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A capacitor is a passive electrical component that can store energy in the electric field between a pair of conductors (called "plates"). The process of storing energy in the capacitor is known as "charging", and involves electric charges of equal magnitude, but opposite polarity, building up on each plate. A capacitor's ability to store charge is measured by its capacitance, in units of farads.

Capacitors are often used in electric and electronic circuits as energy-storage devices. They can also be used to differentiate between high-frequency and low-frequency signals. This property makes them useful in electronic filters. Practical capacitors have series resistance, internal leakage of charge, series inductance and other non-ideal properties not found in a theoretical, ideal, capacitor.

Capacitors are occasionally referred to as condensers. This term is considered archaic in English, but most other languages use a cognate of condenser to refer to a capacitor.

A wide variety of capacitors (see photos) have been invented, including small electrolytic capacitors used in electronic circuits, basic parallel-plate capacitors, mechanical variable capacitors, and the early Leyden jars, among numerous other types of capacitors.

In October 1745, Ewald Georg von Kleist of Pomerania in Germany invented the first recorded capacitor: a glass jar with water inside as one plate was held on the hand as the other plate. A wire in the mouth of the bottle received charge from an electric machine, and released it as a spark.

In the same year, Dutch physicist Pieter van Musschenbroek independently invented a very similar capacitor. It was named the Leyden jar, after the University of Leyden where van Musschenbroek worked. Daniel Gralath was the first to combine several jars in parallel into a "battery" to increase the charge storage capacity.

Benjamin Franklin investigated the Leyden jar, and proved that the charge was stored on the glass, not in the water as others had assumed. Leyden jars began to be made by coating the inside and outside of jars with metal foil, leaving a space at the mouth to prevent arcing between the foils. The earliest unit of capacitance was the 'jar', equivalent to about 1 nanofarad.

Leyden jar or flat plate construction was used exclusively up until the late 1800s. Then the invention of wireless (radio) created a demand for standard capacitors, and the steady move to higher frequencies required capacitors with lower inductance. A more compact construction began to be used of a flexible dielectric sheet such as oiled paper sandwiched between sheets of metal foil, rolled or folded into a small package.

Early capacitors were also known as condensers, a term that is still occasionally used today. It was coined by Alessandro Volta in 1782 (derived from the Italian condensatore), with reference to the device's ability to store a higher density of electric charge than a normal isolated conductor. Most non-English European languages still use a word derived from "condensatore".

A capacitor consists of two conductive electrodes, or plates, separated by a dielectric, which prevents charge from moving directly between the plates. Charge may however move from one plate to the other through an external circuit, such as a battery connected between the terminals.

When any external connection is removed, the charge on the plates persists. The separated charges attract each other, and an electric field is present between the plates. The simplest practical capacitor consists of two wide, flat, parallel plates separated by a thin dielectric layer.

Assuming that the plate size $sqrt\{A\}$, where $A$ is the area of the plates, is much greater than their separation $d$, the instantaneous electric field between the plates $E(t)$ is identical at any location away from the edges. If the instantaneous charge on a plate, $-q(t)$, is spread evenly, then

- $E(t)\; =\; -frac\{q(t)\}\{varepsilon\{\}A\}$,

- $v(t)\; =\; -int\_0^d\; E(t),,,text\{d\}z\; =\; frac\{q(t)d\}\{varepsilon\{\}A\}$,

A capacitor's ability to store charge is measured by its capacitance $C,$, the ratio of the amount of charge stored on each plate to the voltage:

- $q\; =\; Cv,$,

For an ideal parallel plate capacitor with a plate area $A,$ and a plate separation $d,$:

- $C\; =\; frac\{varepsilon\{\}A\}\{d\},$

In SI units, a capacitor has a capacitance of one farad when one coulomb of charge stored on each plate causes a voltage difference of one volt between its plates. Since the farad is a very large unit, capacitance is usually expressed in microfarads (µF), nanofarads (nF), or picofarads (pF). In general, capacitance is greater in devices with large plate areas, separated by small distances. When a dielectric is present between two charged plates, its molecules become polarized and reduce the internal electric field and hence the voltage. This allows the capacitor to store more charge for a given voltage, so a dielectric increases the capacitance of a capacitor, by an amount given by the dielectric constant, $varepsilon,$, of the material.

