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, $i_1=\frac{L_2}{L_1+L_2}\cdot \frac{V}{R},$
$i_2=\frac{L_1}{L_1+L_2}\cdot \frac{V}{R}$