Question

A solenoid of inductance $L$ with resistance $r$ is connected in parallel to a resistance $R$. A battery of emf $E$ and of negligible internal resistance is connected across the parallel combination as shown in the figure. At the time $t=0$, switch $S$ is opened, calculate current through the solenoid after the switch is opened.

Answer 1

When $S$-closed for longtime

$I=\frac{E}{r}$

at $t=0$ $S$-open after that current through solenoid is $i$.

$i=I{e}^{\frac{-t}{T}}$

$T=\frac{L}{R+r}$

$i=\frac{E}{r}{e}^{\frac{-t(R+r)}{L}}$