Capacitance

Capacitance is a property of an arrangement of conductors that quantifies the amount of electric charge separated for a given change in electric potential. For a two-conductor capacitor, the magnitude of charge on either conductor, Q, and the magnitude of the potential difference between them, ΔV, are related by C = Q/ΔV. In an ideal linear capacitor, C is constant: increasing the charge increases the potential difference in proportion. The two conductors carry equal and opposite charges, so the capacitor as a whole can remain electrically neutral.

Capacitance is not itself a quantity of charge or stored energy. It describes how much charge separation corresponds to a specified voltage; energy depends on both capacitance and voltage.

The SI unit of capacitance is the farad, symbol F, named for Michael Faraday. One farad equals one coulomb per volt (1 F = 1 C/V); because a farad is large for many ordinary components, smaller units such as microfarads and picofarads are common.

Capacitance depends on the arrangement of the conductors and the insulating material, or dielectric, between them. In the ideal parallel-plate model, with plate area A, separation d and a uniform dielectric of permittivity ε, C = εA/d. The vacuum case has ε = ε₀; for a material, ε can be written ε₀εᵣ, where εᵣ is its relative permittivity. The formula neglects fringing fields at the plate edges, so it is most accurate when the plates are large compared with their separation. It shows why a larger plate area or a smaller gap increases capacitance, and why inserting a suitable dielectric generally raises it.

Charging a capacitor requires work to separate charge, and the resulting energy is associated with the electric field between its conductors. For a linear capacitor, the stored energy is U = ½CΔV² = ½QΔV = Q²/(2C). Thus, identical capacitances can store different amounts of energy at different voltages.

When capacitors are combined, their equivalent capacitance depends on the connection: in parallel, capacitances add; in series, their reciprocals add. Capacitors are used to store energy briefly, filter or smooth changing signals, delay voltage changes in resistor-capacitor circuits, and form frequency-selective or resonant circuits with other components. Their real performance also depends on factors such as dielectric losses, leakage and voltage limits, so a component's rated capacitance is only one part of its specification.