A parallel plate capacitor with width $$4 \mathrm{~cm}$$, length $$8 \mathrm{~cm}$$ and separation between the plates of $$4 \mathrm{~mm}$$ is connected to a battery of $$20 \mathrm{~V}$$. A dielectric slab of dielectric constant 5 having length $$1 \mathrm{~cm}$$, width $$4 \mathrm{~cm}$$ and thickness $$4 \mathrm{~mm}$$ is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be ____________ $$\epsilon_{0}$$ J. (Where $$\epsilon_{0}$$ is the permittivity of free space)

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness $$\left(t_{1}\right.$$ and $$\left.t_{2}\right)$$ as shown in figure. The two different dielectric materials are separated by a conducting foil $$\mathrm{F}$$. The voltage of the conducting foil is V.

Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be ___________ V.

The displacement current of 4.425 $$\mu$$A is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 10^{6} Vs^{$$-$$1}. The area of each plate of the capacitor is 40 cm^{2}. The distance between each plate of the capacitor is x $$\times$$ 10^{$$-$$3} m. The value of x is __________.

(Permittivity of free space, E_{0} = 8.85 $$\times$$ 10^{$$-$$12} C^{2} N^{$$-$$1} m^{$$-$$2}).