Dielectric Capacitor

In contrast to capacitors separated by a vacuum or air, a dielectric capacitor uses a Dielectric material between plates to increase the total capacitance.

Capacitance §

If we have a Capacitor initially having plates separated by a vacuum, and then insert a dielectric, the new capacitance is given by:

Formula §

$$C=\kappa C_{vacuum}=\frac{\kappa {ϵ}_{0}A}{d}$$

• $\kappa$ = Dielectric constant = $\frac{{ϵ}_{material}}{{ϵ}_0}$ (Dimensionless)
• ${ϵ}_0$ = Permittivity of free space (also called vacuum permittivity)

Justification §

The definition of Capacitance is: $C=\frac{q}{V}$. The of a parallel plate capacitor is given by: to represent the capacitance in terms of the electric field:

$$C=\frac{q}{d\times \vec{E}}$$

In order to increase $C$ for the same amount of charge and separation, we need to decrease $\vec{E}$.

If we have a charged capacitor, it has an existing $\vec{E}$. If we insert a dielectric, polarisation causes the dielectric material to oppose the electric field, reducing it’s strength:

$${\vec{E}}_{withdielectric}=\frac{{\vec{E}}_{vaccuum}}{\kappa }$$