When a potential difference of $10^{3} \, V$ is applied between $A$ and $B$, a charge of $0.75 \, mC$ is stored in the circuit. The value of $C$ is (in $\mu F$):

$27$ similar drops of mercury are maintained at $10 \, V$ each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ....... times that of a smaller drop.

$A$ 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?

Two conducting shells of radius $a$ and $b$ are connected by a conducting wire as shown in the figure. The larger shell is grounded. The capacitance of the system is:

Three identical capacitors, each of capacitance $C$, are connected in series, resulting in a net capacitance $x$. If these three capacitors are then connected in parallel, what is the ratio of the energy stored in the series configuration to the energy stored in the parallel configuration, assuming both configurations are connected to the same voltage source $V$?

Consider an infinite matrix of capacitors as shown in the figure. The effective capacitance between point $A$ and $B$ will be