• # question_answer At a moment $(t=0),$, when the charge on capacitor ${{C}_{1}}$ is zero, the switch is closed, if ${{l}_{0}}$ be the current through inductor at $t=0$, for $t>0$ A)  maximum current through inductor equals $\frac{{{l}_{0}}}{2}$ B)  maximum current through inductor equals $\frac{{{C}_{1}}{{l}_{0}}}{{{C}_{1}}+{{C}_{2}}}$ C)  maximum charge on $\frac{{{C}_{1}}{{l}_{0}}\sqrt{L{{C}_{2}}}}{{{C}_{1}}+{{C}_{2}}}$ D)  maximum charge on ${{C}_{1}}={{C}_{1}}{{l}_{0}}\sqrt{\frac{L}{{{C}_{1}}+{{C}_{2}}}}$

Solution :

For the circuit, $\frac{1}{2}LI_{0}^{2}=\frac{1}{2}\,({{C}_{1}}+{{C}_{2}}){{V}^{2}}$ $\Rightarrow$            $V={{\left[ \frac{LI_{0}^{2}}{({{C}_{1}}+{{C}_{2}})} \right]}^{1/2}}$ As,       ${{Q}_{1}}={{C}_{1}}V={{C}_{1}}{{I}_{0}}\,\sqrt{\frac{L}{{{C}_{1}}+{{C}_{2}}}}$

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