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CapacitorFrom Wikipedia, the free encyclopedia

This article is about the electrical component. For the physical phenomenon, see capacitance. For

an overview of various kinds of capacitors, see types of capacitor .

"Capacitive" redirects here. For the term used when referring to touchscreens, see capacitive

sensing .

 This article needs additional citations for verication. Please help improve this

article by adding citations to reliable sources. Unsourced material may be challenged and

removed. (June 2013)

Capacitor

Type Passive

Invented Ewald Georg von Kleist

Electronic symbol

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Miniature low-voltage capacitors (next to a cm ruler)

 A typical electrolytic capacitor 

electrolytic capacitors of different voltages and capacitance

!olid electrolyte, resin-dipped "# $F %& ' tantalum capacitors he + sign indicates the positive lead

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 A capacitor  (originally known as a condenser ) is a passive two-terminal electrical component usedto store electrical energy temporarily in anelectric field he forms of practical capacitors vary widely,*ut all contain at least two electrical conductors (plates) separated *y a dielectric (iean insulator  that can store energy *y *ecoming polari+ed) he conductors can *e thin films, foils orsintered *eads of metal or conductive electrolyte, etc he nonconducting dielectric acts to increasethe capacitors charge capacity A dielectric can *e glass, ceramic, plastic film, air, vacuum, paper,

mica, oxide layer etc apacitors are widely used as parts of  electrical circuits in many commonelectrical devices .nlike a resistor , an ideal capacitor does not dissipate energy /nstead, acapacitor stores energy in the form of an electrostatic field *etween its plates

When there is a potential difference across the conductors (eg, when a capacitor is attached acrossa *attery), an electric field develops across the dielectric, causing positive charge 0Q to collect onone plate and negative charge 1Q to collect on the other plate /f a *attery has *een attached to acapacitor for a sufficient amount of time, no current can flow through the capacitor 2owever, if atime-varying voltage is applied across the leads of the capacitor, a displacement current can flow

 An ideal capacitor is characteri+ed *y a single constant value, its capacitance apacitance isdefined as the ratio of the electric charge Q on each conductor to the potential difference V  *etweenthem he !/ unit of capacitance is the farad (F), which is e3ual to one coulom* per volt (" 4')ypical capacitance values range from a*out " pF ("#1"5 F) to a*out " mF ("#1% F)

he larger the surface area of the 6plates6 (conductors) and the narrower the gap *etween them, thegreater the capacitance is /n practice, the dielectric *etween the plates passes a small amountof leakage current and also has an electric field strength limit, known as the *reakdown voltage heconductors and leads introduce an undesired inductance and resistance

apacitors are widely used in electronic circuits for *locking direct current while allowing alternatingcurrent to pass /n analog filter  networks, they smooth the output of  power supplies /n resonantcircuits they tune radios to particular fre3uencies /n electric power transmission systems, theysta*ili+e voltage and power flow7"8

Contents

  7hide8 

• " 2istory

• 5 heory of operation

o 5" 9verview

o 55 2ydraulic analogy

o 5% :nergy of electric field

o 5 urrent;voltage relation

o 5& < circuits

o

5= A circuits

o 5> ?aplace circuit analysis (s-domain)

o 5@ arallel-plate model

o 5B Cetworks

• % Con-ideal *ehavior 

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o %" Dreakdown voltage

o %5 :3uivalent circuit

o %% E factor 

o % ipple current

o %& apacitance insta*ility

o %= urrent and voltage reversal

o %> <ielectric a*sorption

o %@ ?eakage

o %B :lectrolytic failure from disuse

• apacitor types

o " <ielectric materials

o 5 !tructure

• & apacitor markings

o &" :xample

• = Applications

o =" :nergy storage

o =5 ulsed power and weapons

o =% ower conditioning

=%" ower factor correction

o = !uppression and coupling

=" !ignal coupling

=5 <ecoupling

=% 2igh-pass and low-pass filters

= Coise suppression, spikes, and snu**ers

o =& Motor starters

o == !ignal processing

==" uned circuits

o => !ensing

o =@ 9scillators

o =B roducing light

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• > 2a+ards and safety

• @ !ee also

• B eferences

• "# Di*liography

• "" :xternal links

History [edit]

Dattery of four  ?eyden Gars inMuseum Doerhaave, ?eiden, theCetherlands

/n 9cto*er ">&, :wald Heorg von Ileist of omerania, Hermany, found that charge could *e stored*y connecting a high-voltage electrostatic generator  *y a wire to a volume of water in a hand-heldglass Gar 758 'on Ileists hand and the water acted as conductors, and the Gar as a dielectric (althoughdetails of the mechanism were incorrectly identified at the time) 'on Ileist found that touching thewire resulted in a powerful spark, much more painful than that o*tained from an electrostaticmachine he following year, the <utch physicist ieter van Musschen*roek invented a similarcapacitor, which was named the ?eyden Gar , after the .niversity of ?eiden where he worked 7%8 2ealso was impressed *y the power of the shock he received, writing, 6/ would not take a second shockfor the kingdom of France6 78

