The measure of a system's ability to store electric charge; symbol C, units F (farad); for a capacitor comprising two separate parallel conductors, the capacitance is equal to the charge on one conductor divided by the potential difference between the two. For an electrical circuit, elements are usually quoted as µF (microfarad, 10?6 F) or pF (picofarad, 10?12 F).
Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential.
Capacitors
The capacitance of the majority of capacitors used in electronic circuits is several orders of magnitude smaller than the farad. The most common units of capacitance in use today are the millifarad (mF), microfarad (µF), the nanofarad (nF) and the picofarad (pF)
The capacitance can be calculated if the geometry of the conductors and the dielectric properties of the insulator between the conductors are known. For example, the capacitance of a parallel-plate capacitor constructed of two parallel plane electrodes of area A separated by a distance d is approximately equal to the following:
where
C is the capacitance in farads, F ε is the permittivity of the insulator used (or ε0 for a vacuum) A is the area of each plane electrode, measured in square metres d is the separation between the electrodes, measured in metresThe equation is a good approximation if d is small compared to the other dimensions of the electrodes.
Energy
The energy (measured in joules) stored in a capacitor is equal to the work done to charge it. 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 C is the capacitance, measured in faradsWe 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:
Combining this with the above equation for the capacitance of a flat-plate capacitor, we get:
.Capacitance and 'displacement current'
The physicist James Clerk Maxwell invented the concept of displacement current, dD/dt, to make Ampere's law consistent with conservation of charge in cases where charge is accumulating, for example in a capacitor. (Integrating both sides, the integral of curl H can be replaced—courtesy of Stokes's theorem—with the integral of H ● dl over a closed contour, thus demonstrating the interconnection with Ampere's formulation.)
Capacitance/inductance duality
In mathematical terms, the ideal capacitance can be considered as an inverse of the ideal inductance, because the voltage-current equations of the two phenomena can be transformed into one another by exchanging the voltage and current terms. Using this method, the self-capacitance of a conducting sphere of radius R is given by:
Typical values of self-capacitance are:
for the top electrode of a van de Graaf generator, typically a sphere 20 cm in diameter: 20 pF the planet Earth: about 710 µFElastance
The inverse of capacitance is called elastance, and its unit is the reciprocal farad, also informally called the daraf.
Stray capacitance
Any two adjacent conductors can be considered as a capacitor, although the capacitance will be small unless the conductors are close together or long.
Stray capacitance is often encountered in amplifier circuits in the form of "feedthrough" capacitance that interconnects the input and output nodes (both defined relative to a common ground). It is often convenient for analytical purposes to replace this capacitance with a combination of one input-to-ground capacitance and one output-to-ground capacitance. (Since impedance varies inversely with capacitance, the internode capacitance, C, will be seen to have been replaced by a capacitance of KC from input to ground and a capacitance of (K-1)C/K from output to ground.) When the input-to-output gain is very large, the equivalent input-to-ground impedance is very small while the output-to-ground impedance is essentially equal to the original (input-to-output) impedance.
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