Question

A circuit containing capacitors $C_1$ and $C_2$ , shown in the figure is in the steady state with key $K_1$ closed and $K_2$ opened. At the instant $t=0,K_1$ is opened and $K_2$ is closed. Find the angular frequency of oscillations of $LC$ circuit.(in $rad/s$)

Answer 1

With key $K_1$ closed, $C_1$ and $C_2$ are in series with the battery in steady state.
$\therefore$ $C_{net}=1\mu F$ or $q_0=C_{net}V=20\mu C$
With $K_1$ opened and $K_2$ closed, charge on $C_2$ will remain as it is, while charge on $C_1$ will oscillate in $L-C_1$ circuit.
$\omega =\frac{1}{\sqrt{L{C}_1}}$
$=\frac{1}{\sqrt{0.2\times {10}^{-3}\times 2\times {10}^{-6}}}$
$=5\times {10}^4$ $rad/s$