farad

farad

SI coherent derived unit with special name and symbol
Name Symbol Derived quantity Expressed in terms of SI base units
farad F capacitance kg-1 m‑2 s4 A2

Definition

The farad, symbol F, is the SI derived unit of electrical capacitance. One farad is defined as the capacitance across which, when charged with one coulomb, there is a potential difference of one volt. One farad can also be defined as the capacitance which stores an electrical charge of one coulomb across a potential difference of one volt.

The farad is named after the English physicist Michael Faraday (1791 – 1867).

Capacitance

Electrical capacitance is the ability of an object to store an electrical charge. It is the ratio of the change in electric charge in a system to the corresponding change in electric potential.

C = \dfrac{Q}{V}

Using SI coherent units, the unit for this ratio is the coulomb per volt, symbol C/V, which is given the special name farad, symbol F.

1\ \text{F} = 1\ \dfrac{\text{C}}{\text{V}}

Self capacitance

Any object that can be electrically charged exhibits self capacitance. Self capacitance is the ratio of the change in electric charge of an isolated conductor to the corresponding change in its electric potential.

The self capacitance of a conducting sphere is given by:

C = 4 \pi \varepsilon _0 R

where:

  • C is the self capacitance of the sphere, measured in farads, symbol F,
  • R is the radius of the sphere, measured in metres, symbol m,
  • ε0 = 8.854 187 812 8(13) × 10-12 F m-1, the permittivity of free space.
Examples of self capacitance
Object Capacitance
20 cm metal sphere 22 pF
Earth 710 µF

Mutual capacitance

In electrical circuits, the general term capacitance usually refers to mutual capacitance.

Mutual capacitance is the capacitance that exists between two adjacent conductors, such as the two plates of a parallel-plate capacitor. The two conductive plates are insulated from each other, usually by a dielectric material.

In a parallel plate capacitor, capacitance is

  • directly proportional to the surface area of the conductor plates,
  • inversely proportional to the distance between the conductor plates,
  • directly proportional to the dielectric constant of the material between the two
    plates.

C \propto \dfrac{\kappa A}{d}

Using SI coherent derived units, the proportionality constant equals ε0, the permittivity of free space:

C = \dfrac{\kappa \varepsilon_0 A}{d}

where:

  • C is the mutual capacitance of the conductor plates, measured in farads, symbol F,
  • A is the surface area of the conductor plates, measured in square metres, symbol m2,
  • d is the distance between the conductor plates, measured in metres, symbol m,
  • κ is the dielectric constant of the material between the two plates.
  • ε0 = 8.854 187 812 8(13) × 10-12 F m-1, the permittivity of free space.

Energy storage

The energy stored in a capacitor is given by:

E = \dfrac {1}{2} \ CV^2 = \dfrac {1}{2} \ QV

where:

  • E is the energy stored, measured in joules, symbol J,
  • C is the capacitance, measured in farads, symbol F,
  • V is the potential difference between the conductor plates, measured in volts, symbol V,
  • Q is the electric charge stored, measured in coulombs, symbol C,