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 begins to flow. Which of the following options is/are correct?

• A. After a long time, the current through $L_1$ will be $\frac{V}{R} \frac{L_{2}}{L_{1}+L_{2}}$
• B. After a long time, the current through $𝐿_2$ will be $L_1$ will be $\frac{V}{R} \frac{L_{2}}{L_{1}+L_{2}}$
• 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

Answer: (A), (B), (C)

Let current through $R , L _{1}$ and $L _{2}$ is i, $i _{1}$ and $i _{2}$ respectively $L_{1} i_{1}=L_{2} i_{2}$ ...(i)
$i _{1}+ i _{2}= i =\frac{ V }{ R }$ ... (ii)
After long time
Solving, $i _{1}=\frac{ L _{2}}{ L _{1}+ L _{2}} \cdot \frac{ V }{ R },$
$i _{2}=\frac{ L _{1}}{ L _{1}+ L _{2}} \cdot \frac{ V }{ R }$