A parallel plate capacitor of capacitance $$12.5 \mathrm{~pF}$$ is charged by a battery connected between its plates to potential difference of $$12.0 \mathrm{~V}$$. The battery is now disconnected and a dielectric slab $$(\epsilon_{\mathrm{r}}=6)$$ is inserted between the plates. The change in its potential energy after inserting the dielectric slab is ________ $$\times10^{-12} \mathrm{~J}$$.

A parallel plate capacitor with plate separation $$5 \mathrm{~mm}$$ is charged up by a battery. It is found that on introducing a dielectric sheet of thickness $$2 \mathrm{~mm}$$, while keeping the battery connections intact, the capacitor draws $$25 \%$$ more charge from the battery than before. The dielectric constant of the sheet is _________.

A capacitor of capacitance $$\mathrm{C}$$ and potential $$\mathrm{V}$$ has energy $$\mathrm{E}$$. It is connected to another capacitor of capacitance $$2 \mathrm{C}$$ and potential $$2 \mathrm{~V}$$. Then the loss of energy is $$\frac{x}{3} \mathrm{E}$$, where $$x$$ is _______.