Find the equivalent capacitance across $AB$ in $\mu F$ (all capacitances are in $\mu F$).

The potential difference that must be applied across the parallel and series combination of three identical capacitors such that the energy stored in them becomes the same. The ratio of potential difference in parallel to series combination is

$512$ identical drops of mercury are charged to a potential of $2 \ V$ each. The drops are joined to form a single drop. The potential of this drop is ......... $V.$

Effective capacitance of parallel combination of two capacitors $C_{1}$ and $C_{2}$ is $10\; \mu F$. When these capacitors are individually connected to a voltage source of $1\; V,$ the energy stored in the capacitor $C_{2}$ is $4$ times that of $C_{1}$. If these capacitors are connected in series,their effective capacitance will be (in $; \mu F$)

Two capacitors of capacitances $1 \ \mu F$ and $2 \ \mu F$ are charged to potential differences $20 \ V$ and $15 \ V$ as shown in the figure. If terminals $B$ and $C$ are connected together and terminals $A$ and $D$ are connected together,then find the final charge on the $1 \ \mu F$ capacitor.

The radii of two metallic spheres $P$ and $Q$ are $r_1$ and $r_2$ respectively. They are given the same charge. If $r_1 > r_2$,then on connecting them with a thin wire,the charge will flow