Q. An inductance $L$ and a resistance $R$ are first connected to a battery. After some time the battery is disconnected but $L$ and $R$ remain connected in a closed circuit. Then the current reduces to 37% of its initial value in
A) $RL\ sec$
B) $R/L\ \sec$
C) $L/R\ \sec$
D) $1/LR\ \sec$
Explanation
(c) When battery is disconnected current through the circuit starts decreasing exponentially according to $i = i_{0}e^{- Rt/L}$
$\Rightarrow 0.37i_{0} = i_{0}e^{- Rt/L} \Rightarrow 0.37 = \frac{1}{e} = e^{- Rt/L} \Rightarrow t = \frac{L}{R}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.