04 Capacitance and Dielectrics

Capacitor

A circuit element consisting of two conductors separated by an insulator or vacuum that stores electric charge and electric potential energy.

Capacitance (C)

A measure of a capacitor's ability to store charge per unit potential difference.

Capacitance formula

C = Q/V

Charge formula

Q = CV

Potential difference formula

V = Q/C

SI unit of capacitance

Farad (F); 1 F = 1 C/V.

Parallel-plate capacitor formula

C = ε₀A/d

Permittivity of free space (ε₀)

Approximately 8.85 × 10⁻¹² F/m.

Plate area (A)

Area of each capacitor plate, measured in m².

Plate separation (d)

Distance between the capacitor plates, measured in meters.

Effect of increasing plate area

Capacitance increases.

Effect of increasing plate separation

Capacitance decreases.

Spherical capacitor formula

C = 4πε₀ab/(b − a), where a and b are the inner and outer radii.

Cylindrical capacitor capacitance per unit length

C′ = 2πε₀/ln(b/a), where a and b are the inner and outer radii.

Capacitors in series

1/Ceq = 1/C₁ + 1/C₂ + …

Charge in series capacitors

The magnitude of charge on each capacitor is the same.

Voltage in series capacitors

The total voltage equals the sum of the individual voltages.

Capacitors in parallel

Ceq = C₁ + C₂ + …

Voltage in parallel capacitors

The voltage across each capacitor is the same.

Charge in parallel capacitors

The total charge equals the sum of individual charges.

Energy stored in a capacitor

U = ½CV²

Energy using charge and voltage

U = ½QV

Energy using charge and capacitance

U = Q²/(2C)

Dielectric

An insulating material inserted between capacitor plates.

Dielectric constant (κ)

Ratio of capacitance with a dielectric to capacitance without it.

Capacitance with a dielectric

C = κC₀, when the dielectric completely fills the space.

Capacitance without a dielectric

C₀ = ε₀A/d for a parallel-plate capacitor in vacuum.

Electric field between parallel plates

E = V/d, for a uniform field.

Effect of inserting a dielectric

Capacitance increases; for an isolated capacitor, voltage and electric field decrease while charge remains constant.

Electric potential energy in a capacitor

The work required to charge the capacitor is stored as electric potential energy.