# Capacitance

Capacitance is the ability of a body to store an electrical charge. Any body or structure that is capable of being charged, either with static electricity or by an electric current, exhibits capacitance. A common form of energy storage device is a parallel-plate capacitor. In a parallel plate capacitor, capacitance is directly 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 +q and −q, and V gives the voltage between the plates, then the capacitance C is given by

The capacitance is a function only of the physical dimensions (geometry) of the conductors and the permittivity of the dielectric. It is independent of the potential difference between the conductors and the total charge on them.

The SI unit of capacitance is the farad (named after the English physicist Michael Faraday); a 1 farad capacitor when charged with 1 coulomb of electrical charge will have a potential difference of 1 volt between its plates. Historically, a farad was regarded as an inconveniently large unit, both electrically and physically. Its subdivisions were invariably used, namely the microfarad, nanofarad and picofarad. More recently, technology has advanced such that capacitors of 1 farad and greater can be constructed in a structure little larger than a coin battery (so-called 'supercapacitors'). Such capacitors are principally used for energy storage replacing more traditional batteries.

The energy (measured in joules) stored in a capacitor is equal to the work done to charge it. Consider a capacitor of capacitance C, holding a charge +q on one plate and −q on the other. Moving a small element of charge dq from one plate to the other against the potential difference V = q/C requires the work dW:

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

The energy stored in a capacitor is found 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:

Read more about Capacitance:  Capacitors, Capacitance Matrix, Self-capacitance, Elastance, Stray Capacitance, Capacitance of Simple Systems

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