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

Answer 1

Answer: (A), (C), (D)

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

After long time:
Current through $R$ is given by , $I=\frac{V}{R}$
and also, $L{I}_1=L_2{I}_2$

$\Rightarrow \frac{I_1}{I_2}=\frac{L_2}{L_1}$

Current through $L_1$ is , $I_1=\frac{L_{2}I}{L_1+L_2}=\left(\frac{V{L}_2}{R(L_1+L_2)}\right)$

Current through $L_2$ is , $I_2=\frac{L_{1}I}{L_1+L_2}=\left(\frac{V{L}_1}{R(L_1+L_2)}\right)$

At $t=0$, Both inductors are open, So current through the resistor is zero.

Hence, options (a) , (c) and (d) are the correct answers.