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Capacitor

A capacitor (formerly known as a "condenser") is a device that stores
electric charge, or, more accurately, consists of two plates which each
store an opposite charge. These two plates are conductive and separated by
an insulator or dielectric. The charge is stored on the inside of the
plates, at the boundary with the dielectric.

The capacitor's capacitance (C) is a measure of how much voltage (V) appears
across the plates for a given charge (Q) stored in it:

[C = \frac{Q}{V}]

The above equation is only accurate for values of Q which are much larger
than the electron charge e = 1.602á10-19 C. For example, if a capacitance of
1 pF is charged to a voltage of 1 µV, the equation would predict a charge Q
= 10-19 C, but this is impossible as it is smaller than the charge on a
single electron. However, recent experiments and theories (e.g. the
fractional quantum Hall (FQH) effect) have suggested the existence of
fractional charges.

A capacitor has a capacitance of one farad when one coulomb of charge causes
a potential difference of one volt across the plates. Since the farad is a
very large unit, values of capacitors are usually expressed in microfarads

When the voltage across a capacitor changes, the capacitor will be charged
or discharged. The associated current is given by

[i = C \frac{dV}{dt}]

where i is the current flowing in the conventional direction, and dV/dt is
the time derivative of voltage.

The energy (in joules) stored in a capacitor is given by:

[E = \frac{1}{2} C V^2;]

Moving a charge Q across a potential difference of V requires an energy QV;
here the charge is CV but the energy is not CV², but less (in fact half
of that) because while charging the potential difference is not yet equal to
the final value; therefore (simple) integration is required to find the
formula above.

The capacitance of a parallel-plate capacitor is approximately equal to the
following:

[C = \epsilon_0 \epsilon_r \frac{A}{D}]

where C is the capacitance in farads, ε0 is the electrostatic
permittivity of vacuum or free space, εr is the dielectric constant
or relative permittivity of the insulator used, A is the area of the each of
the two plates, and D is the distance between the plates.

In a tuned circuit such as a radio receiver, the frequency selected is a
function of the inductance (L) and the capacitance (C) in series, and is
given by

[f = \frac{1}{2 \pi \sqrt{LC}}]

This is the frequency at which resonance occurs in a RLC series circuit.

Electrons cannot pass from one plate of the capacitor to the other. When a
voltage is applied to a capacitor, current flows to one plate, charging it,
while flowing away from the other plate, charging it oppositely. In the case
of a constant voltage (DC) soon an equilibrium is reached, where the charge
of the plates corresponds with the applied voltage, and no further current
will flow in the circuit. Therefore direct current cannot pass. However,
effectively alternating current (AC) can: every change of the voltage gives
rise to a further charging or a discharging of the plates and therefore a
current. The amount of "resistance" of a capacitor to AC is known as
capacitive reactance, and varies depending on the AC frequency. Capacitive
reactance is given by this formula:

[X_C = \frac{1}{2 \pi f  C}]

where:

* XC = capacitive reactance, measured in ohms
* f = frequency of AC in hertz
* C = capacitance in farads

It is called reactance because the capacitor reacts to changes in the
voltage.

Thus the reactance is inversely proportional to the frequency. Since DC has
a frequency of zero, the formula confirms that capacitors completely block
direct current. For high-frequency alternating currents the reactance is
small enough to be considered as zero in approximate analyses.

The impedance of a capacitor is given by:

[Z = \frac{-j}{2 \pi f C}]

where j is the imaginary number.

Hence, capacitive reactance is the negative imaginary component of
impedance.

Practical capacitors

Capacitors are often classified according to the material used as the
dielectric. The following types of dielectric are used.

* ceramic (low values up to about 1μF)
* polystyrene (usually in the picofarad range)
* polyester (from about 1nF to 1μF)
* polypropylene (low-loss, high voltage, resistant to breakdown)
* tantalum (compact, low-voltage devices up to about 100μF)
* electrolytic (high-power, compact but lossy, in the 1μF-1000μF
range)
* air-gap

Important properties of capacitors, apart from the capacitance, are the
maximum working voltage and the amount of energy lost in the dielectric. For
high-power capacitors the maximum ripple current and equivalent series
resistance (ESR) are further considerations.

Capacitors can be fabricated in semiconductor integrated circuit devices
using metal lines and insulators on a substrate. Such capacitors are used to
store analogue signals in switched-capacitor filters, and to store digital
data in dynamic random-access memory (DRAM).

Variable capacitors

There are two distinct types of variable capacitors.

* Those that use a mechanical construction to change the distance between
the plates, or the surface of the area of the overlapping plates. These
devices are called tuning capacitors or simply "variable capacitors",
and are used in telecommunication equipment for tuning and frequency
control.
* Those that use the the fact that the thickness of the depletion layer
of a diode varies with the DC voltage across the diode. These diodes
are called variable capacitance diodes, varactors or varicaps. Any
diode exhibits this effect, but devices specifically sold as varactors
have a large junction area and a doping profile specifically designed
to maximize capacitance.

History

The Leyden jar, the first form of capacitor, was invented at Leiden
University in the Netherlands. It was a glass jar coated inside and out with
metal. The inner coating was connected to a rod that passed through the lid
and ended in a metal ball.


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