Question

At the moment $t=0$ , when the charge on the capacitor $C_1$ is zero, the switch is closed. If $I_0$ be the current through inductor at $t=0$ , then for $t>0$ (initially $C_2$ is uncharged)

• A. maximum current through inductor equals $\frac{I_0}{2}$
• B. maximum current through inductor equals $\frac{C_1{I}_0}{C_1+C_2}$
• C. maximum charge on $C_1=\frac{C_1{I}_0\sqrt{L{C}_2}}{C_1+C_2}$
• D. maximum charge on $C_1=C_1{I}_0\sqrt{\frac{L}{C_1+C_2}}$

Answer 1

Answer: (D)

The maximum current through the inductor is $I_0$ .
By conservation of energy,
$\frac{1}{2}L{I}_0^2=\frac{1}{2}\left(C_1+C_2\right)V^2$
$V=\sqrt{\frac{L}{\left(C_1+C_2\right)}}{I}_0$
$Q_1=C_{1}V=C_1{I}_0\sqrt{\frac{L}{C_1+C_2}}$