At time $t=0$, terminal $A$ in the circuit shown in the figure is connected to $B$ by a key and an alternating current $I ( t )= I _{0} \cos (\omega t)$, with $I _{0}=1 A$ and $\omega=500\, rad / s$ 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 only $A$ and $D$ are connected. $A$ total charge $Q$ flows from the battery to charge the capacitor fully. If $C =20 \,\mu F , R =10 \,\Omega$ and the battery is ideal with emf of $50\, V$, identify the correct statement $( s )$.