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



            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/Vab,


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


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