It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities.

For many dielectric materials, the permittivity, and thus the capacitance, is independent of the potential difference between the conductors and the total charge on them.

The SI unit of capacitance is the farad (symbol: F), named after the English physicist Michael Faraday.

This self capacitance is an important consideration at high frequencies: it changes the impedance of the coil and gives rise to parallel resonance.

In many applications this is an undesirable effect and sets an upper frequency limit for the correct operation of the circuit.

[citation needed] A common form is a parallel-plate capacitor, which consists of two conductive plates insulated from each other, usually sandwiching a dielectric material.

The discussion above is limited to the case of two conducting plates, although of arbitrary size and shape.

To handle this case, James Clerk Maxwell introduced his coefficients of potential.

Hermann von Helmholtz and Sir William Thomson showed that the coefficients of potential are symmetric, so that

Since no actual device holds perfectly equal and opposite charges on each of the two "plates", it is the mutual capacitance that is reported on capacitors.

The capacitance of the majority of capacitors used in electronic circuits is generally several orders of magnitude smaller than the farad.

The most common units of capacitance are the microfarad (μF), nanofarad (nF), picofarad (pF), and, in microcircuits, femtofarad (fF).

Some applications also use supercapacitors that can be much larger, as much as hundreds of farads, and parasitic capacitive elements can be less than a femtofarad.

Historical texts use other, obsolete submultiples of the farad, such as "mf" and "mfd" for microfarad (μF); "mmf", "mmfd", "pfd", "μμF" for picofarad (pF).

where The equation is a good approximation if d is small compared to the other dimensions of the plates so that the electric field in the capacitor area is uniform, and the so-called fringing field around the periphery provides only a small contribution to the capacitance.

Moving a small element of charge dq from one plate to the other against the potential difference V = q/C requires the work dW:

In particular, the electrostatic potential difference experienced by electrons in conventional capacitors is spatially well-defined and fixed by the shape and size of metallic electrodes in addition to the statistically large number of electrons present in conventional capacitors.

[24] The derivation of a "quantum capacitance" of a few-electron device involves the thermodynamic chemical potential of an N-particle system given by

However, within the framework of purely classical electrostatic interactions, the appearance of the factor of ⁠1/2⁠ is the result of integration in the conventional formulation involving the work done when charging a capacitor,

[26] In particular, to circumvent the mathematical challenges of spatially complex equipotential surfaces within the device, an average electrostatic potential experienced by each electron is utilized in the derivation.

In nanoscale devices, nanowires consisting of metal atoms typically do not exhibit the same conductive properties as their macroscopic, or bulk material, counterparts.

In electronic and semiconductor devices, transient or frequency-dependent current between terminals contains both conduction and displacement components.

Conduction current is related to moving charge carriers (electrons, holes, ions, etc.

As a result, device admittance is frequency-dependent, and a simple electrostatic formula for capacitance

A paper by Steven Laux[27] presents a review of numerical techniques for capacitance calculation.

In particular, capacitance can be calculated by a Fourier transform of a transient current in response to a step-like voltage excitation:

Non-monotonic behavior of the transient current in response to a step-like excitation has been proposed as the mechanism of negative capacitance.

[28] Negative capacitance has been demonstrated and explored in many different types of semiconductor devices.

DVMs can usually measure capacitance from nanofarads to a few hundred microfarads, but wider ranges are not unusual.

Through the use of Kelvin connections and other careful design techniques, these instruments can usually measure capacitors over a range from picofarads to farads.