Find the potentials at points $A$ and $B$ in the circuit shown in the figure.

$A$ 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 plate 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:

Two capacitors of $2 \mu F$ and $3 \mu F$ are charged to $150 \ V$ and $120 \ V$ respectively. The plates of the capacitors are connected as shown in the figure. $A$ discharged capacitor of capacity $1.5 \mu F$ is connected to the free ends of the wire. Then:

In the circuit shown in the figure,the charge stored in the capacitor of capacity $5 \ \mu F$ is......$ \mu C$.

$A$ spherical drop of mercury having a potential of $2.5\, V$ is obtained as a result of merging $125$ droplets. The potential of constituent droplets would be........$V$

Six point charges are kept at the vertices of a regular hexagon of side $L$ and centre $O$,as shown in the figure. Given that $K = \frac{1}{4 \pi \varepsilon_0} \frac{q}{L^2}$,which of the following statement$(s)$ is (are) correct?
$(A)$ The electric field at $O$ is $6K$ along $OD$
$(B)$ The potential at $O$ is zero
$(C)$ The potential at all points on the line $PR$ is same
$(D)$ The potential at all points on the line $ST$ is same.