Q. An emf is 15 V is applied in a circuit coil containing 5 H inductance and $10\ \Omega$ resistance. The ratio of currents at time $t = \infty\ $ and $t = 1$ s is
A) $\frac{e^{1/2}}{e^{1/2} - \ 1}$
B) $\frac{e^{2}}{e^{2} - 1}$
C) $1 - e^{- 1}$
D) $e^{- 1}$
Explanation
(b) Here, $i = i_{0}\ at\ t = \infty.Let\ i$ be the current at $t$ = 1 s
From $i = i_{0}\left( 1 - e^{- \frac{R}{L}t} \right)$
= $i_{0}\left( 1 - e^{- \frac{10}{5} \times 1} \right) = i_{0}\left( 1 - \frac{1}{e^{2}} \right)$
$\therefore\ \ \frac{i_{0}}{i} = \ \frac{e^{2}}{e^{2} - 1\ }$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.