At time $t =0$, terminal $A$ in the circuit shown in the figure is connected to $B$ by a key and alternating current $I ( t )= I _0 \cos (\omega t$,$) , with I _0=1 A$ and $\omega=500 \ rad s ^{-1}$ starts flowing in it with the initial direction shown in the figure.
At $t=\frac{7 \pi}{6 \omega}$, the key is switched from $B$ to $D$. Now onwards on ly $A$ and $D$ are connected. $A$ total charge $Q$ flows from the battery to charge the capacitor fully. If $C =20 \mu, R =10 \Omega$ and the battery is ideal with emf of $50 \ V$, identify the correct statement $(s)$
$(A)$ Magnitude of the maximum charge on the capacitor before $t=\frac{7 \pi}{6 \omega}$ is $1 \times 10^{-3} C$.
$(B)$ The current in the left part of the circuit just before $t=\frac{7 \pi}{6 \omega}$ is clockwise
$(C)$ Immediately after $A$ is connected to $D$. the current in $R$ is $10 A$.
$(D)$ $Q =2 \times 10^{-3} C$.
