Common symbols	C
SI unit	farad
Other units	μF, nF, pF
In SI base units	F = A2 s4 kg−1 m−2
Derivations from other quantities	C = charge / voltage
Dimension	${\displaystyle {\mathsf {L}}^{-2}{\mathsf {M}}^{-1}{\mathsf {T}}^{4}{\mathsf {I}}^{2}}$

Articles about
Electromagnetism
Electricity Magnetism Optics History Computational Textbooks Phenomena
Electrostatics Charge density Conductor Coulomb law Electret Electric charge Electric dipole Electric field Electric flux Electric potential Electrostatic discharge Electrostatic induction Gauss law Insulator Permittivity Polarization Potential energy Static electricity Triboelectricity
Magnetostatics Ampère law Biot–Savart law Gauss magnetic law Magnetic dipole Magnetic field Magnetic flux Magnetic scalar potential Magnetic vector potential Magnetization Permeability Right-hand rule
Electrodynamics Bremsstrahlung Cyclotron radiation Displacement current Eddy current Electromagnetic field Electromagnetic induction Electromagnetic pulse Electromagnetic radiation Faraday law Jefimenko equations Larmor formula Lenz law Liénard–Wiechert potential London equations Lorentz force Maxwell equations Maxwell tensor Poynting vector Synchrotron radiation
Electrical network Alternating current Capacitance Current density Direct current Electric current Electrolysis Electromotive force Impedance Inductance Joule heating Kirchhoff laws Network analysis Ohm law Parallel circuit Resistance Resonant cavities Series circuit Voltage Waveguides
Magnetic circuit AC motor DC motor Electric machine Electric motor Gyrator–capacitor Induction motor Linear motor Magnetomotive force Permeance Reluctance (complex) Reluctance (real) Rotor Stator Transformer
Covariant formulation Electromagnetic tensor Electromagnetism and special relativity Four-current Four-potential Mathematical descriptions Maxwell equations in curved spacetime Relativistic electromagnetism Stress–energy tensor
Scientists Ampère Biot Coulomb Davy Einstein Faraday Fizeau Gauss Heaviside Helmholtz Henry Hertz Hopkinson Jefimenko Joule Kelvin Kirchhoff Larmor Lenz Liénard Lorentz Maxwell Neumann Ohm Ørsted Poisson Poynting Ritchie Savart Singer Steinmetz Tesla Volta Weber Wiechert
v t e

Capacitance is the capability of a material object or device to store electric charge. It is measured by the charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related notions of capacitance: self capacitance and mutual capacitance.^{[1]: 237–238} An object that can be electrically charged exhibits self capacitance, for which the electric potential is measured between the object and ground. Mutual capacitance is measured between two components, and is particularly important in the operation of the capacitor, an elementary linear electronic component designed to add capacitance to an electric circuit.

The capacitance between two conductors is a function only of the geometry; the opposing surface area of the conductors and the distance between them, and the permittivity of any dielectric material between them. 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. A 1 farad capacitor, when charged with 1 coulomb of electrical charge, has a potential difference of 1 volt between its plates.^[2] The reciprocal of capacitance is called elastance.

Self capacitance

In discussing electrical circuits, the term capacitance is usually a shorthand for the mutual capacitance between two adjacent conductors, such as the two plates of a capacitor. However, every isolated conductor also exhibits capacitance, here called self capacitance. It is measured by the amount of electric charge that must be added to an isolated conductor to raise its electric potential by one unit of measurement, e.g., one volt.^[3] The reference point for this potential is a theoretical hollow conducting sphere, of infinite radius, with the conductor centered inside this sphere.

Self capacitance of a conductor is defined by the ratio of charge and electric potential:

where

• ${\textstyle q}$ is the charge held,
• ${\textstyle V={\frac {1}{4\pi \varepsilon _{0}}}\int {\frac {\sigma }{r}}\,dS}$ is the electric potential,
• ${\textstyle \sigma }$ is the surface charge density,
• ${\textstyle dS}$ is an infinitesimal element of area on the surface of the conductor,
• ${\textstyle r}$ is the length from ${\textstyle dS}$ to a fixed point M on the conductor,
• ${\displaystyle \varepsilon _{0}}$ is the vacuum permittivity.

Using this method, the self capacitance of a conducting sphere of radius ${\textstyle R}$ in free space (i.e. far away from any other charge distributions) is:^[4]

Example values of self capacitance are:

• for the top "plate" of a van de Graaff generator, typically a sphere 20 cm in radius: 22.24 pF,
• the planet Earth: about 710 μF.^[5]

The inter-winding capacitance of a coil is sometimes called self capacitance,^[6] but this is a different phenomenon. It is actually mutual capacitance between the individual turns of the coil and is a form of stray or parasitic capacitance. 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]}

Mutual capacitance

A common form is a parallel-plate capacitor, which consists of two conductive plates insulated from each other, usually sandwiching a dielectric material. In a parallel plate capacitor, capacitance is very nearly proportional to the surface area of the conductor plates and inversely proportional to the separation distance between the plates.

If the charges on the plates are ${\textstyle +q}$ and ${\textstyle -q}$, and ${\textstyle V}$ gives the voltage between the plates, then the capacitance ${\textstyle C}$ is given by

which gives the voltage/current relationship where ${\textstyle {\frac {dv(t)}{dt}}}$ is the instantaneous rate of change of voltage, and ${\textstyle {\frac {dC}{dt}}}$ is the instantaneous rate of change of the capacitance. For most applications, the change in capacitance over time is negligible, so you can reduce to:

The energy stored in a capacitor is found by integrating the work ${\textstyle W}$:

Capacitance matrix

The discussion above is limited to the case of two conducting plates, although of arbitrary size and shape. The definition ${\displaystyle C=Q/V}$ does not apply when there are more than two charged plates, or when the net charge on the two plates is non-zero. To handle this case, James Clerk Maxwell introduced his coefficients of potential. If three (nearly ideal) conductors are given charges ${\displaystyle Q_{1},Q_{2},Q_{3}}$, then the voltage at conductor 1 is given by

and similarly for the other voltages. Hermann von Helmholtz and Sir William Thomson showed that the coefficients of potential are symmetric, so that ${\displaystyle P_{12}=P_{21}}$Zdroj:https://en.wikipedia.org?pojem=Capacitance
Text je dostupný za podmienok Creative Commons Attribution/Share-Alike License 3.0 Unported; prípadne za ďalších podmienok. Podrobnejšie informácie nájdete na stránke Podmienky použitia.

---