Work must be done by an external influence to move charge between the plates in a capacitor. When the external influence is removed, the charge separation persists and energy is stored in the electric field. If charge is later allowed to return to its equilibrium position, the energy is released. The work done in establishing the electric field, and hence the amount of energy stored, is given by

- $W(t)\; =\; -q(t)\; int\_0^d\; E(t)\; text\{d\}z\; =\; \{1\; over\; 2\}\; \{q(t)^2\; over\; C\}\; =\; \{1\; over\; 2\}\; C\; v(t)^2\; =\; \{1\; over\; 2\}\; \{v(t)\; q(t)\}$

The maximum energy that can be stored safely in a capacitor is limited by the breakdown voltage of the capacitor, which is the breakdown field strength of the dielectric material times the dielectric thickness. Due to the scaling of capacitance and breakdown voltage with dielectric thickness, all capacitors made with a particular dielectric have approximately equal maximum energy density, to the extent that the dielectric dominates their volume.

- The pressure difference (voltage difference) across the unit is proportional to the integral of the flow (current).
- A steady state current cannot pass through it because the pressure will build up across the diaphragm until it equally opposes the source pressure,
- but a transient pulse or alternating current can be transmitted.
- An overpressure results in bursting of the diaphragm, analogous to dielectric breakdown.
- The capacitance of units connected in parallel is equivalent to the sum of their individual capacitances.

- $v(t)\; =\; frac\{1\}\{C\}q(t)\; =\; frac\{1\}\{C\}int\_0^t\; i(tau),,text\{d\}tau$.

- $i(t)\; =\; Cfrac\{text\{d\}v(t)\}\{text\{d\}t\}$.

- $i\; =\; Cfrac\{text\{d\}v\}\{text\{d\}t\}\; =\; (1000\; times\; 10^\{-6\}\; text\{\; F\})(2.5\; text\{\; V/s\})\; =\; 2.5text\{\; mA\}$.

A circuit containing only a resistor, a capacitor, a switch and a constant (DC) voltage source $v\_\{text\{src\}\}(t)=V\_0$ in series is known as a charging circuit. From Kirchhoff's voltage law it follows that

- $V\_0\; =\; v\_r(t)\; +\; v\_c(t)\; =\; i(t)R\; +\; frac\{1\}\{C\}int\_0^t\; i(tau),,text\{d\}tau$,

where $v\_r(t)$ and $v\_c(t)$ are the voltages across the resistor and capacitor respectively. This reduces to a first order differential equation

- $RCfrac\{text\{d\}i(t)\}\{text\{d\}t\}\; =\; -\; i(t)$

Assuming that the capacitor is initially uncharged, there is no internal electric field, and the initial current is $I\_0=V\_0/R$. This initial condition allows solution of the differential equation as

- $i(t)\; =\; frac\{V\_0\}\{R\}expleft(-frac\{t\}\{RC\}right)$.

The corresponding voltage drop across the capacitor is

- $v(t)\; =\; V\_0left[1-expleft(frac\{-t\}\{RC\}right)right]$.

Therefore, as charge increases on the capacitor plates, the voltage across the capacitor increases, until it reaches a steady-state value of $V\_0$, and the current drops to zero. Both the current, and the difference between the source and capacitor voltage decay exponentially with respect to time. The time constant of the decay is given by $tau\; =\; RC$.

- $v(t)=V\_0sin(omega\_0\; t\; +\; phi)$,

- $i(t)=Cfrac\{text\{d\}v\_0(t)\}\{text\{d\}t\}=CV\_0omega\_0sinleft(omega\_0t+phi+frac\{pi\}\{2\}right)$.

$Z\_C\; =\; frac\{V\_C\}\{I\_C\}\; =\; frac\{1\}\{2\; pi\; j\; f\; C\}\; =\; j\; X\_C\; ,$

where $X\_C\; =\; -\; frac\{1\}\{omega\; C\}$ is the capacitive reactance, $omega\; =\; 2\; pi\; f\; ,$ is the angular frequency, f is the frequency), C is the capacitance in farads, and j is the imaginary unit.

While this relation (between the frequency domain voltage and current associated with a capacitor) is always true, the ratio of the time domain voltage and current amplitudes is equal to $X\_C$ only for sinusoidal (AC) circuits in steady state.

See derivation Deriving capacitor impedance.

Hence, capacitive reactance is the negative imaginary component of impedance. The negative sign indicates that the current leads the voltage by 90° for a sinusoidal signal, as opposed to the inductor, where the current lags the voltage by 90°.

The impedance is analogous to the resistance of a resistor. The impedance of a capacitor is inversely proportional to the frequency - that is, for very high-frequency alternating currents the reactance approaches zero - so that a capacitor is nearly a short circuit to a very high frequency AC source. Conversely, for very low frequency alternating currents, the reactance increases without bound so that a capacitor is nearly an open circuit to a very low frequency AC source. This frequency dependent behaviour accounts for most uses of the capacitor (see "Applications", below).

