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 _______.
In the given figure, the charge stored in $$6 \mu F$$ capacitor, when points $$A$$ and $$B$$ are joined by a connecting wire is __________ $$\mu C$$.
