$27$ 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.

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	$(4)$ $2 C_0 / 3$
	$(5)$ $2 C_0$

Three uncharged capacitors of capacitance $C_1$,$C_2$ and $C_3$ are connected as shown in the figure to one another and to points $A$,$B$ and $D$ at potentials $V_A$,$V_B$ and $V_D$. Then the potential at point $O$ will be

$A$ capacitor of capacitance $5\,\mu F$ is connected as shown in the figure. The internal resistance of the cell is $0.5\,\Omega$. The amount of charge on the capacitor plate is......$\mu C$.

Each capacitor shown in the figure has a capacitance of $5.0 \ \mu F$. The battery has an $emf$ of $50 \ V$. If the switch $S$ is closed,what amount of charge will flow through $AB$?

The capacities and connection of five capacitors are shown in the adjoining figure. The potential difference between the points $A$ and $B$ is $60\;V$. Then the equivalent capacity between $A$ and $B$ and the charge on $5\;\mu F$ capacitor will be respectively: