Find the potential difference, capacitance across A and B, the net capacitance and charge across battery.

Find the ratio of the potential difference that must be applied across the $\left(i\right)$ parallel

$\left(\mathrm{ii}\right)$ series combination of two identical capacitors so that the energy stored in the two cases becomes the same.

Find the voltage between the two points $A$  and $\mathrm{B}$ of the circuit shown in Fig. 

The section$\mathrm{AB}$ of a circuit is shown in Figure The e.mf of the cell is $\mathrm{E}=15 \mathrm{V}$ and the capacitances of $C_1=1\mathrm{\mu F}$ and $C_2=2\mu \mathrm{F}$. The potential difference of $\mathrm{A}$ and $\mathrm{B}$ is $6 \mathrm{V}$. Find the potential difference across each capacitor.