2.12 Capacitors and Dielectrics

What a capacitor stores

A capacitor stores charge and electric potential energy using two conductors separated by an insulator. Capacitance (C = Q/V) measures how much charge a capacitor holds per volt applied, in farads (F). For a parallel-plate capacitor, C = ε₀A/d, so capacitance increases with larger plate area (A) and decreases with larger plate separation (d).

Energy stored in a capacitor

Charging a capacitor requires work, stored as potential energy: U = ½QV = ½CV² = Q²/2C. The electric field between the plates is uniform (E = V/d) and stores this energy in the space itself. Discharging releases this stored energy, powering flashes, defibrillators, and backup circuits.

Dielectrics boost capacitance

Inserting a dielectric (insulating material) between plates increases capacitance by a factor of the dielectric constant (κ): C = κε₀A/d. The dielectric's molecules polarize, creating an internal field that opposes the external field, reducing net voltage for the same charge — allowing more charge storage at the same voltage and preventing plates from touching.

Key terms

Capacitance

C = Q/V; measured in farads (F); the amount of charge stored per volt of potential difference.

Parallel-plate capacitance formula

C = ε₀A/d — proportional to plate area A, inversely proportional to separation d.

Energy stored in a capacitor

U = ½QV = ½CV² = Q²/2C

Dielectric

An insulating material placed between capacitor plates that polarizes, increasing capacitance by factor κ: C = κε₀A/d.

Effect of dielectric at constant charge

Increases capacitance and decreases voltage (since V = Q/C and C increases).

Try an AP-style question

The plate area of a parallel-plate capacitor doubles. What happens to its capacitance?

1. It quadruples
2. It halves
3. It stays the same
4. It doubles