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.
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 ____________.
