) $i = i_{0}\left( 1 - e^{- \frac{Rt}{L}} \right)$
$\Rightarrow \ \ \ \ \ \ \ \ \frac{di}{dt} = \frac{d}{dt}\ i_{0} - \frac{d}{dt}\left( i_{0}e^{- \frac{Rt}{L}} \right) = 0 + \frac{i_{0}R}{L}\ e^{- \frac{Rt}{L}}$
Initially, t = 0
$\Rightarrow \ \ \ \ \ \ \ \ \frac{di}{dt} = \frac{i_{0} \times R}{L} = \frac{E}{L} = \frac{5}{2} = 2.5\ As^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.