Question

In the circuit shown below, the key $K$ is closed at $t=0$. The current through the battery is

• A. $\frac{V{R}_1{R}_2}{\sqrt{R_1^2+R_2^2}}$ at $t=0$ and $\frac{V}{R^2}$ at $t=\infty$
• B. $\frac{V}{R^2}$ at $t=0$ and $\frac{V\left(R_1+R_2\right)}{R_1^2{R}_2^2}$ at $t=\infty$
• C. $\frac{V}{R^2}$ at $t=0$ and $\frac{V{R}_1{R}_2}{\sqrt{R_1^2+R_2^2}}$ at $t=\infty$
• D. $\frac{V\left(R_1+R_2\right)}{R_1^2{R}_2^2}$ at $t=0$ and $\frac{V}{R^2}$ at $t=\infty$

Answer 1

Answer: (B)

At $t=0$, inductor behaves like an infinite resistance
So at $t=0,i=\frac{V}{R_2}$
and at $t=\infty$ , inductor behaves like a conducting wire
$i=\frac{V}{R_{eq}}=\frac{V\left(R_1+R_2\right)}{R_1^2{R}_2^2}$