What is the total electrostatic potential energy of the given system in $J$? (Given: $\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9} \ N \cdot m^2/C^2$)

Find the charge on the capacitor $C$ in the following circuit in $\mu C$.

Minimum number of $2\,\mu F$ and $250\, V$ capacitors required to make a combination of $12\,\mu F$ and $500\, V$ is:

Three capacitors $C_{1} = 2 \, \mu F$,$C_{2} = 6 \, \mu F$,and $C_{3} = 12 \, \mu F$ are connected as shown in the figure. Find the ratio of the charges on capacitors $C_{1}$,$C_{2}$,and $C_{3}$ respectively.

$A$ series combination of $n_1$ capacitors,each of value $C_1$,is charged by a source of potential difference $4V$. When another parallel combination of $n_2$ capacitors,each of value $C_2$,is charged by a source of potential difference $V$,it has the same total energy stored in it as the first combination has. The value of $C_2$ in terms of $C_1$ is:

$A$ thin metallic partition of negligible thickness is inserted between two shaded metallic plates as shown. The remaining ends are then packed with insulating plates to form a container-like structure. Two taps shown are opened at $t = 0$ and finally closed at $t = 5 \ s$. Find the capacitance of the system between $A$ and $B$ after closing the taps. (Assume the liquid to be non-conducting). Volumetric flow rates and dielectric constants of the liquid are given.