Reactance is so called because the capacitor does not dissipate power, but merely stores energy. In electrical circuits, as in mechanics, there are two types of load, resistive and reactive. Resistive loads (analogous to an object sliding on a rough surface) dissipate the energy delivered by the circuit as heat, while reactive loads (analogous to a spring or frictionless moving object) store this energy, ultimately delivering the energy back to the circuit.

Also significant is that the impedance is inversely proportional to the capacitance, unlike resistors and inductors for which impedances are linearly proportional to resistance and inductance respectively. This is why the series and shunt impedance formulae (given below) are the inverse of the resistive case. In series, impedances sum. In parallel, conductances sum.

$Z(s)=frac\{1\}\{Cs\}$

where C is the capacitance, and s (= σ+jω) is the complex frequency.

Ceramic capacitors are well suited for frequency applications due to their low ESR values. However, most tantalum capacitors are rated for a maximum ripple current due to their much higher ESR values.

The electric current,$I\_\{RMS\}$, and electric power, $P\_\{RMS\}$ produced by an AC voltage source across a capacitor is given as:

$V\_\{ESR\}\; =\; V\_\{RMS\}frac\{R\_\{RMS\}\}\{|R\_\{ESR\}\; +\; frac\{1\}\{j2\; pi\; f\; C\}|\}\; =\; V\_\{RMS\}\; frac\{R\_\{ESR\}\}\{|R\_\{ESR\}\; +\; Z\_C|\}\; =\; frac\{V\_\{PP\}\}\{2sqrt(2)\}frac\{R\_\{ESR\}\}\{sqrt(\{R\_\{ESR\}\}^2\; +\; \{frac\{1\}\{2\; pi\; f\; C\}\}^2)\}$

$P\_\{RMS\}\; =\; V\_\{RMS\}I\_\{RMS\}\; =\; frac^2\}\{R\_\{ESR\}\}\; =\; frac^2\; R\_\{ESR\}\}^2\; +\; [frac\{1\}\{2\; pi\; fC\}]^2\}$

$I\_\{RMS\}\; =\; frac\{P\_\{RMS\}\}\{V\_\{ESR\}\}\; =\; frac\{2\; sqrt(2)\; sqrt(\{R\_\{ESR\}\}^2\; +\; \{frac\{1\}\{2\; pi\; f\; C\}\}^2)\; P\_\{RMS\}\}\{R\_\{ESR\}\; V\_\{PP\}\}$

Capacitors in a parallel configuration each have the same potential difference (voltage). Their total capacitance (C_{eq}) is given by:

- $C\_\{eq\}\; =\; C\_1\; +\; C\_2\; +\; cdots\; +\; C\_n\; ,$

The reason for putting capacitors in parallel is to increase the total amount of charge stored. In other words, increasing the capacitance also increases the amount of energy that can be stored. Its expression is:

- $E\_mathrm\{stored\}\; =\; \{1\; over\; 2\}\; C\; V^2\; .$

The current through capacitors in series stays the same, but the voltage across each capacitor can be different. The sum of the potential differences (voltage) is equal to the total voltage. Their total capacitance is given by:

- $frac\{1\}\{C\_\{eq\}\}\; =\; frac\{1\}\{C\_1\}\; +\; frac\{1\}\{C\_2\}\; +\; cdots\; +\; frac\{1\}\{C\_n\}$

In parallel, the effective area of the combined capacitor has increased, increasing the overall capacitance. However, in series, the distance between the plates has effectively been increased, reducing the overall capacitance.

Capacitors are used in series for higher working voltage, for example for smoothing in a high voltage power supply. Three "600 volt maximum" capacitors in series can be used at 1800 volts. This is offset by the total capacitance obtained being only one third of the value of the capacitors used. This can be countered by connecting 3 of these series set-ups in parallel, resulting in a 3x3 matrix of capacitors with the same overall capacitance as an individual capacitor but operable under three times the voltage. In this application, a large resistor would be connected across each capacitor to ensure that the total voltage is divided equally across each capacitor and also to discharge the capacitors for safety when the equipment is not in use.

Another application is for use of polarized capacitors in alternating current circuits; the capacitors are connected in series, in reverse polarity, so that at any given time one of the capacitors is not conducting.

Most types of capacitor include a dielectric spacer, which increases their capacitance. However, low capacitance devices are available with a vacuum between their plates, which allows extremely high voltage operation and low losses. Air filled variable capacitors are also commonly used in radio tuning circuits.

