Question

What is an electrical capacitor? Find the expression for the capacity of a parallel plate capacitor. On which factors does the capacitance depend?

Hint:

The capacitance of a capacitor increases with the dielectric constant of the material between the plates and decreases with the distance between the plates.

Answer 1

An electrical capacitor is a device that stores electrical energy in an electric field. It consists of two conductive plates separated by an insulating material (called the dielectric). When a potential difference is applied across the plates, a charge is stored on each plate.
The capacitance \(C\) of a parallel plate capacitor is given by the expression: \[ C = \epsilon_0 \frac{A}{d} \] Where:
- \(C\) is the capacitance,
- \(\epsilon_0\) is the permittivity of free space (\(\epsilon_0 = 8.85 \times 10^{-12}~\text{F/m}\)),
- \(A\) is the area of one of the plates,
- \(d\) is the separation between the plates.
The capacitance depends on the following factors:
1. The area of the plates: A larger area increases the capacitance.
2. The separation between the plates: A smaller distance between the plates increases the capacitance.
3. The dielectric material between the plates: The dielectric constant (\(\kappa\)) of the material increases the capacitance. The capacitance with a dielectric is given by: \[ C = \kappa \epsilon_0 \frac{A}{d} \] Where \(\kappa\) is the dielectric constant of the material.