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 10⁶ Vs^$$-$$1. The area of each plate of the capacitor is 40 cm². The distance between each plate of the capacitor is x $$\times$$ 10^$$-$$3 m. The value of x is __________.

(Permittivity of free space, E₀ = 8.85 $$\times$$ 10^$$-$$12 C² N^$$-$$1 m^$$-$$2).

A capacitor C₁ of capacitance 5 $$\mu$$F is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C₂ of capacitance 10 $$\mu$$F as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C₂ is __________ $$\mu$$C.

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $${x \over {15}}{{{ \in _0}A} \over b}$$. The value of x is ____________.