Three capacitors of capacitances $$25 \mu \mathrm{F}, 30 \mu \mathrm{F}$$ and $$45 \mu \mathrm{F}$$ are connected in parallel to a supply of $$100 \mathrm{~V}$$. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is $$\frac{9}{x} \mathrm{E}$$. The value of $$x$$ is _________.

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 _________.