Several solid dielectrics are available, including paper, plastic, glass, mica and ceramic materials. Paper was used extensively in older devices and offers relatively high voltage performance. However, it is susceptible to water absorption, and has been largely replaced by plastic film capacitors. Plastics offer better stability and aging performance, which makes them useful in timer circuits, although they may be limited to low operating temperatures and frequencies. Ceramic capacitors are generally small, cheap and useful for high frequency applications, although their capacitance varies strongly with voltage, and they age poorly. They are broadly categorized as Class 1 dielectrics, which have predictable variation of capacitance with temperature or Class 2 dielectrics, which can operate at higher voltage. Glass and mica capacitors are extremely reliable, stable and tolerant to high temperatures and voltages, but are too expensive for most mainstream applications.

Electrolytic capacitors use an aluminum or tantalum plate with an oxide dielectric layer. The second electrode is a liquid electrolyte. Electrolytic capacitors offer very high capacitance but suffer from poor tolerances, high instability, gradual loss of capacitance especially when subjected to heat, and high leakage current. The conductivity of the electrolyte drops at low temperatures, which increases equivalent series resistance. While widely used for power-supply conditioning, poor high-frequency characteristics make them unsuitable for many applications. Tantalum capacitors offer better frequency and temperature characteristics than aluminum, but higher dielectric absorption and leakage. OS-CON (or OC-CON) capacitors are a polymerized organic semiconductor solid-electrolyte type that offer longer life at higher cost than standard electrolytic capacitors.

Several other types of capacitor are available for specialist applications. Supercapacitors made from carbon aerogel, carbon nanotubes, or highly porous electrode materials offer extremely high capacity and can be used in some applications instead of rechargeable batteries. Alternating current capacitors are specifically designed to work on line (mains) voltage AC power circuits. They are commonly used in electric motor circuits and are often designed to handle large currents, so they tend to be physically large. They are usually ruggedly packaged, often in metal cases that can be easily grounded/earthed. They also tend to have rather high direct current breakdown voltages.

The assembly is encased to prevent moisture entering the dielectric - early radio equipment used a cardboard tube sealed with wax. Modern paper or film dielectric capacitors are dipped in a hard thermoplastic. Large capacitors for high-voltage use may have the roll form compressed to fit into a rectangular metal case, with bolted terminals and bushings for connections. The dielectric in larger capacitors is often impregnated with a liquid to improve its properties.

Capacitors may have their connecting leads arranged in many configurations, for example axially or radially. Small, cheap discoidal ceramic capacitors have existed since the 1930s, and remain in widespread use. Since the 1980s, surface mount packages for capacitors have been widely used. These packages are extremely small and lack connecting leads, allowing them to be soldered directly onto the surface of printed circuit boards. Surface mount components avoid undesirable high-frequency effects due to the leads and simplify automated assembly, although manual handling is made difficult due to their small size.

Mechanically controlled variable capacitors allow the plate spacing to be adjusted, for example by rotating or sliding a set of movable plates into alignment with a set of stationary plates. Low cost variable capacitors squeeze together alternating layers of aluminum and plastic with a screw. Electrical control of capacitance is achievable with varactors (or varicaps), which are reverse-biased semiconductor diodes whose depletion region width varies with applied voltage. They are used in phase-locked loops, amongst other applications.

UPSes can be equipped with maintenance-free capacitors to extend service life.

Capacitor | Polarized capacitors | Variable capacitor |
---|---|---|

Large capacitor banks(Reservoir) are used as energy sources for the exploding-bridgewire detonators or slapper detonators in nuclear weapons and other specialty weapons. Experimental work is under way using banks of capacitors as power sources for electromagnetic armour and electromagnetic railguns or coilguns.

Capacitors are connected in parallel with the power circuits of most electronic devices and larger systems (such as factories) to shunt away and conceal current fluctuations from the primary power source to provide a "clean" power supply for signal or control circuits. Audio equipment, for example, uses several capacitors in this way, to shunt away power line hum before it gets into the signal circuitry. The capacitors act as a local reserve for the DC power source, and bypass AC currents from the power supply. This is used in car audio applications, when a stiffening capacitor compensates for the inductance and resistance of the leads to the lead-acid car battery.

Capacitors are also used in parallel to interrupt units of a high-voltage circuit breaker in order to equally distribute the voltage between these units. In this case they are called grading capacitors.

In schematic diagrams, a capacitor used primarily for DC charge storage is often drawn vertically in circuit diagrams with the lower, more negative, plate drawn as an arc. The straight plate indicates the positive terminal of the device, if it is polarized (see electrolytic capacitor).

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 an LC circuit.

