Find the charge on capacitor $C_3$. Given that $C_1 = C_2 = C$ and $C_3 = C_4 = 3C$.

$A$ capacitor of $2\,\mu F$ capacitance is charged steadily from $0$ to $5\,C$. Which of the following graphs correctly represents the variation of potential difference $(V)$ across its plates with respect to the charge $(Q)$ on the capacitor?

Four identical thin, square metal sheets, $S_1, S_2, S_3$, and $S_4$, each of side $a$ are kept parallel to each other with equal distance $d( < < a)$ between them, as shown in the figure. Let $C_0 = \varepsilon_0 a^2 / d$, where $\varepsilon_0$ is the permittivity of free space.
Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option.

$List-I$	$List-II$
$(P)$ The capacitance between $S_1$ and $S_4$, with $S_2$ and $S_3$ not connected, is	$(1)$ $3 C_0$
$(Q)$ The capacitance between $S_1$ and $S_4$, with $S_2$ shorted to $S_3$, is	$(2)$ $C_0 / 2$
$(R)$ The capacitance between $S_1$ and $S_3$, with $S_2$ shorted to $S_4$, is	$(3)$ $C_0 / 3$
$(S)$ The capacitance between $S_1$ and $S_2$, with $S_3$ shorted to $S_1$, and $S_2$ shorted to $S_4$, is	$(4)$ $2 C_0 / 3$
	$(5)$ $2 C_0$

Four equal capacitors are connected to a $10 \, V$ battery as shown in the figure. The potentials of $A$ and $B$ are:

Two metal spheres,one of radius $R$ and the other of radius $2R$,both have the same surface charge density $\sigma$. They are brought in contact and then separated. What will be the new surface charge densities on them?

In the circuit shown in the figure,four capacitors are connected to a battery. The charge on the $5 \ \mu\text{F}$ capacitor is ....... $\mu\text{C}$.