Four capacitors of capacitance $10\,\mu F$ and a battery of $200\, V$ are arranged as shown. How much charge will flow through $AB$ after the switch $S$ is closed? (in $\mu C$)

If $V_{A}-V_{B}=7 \text{ V}$,then find the stored energy in $C_1$.

For the circuit shown in the figure,the charge on the $4 \mu F$ capacitor is $....... \mu C$.

The space between the plates of a parallel plate capacitor of plate area $4 \ cm^2$ and separation $d = 1.77 \ mm$ is filled with uniform dielectric materials with dielectric constants $k_1 = 5$ and $k_2 = 3$ as shown in the figure. Another capacitor of capacitance $7.5 \ pF$ is connected in parallel with it. The effective capacitance of this combination is . . . . . . $pF$. (Given $\varepsilon_0 = 8.85 \times 10^{-12} \ F/m$)

$A$ capacitor,$C_1 = 6 \ \mu F$ is charged to a potential difference of $V_0 = 5 \ V$ using a $5 \ V$ battery. The battery is removed and another capacitor,$C_2 = 12 \ \mu F$ is inserted in place of the battery. When the switch $S$ is closed,the charge flows between the capacitors for some time until an equilibrium condition is reached. What are the charges ($q_1$ and $q_2$) on the capacitors $C_1$ and $C_2$ when the equilibrium condition is reached?

The two plates of a parallel plate capacitor are given charges $Q_1$ and $Q_2$. The capacity of the capacitor is $C$. When the switch $(S)$ is closed,mark the correct statement. (Assume both $Q_1$ and $Q_2$ to be positive)