Find the heat produced in the circuit shown in the figure, on closing the switch $S$

Three capacitors each having capacitance $C=2 \mathrm{\mu F}$ are connected with a battery of emf $30 \mathrm{V}$, as shown in the figure. When the switch $S$ is closed, find
(i) the amount of charge flown through the battery,
(ii) the heat generated in the circuit,
(iii) the energy supplied by the battery,
(iv) the amount of charge flown through the switch $S$.

Two parallel plate capacitors whose capacities are$C$ and $2C$ respectively, are joined in parallel. These are charged by $V$ potential difference. If the battery is now removed and a dielectric of dielectric constant $K$ is filled in between the plates of the capacitor $C$, then, what will be the potential difference across each capacitor?

The effective capacitance of the system in the figure given below will be

The capacitance of a parallel capacitor is $C$. If it is half filled with a dielectric of constant $K$, then, the new capacitance will become

$X$ and $Y$ are two parallel plate capacitors having same area of plates and same separation between the plates. $X$ has air between the plates and $Y$ contains a dielectric medium ${\epsilon }_{\mathrm{r}}=5$.
(i) Calculate the voltage of the plates $X$ and $Y$.
(ii) What is the ratio of electrostatic energy stored in $X$ and $Y?$