Parallel Plate Capacitor Formulas

Parallel plate capacitor formulas: the capacitance from the plate area, the gap and the relative permittivity, the charge, the energy and the electric field.

The formulas

ε0 = 8.854 × 10⁻¹² F/m is the permittivity of free space, εr the relative permittivity of the insulator between the plates, A the area of one plate in m², d the gap in metres and V the voltage. The formula ignores the fringing field at the edges, so it is good when the gap is small against the plate size. The field must stay below the breakdown strength of the insulator, which the material data gives. The relative permittivities in the table are typical values, and real parts vary. The sizes here are examples.

Worked example: plates of 100 cm² with a 1 mm gap and an insulator with εr = 4, at 100 V

1. A = 100 cm² = 0.01 m², so with air C = 8.854 × 10⁻¹² × 0.01 / 0.001 = 88.54 pF
2. With εr = 4, C = 4 × 88.54 = 354.2 pF
3. Q = 354.2 pF × 100 V = 35.42 nC
4. E = ½ × 354.2 pF × 100² = 1.771 µJ
5. Field = 100 / 0.001 = 100 kV/m

Capacitance of the same plates by insulator

Frequently asked questions

Why does a thinner gap give more capacitance?

The field is stronger for the same voltage, so the plates hold more charge. The capacitance is inversely proportional to the gap.

What does the insulator do?

It reduces the field for the same charge by its relative permittivity, so the capacitance rises by εr. It also sets the voltage that the capacitor can take.

What limits a thin gap?

The breakdown strength of the insulator. At a field above it, the insulator fails, so a thinner gap needs a lower voltage rating.

Does this apply to real capacitors?

Rolled and stacked capacitors are many such plates in parallel, so the area is the total area of the plates.

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