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Derive. The capacitance of a parallel plate capacitor is given by the formula

where

            A = area of the plates (m²)

            d = distance between the plates (m)

            K = dielectric constant for the dielectric between the plates

            ε₀ = 8.85×10^-12 coul²/nt-m²

            C = capacitance (farads)

Derivation. Let us first assume the plates are in a vacuum. We have shown that the electric field intensity between a pair of closely spaced parallel plates in vacuum is

where σ is charge density (charge per unit area), A is the area of each plate, and Q is the charge on either plate.

Since the electric intensity between the plates is uniform, the potential difference between the plates is

Now, by definition, C = Q/V_ab,

When there is a dielectric between the plates with a dielectric constant of K, we get