$A$ capacitor of capacity $C$ is connected to a battery of potential $V$ in parallel. The distance between its plates is reduced to half at once,while the battery remains connected. Then,the energy supplied by the battery to charge the capacitor to potential $V$ again is:

$125$ identical drops,each charged to a potential of $50\;V$,are combined to form a single drop. The potential of the new drop will be......$V$.

Condenser $A$ has a capacity of $15\,\mu F$ when it is filled with a medium of dielectric constant $15$. Another condenser $B$ has a capacity of $1\,\mu F$ with air between the plates. Both are charged separately by a battery of $100\,V$. After charging,both are connected in parallel without the battery and the dielectric medium being removed. The common potential now is.....$V$

Four capacitors of capacitances $2 \mu F$,$3 \mu F$,$4 \mu F$,and $x \mu F$ are connected to a battery of emf $6 \text{ V}$ and of negligible internal resistance,as shown in the figure. If the ratio of the charges on $x \mu F$ and $4 \mu F$ capacitances is $\frac{3}{8}$,then the value of $x$ is

Two parallel plate capacitors with capacitances $C$ and $2C$ are connected in parallel. They are charged to a potential difference $V$. Now,if the battery is disconnected and a dielectric of dielectric constant $K$ is inserted between the plates of the capacitor with capacitance $C$,find the potential difference across each capacitor.

The dielectric strength of air is $E = 3 \times 10^6 \ V/m$. What is the maximum charge that can be given to a sphere of diameter $6 \ m$? (in Coulombs)