In electromagnetism and electronics, capacitance is the ability of a body to hold an electrical charge.

Capacitance is also a measure of the amount of electric charge stored (or separated) for a given electric potential. A common form of charge storage device is a two-plate capacitor. If the charges on the plates are +Q and −Q, and V gives the voltage between the plates, then the capacitance is given by

$C\; =\; \backslash frac\{Q\}\{V\}.$

The SI unit of capacitance is the farad; 1 farad = 1 coulomb per volt.

The energy (measured in joules) stored in a capacitor is equal to the work done to charge it. Consider a capacitance C, holding a charge +q on one plate and -q on the other. Moving a small element of charge $\backslash mathrm\{d\}q$ from one plate to the other against the potential difference V = q/C requires the work $\backslash mathrm\{d\}W$:

$\backslash mathrm\{d\}W\; =\; \backslash frac\{q\}\{C\}\backslash ,\backslash mathrm\{d\}q$

where W is the work measured in joules, q is the charge measured in coulombs and C is the capacitance, measured in farads.

We can find the energy stored in a capacitance by integrating this equation. Starting with an uncharged capacitance (q=0) and moving charge from one plate to the other until the plates have charge +Q and -Q requires the work W:

$W\_\backslash text\{charging\}\; =\; \backslash int\_\{0\}^\{Q\}\; \backslash frac\{q\}\{C\}\; \backslash ,\; \backslash mathrm\{d\}q\; =\; \backslash frac\{1\}\{2\}\backslash frac\{Q^2\}\{C\}\; =\; \backslash frac\{1\}\{2\}CV^2\; =\; W\_\backslash text\{stored\}.$

Capacitance and 'displacement current'

The physicist James Clerk Maxwell invented the concept of displacement current in his 1861 paper in connection with the displacement of electrical particles:See On Physical Lines of Force: Part III–The Theory of Molecular Vortices applied to Statical Electricity Cquote: Bodies which do not permit a current of electricity to flow through them are called insulators. But though electricity does not flow through them, electrical effects are propagated through them … a dielectric is like an elastic membrane which may be impervious to the fluid, but transmits the pressure of the fluid on one side to that on the other. Cquote: Electromotive force acting on a dielectric produces a state of polarization of its parts...capable of being described as a state in which every particle has its poles in opposite conditions. Cquote: ...we may conceive that the electricity in each molecule is so displaced that one side is rendered positively, and the other negatively electrical, but that the electricity remains entirety connected with the molecule, and does not pass from one molecule to another. Cquote: This displacement does not amount to a current, because when it attains a certain value it remains constant, but it is the commencement of a current, and its variations constitute currents in the positive or negative direction, according as the displacement is increasing or diminishing. Cquote: ...when the electromotive force varies, the electric displacement also varies. But a variation of displacement is equivalent to a current, and this current must be taken into account...