$A$ capacitor $C_1 = 1\,\mu F$ can withstand a maximum voltage of $V_1 = 6\,kV$,and a capacitor $C_2 = 3\,\mu F$ can withstand a maximum voltage of $V_2 = 4\,kV$. If these two capacitors are connected in series,what is the maximum voltage (in $kV$) that can be applied to the combination?

In the circuit shown in the figure, if the point $R$ is earthed and point $P$ is given a potential of $+1800 \, V$, then the charges on $C_2$ and $C_3$ are respectively:

$A$ 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.

The switch $K$ is closed. Now,the switch $K$ is opened and both capacitors are filled with a dielectric of constant $K = 3$. What is the ratio of the energy of the system when the switch is closed to when it is open,$\frac{U_1}{U_2}$?

Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$. Their centers have an initial separation of $4 R$. Both the spheres are given an initial speed of $u$ towards each other. The minimum value of $u$, so that they can just touch each other is: (Take $k=\frac{1}{4 \pi \epsilon_0}$ and assume $k Q^2 > G m^2$ where $G$ is the Gravitational constant)

$(a)$ $A$ $900 \; pF$ 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?