Changing the dielectric: The effects of varying the physical and/or electrical characteristics of the dielectric can also be of use. Capacitors with an exposed and porous dielectric can be used to measure humidity in air. Capacitors are used to accurately measure the fuel level in airplanes; as the fuel covers more of a pair of plates, the circuit capacitance increases.

Changing the distance between the plates: Capacitors with a flexible plate can be used to measure strain or pressure. Industrial pressure transmitters used for process control use pressure-sensing diagphragms, which form a capacitor plate of an oscillator circuit. Capacitors are used as the sensor in condenser microphones, where one plate is moved by air pressure, relative to the fixed position of the other plate. Some accelerometers use MEMS capacitors etched on a chip to measure the magnitude and direction of the acceleration vector. They are used to detect changes in acceleration, eg. as tilt sensors or to detect free fall, as sensors triggering airbag deployment, and in many other applications. Some fingerprint sensors use capacitors. Additionally, a user can adjust the pitch of a theremin musical instrument by moving his hand since this changes the effective capacitance between the user's hand and the antenna.

Changing the effective area of the plates: capacitive touch switches

Capacitors may retain a charge long after power is removed from a circuit; this charge can cause shocks or damage to connected equipment. For example, even a seemingly innocuous device such as a disposable camera flash unit powered by a 1.5 volt AA battery contains a capacitor which may be charged to over 300 volts. This is easily capable of delivering a shock. Service procedures for electronic devices usually include instructions to discharge large or high-voltage capacitors. Capacitors may also have built-in discharge resistors to dissipate stored energy to a safe level within a few seconds after power is removed. High-voltage capacitors are stored with the terminals shorted, as protection from potentially dangerous voltages due to dielectric absorption.

Some old, large oil-filled capacitors contain polychlorinated biphenyls (PCBs). It is known that waste PCBs can leak into groundwater under landfills. Capacitors containing PCB were labelled as containing "Askarel" and several other trade names. PCB-filled capacitors are found in very old (pre 1975) fluorescent lamp ballasts, and other applications.

High-voltage capacitors may catastrophically fail when subjected to voltages or currents beyond their rating, or as they reach their normal end of life. Dielectric or metal interconnection failures may create arcing that vaporizes dielectric fluid, resulting in case bulging, rupture, or even an explosion. Capacitors used in RF or sustained high-current applications can overheat, especially in the center of the capacitor rolls. Capacitors used within high-energy capacitor banks can violently explode when a short in one capacitor causes sudden dumping of energy stored in the rest of the bank into the failing unit. High voltage vacuum capacitors can generate soft X-rays even during normal operation. Proper containment, fusing, and preventive maintenance can help to minimize these hazards.

High-voltage capacitors can benefit from a pre-charge to limit in-rush currents at power-up of HVDC circuits. This will extend the life of the component and may mitigate high-voltage hazards.

- Capacitance
- Capacitance meter
- Capacitor plague: capacitor failures on computer motherboards
- Circuit design
- Decoupling capacitor
- Electronic component
- Electric displacement field
- Electronics
- Electronic oscillator
- Filter capacitor
- Leyden jar
- Light emitting capacitor
- Memristor
- Reservoir capacitor
- Supercapacitor
- Vacuum variable capacitor
- Variable capacitor

- Zorpette, Glenn (2005). "Super Charged: A Tiny South Korean Company is Out to Make Capacitors Powerful enough to Propel the Next Generation of Hybrid-Electric Cars".
*IEEE Spectrum*42 (1): - (1991).
*The ARRL Handbook for Radio Amateurs*. 68th ed, Newington CT USA: The Amateur Radio Relay League. - Huelsman, Lawrence P. (1972).
*Basic Circuit Theory with Digital Computations*. Englewood Cliffs: Prentice-Hall. - Philosophical Transactions of the Royal Society LXXII, Appendix 8, 1782 (Volta coins the word condenser)
- A. K. Maini "Electronic Projects for Beginners", "Pustak Mahal", 2nd Edition: March, 1998 (INDIA)
- Spark Museum (von Kleist and Musschenbroek)
- Biography of von Kleist

- The Capacitor Tutorial
- Capacitance and Inductance - a chapter from an online textbook
- Howstuffworks.com: How Capacitors Work
- CapSite 2008: Introduction to Capacitors
- AC circuits
- Capacitor Tutorial - Includes how to read capacitor temperature codes
- Capacitors in Circuits by Ernest Lee, The Wolfram Demonstrations Project.
- Instructables: DIY Make a Toy Capacitor
- Capacitor Converters and Calculators

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Last updated on Friday October 10, 2008 at 11:56:05 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Friday October 10, 2008 at 11:56:05 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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