Question

A source of constant voltage $V$ is connected to a resistance $R$ and two ideal inductors $L_1$ and $L_2$ through a switch $S$ as shown. There is no mutual inductance between the two inductors. The switch $S$ is initially open. At $t=0$, the switch is closed and current beings to flow. Which of the following options is/are correct?

• A. After a long time, the current through $L_1$ will be $\frac{V{L}_2}{R{L}_1+L_2}$
• B. After a long time, the current through $L_2$ will be $\frac{V{L}_2}{R{L}_1+L_2}$
• C. The ratio of the currents through $L_1$ and $L_2$ is fixed at all times $(t>0)$
• D. At $t=0$, the current through the resistance $R$ is $\frac{V}{R}$

Answer 1

The correct option is C The ratio of the currents through $L_1$ and $L_2$ is fixed at all times $(t>0)$

After a long time current through $L_1$ will be, $\frac{V}{R}\times \frac{L_2}{L_1+L_2}$

After a long time current through $L_2$ will be ,$\frac{V}{R}\times \frac{L_1}{R_2}$

Time can be inferred from that $I_{L1}:I_{L2}=L_2:L_1$

The ratio of current is fixed all the time in $L_1$ and $L_2$.