Find the potential difference between $A$ and $B$ in the given circuit in the steady state. (in $V$)

For the shown situation, in the steady state condition, what is the ratio of the charge stored in the first capacitor to the charge stored in the last $(n^{th})$ capacitor?

$A$ parallel plate capacitor of capacity $C_0$ is charged to a potential $V_0$.
$(i)$ The energy stored in the capacitor when the battery is disconnected and the separation is doubled is $E_1$.
$(ii)$ The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is $E_2$.
Then the value of $E_1/E_2$ is:

Find the effective capacitance between points $P$ and $Q$ in the circuit shown in the figure in $\mu F$.

Two positrons $(e^+)$ and two protons $(p)$ are kept on four corners of a square of side $a$ as shown in the figure. The mass of a proton is much larger than the mass of a positron. Let $q$ denote the charge on the proton as well as the positron. Then,the kinetic energies of one of the positrons and one of the protons,respectively,after a very long time will be:

Two capacitors $C_1 = 2\,\mu F$ and $C_2 = 6\,\mu F$ in series are connected in parallel to a third capacitor $C_3 = 4\,\mu F$. This arrangement is then connected to a battery of $e.m.f. = 2\,V$,as shown in the figure. How much energy is lost by the battery in charging the capacitors?