Two capacitors of capacities $1 \mu F$ and $C \mu F$ are connected in series and the combination is charged to a potential difference of $120 \ V$. If the charge on the combination is $80 \mu C$,the energy stored in the capacitor of capacity $C$ in $\mu J$ is

In the given circuit, what are the potential differences between points $A$ and $B$ $(V_{AB})$ and between points $B$ and $C$ $(V_{BC})$?

$(a)$ $A$ $900 \; pF$ capacitor is charged by a $100 \; V$ battery [Figure $(a)$]. How much electrostatic energy is stored by the capacitor?
$(b)$ The capacitor is disconnected from the battery and connected to another $900 \; pF$ capacitor [Figure $(b)$]. What is the electrostatic energy stored by the system?

The following figure shows a $9 \ V$ battery and $3$ uncharged capacitors of capacitances $C_1 = C_2 = C_3 = 1 \ \mu F$. The switch is thrown to the right side until capacitor $C_1$ is fully charged,then the switch is thrown to the left. The final charge on capacitor $C_2$ is (in $\mu C$)

Four capacitors are connected to a battery as shown in the circuit. The ratio of charges on capacitors $C_2$ and $C_4$ is (Assume $C_1 = 1 \mu F, C_2 = 2 \mu F, C_3 = 3 \mu F, C_4 = 4 \mu F$ and the battery voltage $V = 10 \ V$ connected across the combination).

Three capacitors $C_1, C_2$ and $C_3$ are connected as shown in the figure to a battery of $V$ volt. If the capacitor $C_3$ breaks down electrically,the change in total charge on the combination of capacitors is