Capacitance of parallel plate capacitor with a dielectric slab:

The capacitance of a parallel plate capacitor of plate area A and plate separation d with vacuum between its plates is given by

The electric field set up between the plates is

When a dielectric plate of thickness t<d is placed between the plates, then the induced field in the dielectric is given by

The net field inside the dielectric is

The potential difference between the capacitor palates is

The capacitance of a capacitor on introduction of dielectric slab becomes

Special cases:

If t = d then

Thus the capacitance of a parallel plate capacitor increases k times when entire space is filled with dielectric material.

Clearly,

If capacitor with a conducting slab then: The capacitance of a parallel plate capacitor of plate area A and plate separation d with vacuum between its plates is given by

The electric field set up between the plates is

The potential difference between the capacitor plates is

V = E₀ (d - t)

Capacitance is given by

Clearly,

C > C₀. Thus introduction of a conducting slab of thickness t in a parallel plate capacitor increase its capacitance by a factor of d/(d-t)

Uses of capacitors:

1. To produce electric fields of desired patterns.
2. In radio circuit for tuning.
3. In power supplies for smoothing the rectified current.
4. For producing rotating magnetic fields in induction motors.
5. In the tank ckt of oscillations.

They store not only charge, but also energy in the electric field between their plates.