Derive an expression for the energy stored in a capacitor. What is the energy stored when space between the plates is filled with a dielectric, with charging battery connected in the circuit.

An equilateral triangle has a side length $L$. A charge $+q$ is kept at the centroid of the triangle. $P$ is a point on the perimeter of the triangle. The ratio of the minimum and maximum possible electric potentials for the point $P$ is

$ABC$ is an equilateral triangle of side $2 m$. There is a uniform electric field of intensity $100 V/m$ in the plane of the triangle and parallel to $BC$ as shown. If the potential at A is $200 V$, then the electric potentials at $B$ and $C$ are respectively.

Three identical metal plates each of area $\mathrm{A}$ are arranged parallel to each other, $\mathrm{d}$ is the distance between the plates as shown. A battery of $\mathrm{V}$ volts is connected as shown. The charge stored in the system of plate is - 

Four identical metal plates each of area $A$ are separated mutually by a distance $d$ and are connected as shown. Find the capacity of the system between the terminal $A$ and $B$.