<aniel Hralath was the first to com*ine several Gars in parallel into a 6*attery6 to increase the chargestorage capacity DenGamin Franklin investigated the ?eyden Gar  and came to the conclusion that thecharge was stored on the glass, not in the water as others had assumed 2e also adopted the term6*attery6,7&87=8 (denoting the increasing of power with a row of similar units as in a *attery of cannon),su*se3uently applied to clusters of electrochemical cells7>8 ?eyden Gars were later made *y coatingthe inside and outside of Gars with metal foil, leaving a space at the mouth to prevent arcing *etweenthe foils7citation needed 8 he earliest unit of capacitance was the Gar , e3uivalent to a*out """ nanofarads7@8

?eyden Gars or more powerful devices employing flat glass plates alternating with foil conductorswere used exclusively up until a*out "B##, when the invention of  wireless (radio) created a demandfor standard capacitors, and the steady move to higher fre3uencies re3uired capacitors withlower inductance More compact construction methods *egan to *e used, such as a flexi*ledielectric sheet (like oiled paper) sandwiched *etween sheets of metal foil, rolled or folded into asmall package

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:arly capacitors were also known as condensers, a term that is still occasionally used today,particularly in high power applications, like automotive systems he term was first used for thispurpose *y Alessandro 'olta in ">@5, with reference to the devices a*ility to store a higher densityof electric charge than a normal isolated conductor 7B8

!ince the *eginning of the study of electricity non conductive materialslike glass, porcelain, paper  and mica have *een used as insulators hese materials some decadeslater were also well-suited for further use as the dielectric for the first capacitors apercapacitors made *y sandwiching a strip of impregnated paper *etween strips of metal, and rollingthe result into a cylinder were commonly used in the late "BcenturyJ their manufacture started in"@>=,7"#8 and they were used from the early 5#th century as decoupling capacitors intelecommunications (telephony) orcelain was the precursor in case of all capacitors now *elongingto the family of ceramic capacitors :ven in the early years of MarconiKs wireless transmittingapparatus porcelain capacitors were used for high voltage and high fre3uency application inthe transmitters

9n receiver side the smaller mica capacitors were used for resonant circuits Mica dielectriccapacitors were invented in "B#B *y William <u*ilier rior to World War //, mica was the mostcommon dielectric for capacitors in the .nited !tates, 7"#8 see eramic capacitorL2istory

harles ollak (*orn Iarol ollak), the inventor of Aluminum electrolytic capacitors, found out thatthat the oxide layer on an aluminum anode remained sta*le in a neutral or alkaline electrolyte, evenwhen the power was switched off /n "@B= he filed a patent for an 6:lectric li3uid capacitor withaluminum electrodes6 *ased on his idea of using the oxide layer in a polari+ed capacitor incom*ination with a neutral or slightly alkaline electrolyte, see :lectrolytic capacitorL2istory

With the development of plastic materials *y organic chemists during the !econd World War , thecapacitor industry *egan to replace paper with thinner polymer films 9ne very early development infilm capacitors was descri*ed in Dritish atent &@>,B&% in "B,7"#8 see Film capacitorL2istory

!olid electrolyte tantalum capacitors were invented *y Dell ?a*oratories in the early "B&#s as aminiaturi+ed and more relia*le low-voltage support capacitor to complement their newlyinventedtransistor , see antalum capacitorL2istory

?ast *ut not least the electric dou*le-layer capacitor (now !upercapacitors) were invented /n "B&>2 Decker developed a 6?ow voltage electrolytic capacitor with porous car*on electrodes6 7"#87""87"58 2e*elieved that the energy was stored as a charge in the car*on pores used in his capacitor as in thepores of the etched foils of electrolytic capacitors Decause the dou*le layer mechanism was notknown *y him at the time, he wrote in the patent 6/t is not known exactly what is taking place in thecomponent if it is used for energy storage, *ut it leads to an extremely high capacity6,see !upercapacitorL2istory

Theory of operation[edit]

ain article! Capacitance

Overview[edit]

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harge separation in a parallel-plate capacitor causes an internal electric field A dielectric (orange) reduces the field and increases the capacitance

 A simple demonstration of a parallel-plate capacitor 

 A capacitor consists of two conductors separated *y a non-conductive region 7"%8 he non-conductiveregion is called the dielectric /n simpler terms, the dielectric is Gust an electrical insulator  :xamplesof dielectric media are glass, air, paper, vacuum, and even a semiconductor  depletionregion chemically identical to the conductors A capacitor is assumed to *e self-contained andisolated, with no net electric charge and no influence from any external electric field he conductorsthus hold e3ual and opposite charges on their facing surfaces, 7"8 and the dielectric develops anelectric field /n !/ units, a capacitance of one farad means that one coulom* of charge on eachconductor causes a voltage of one volt across the device 7"&8

 An ideal capacitor is wholly characteri+ed *y a constant capacitance C , defined as the ratio ofcharge NQ on each conductor to the voltage V  *etween them7"%8

Decause the conductors (or plates) are close together, the opposite charges on the conductorsattract one another due to their electric fields, allowing the capacitor to store more charge for agiven voltage than if the conductors were separated, giving the capacitor a large capacitance

!ometimes charge *uild-up affects the capacitor mechanically, causing its capacitance to vary/n this case, capacitance is defined in terms of incremental changes

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Hydraulic analogy[edit]

/n the hydraulic analogy, a capacitor is analogous to a ru**er mem*rane sealed inside a pipe his animation illustrates a mem*rane *eing

repeatedly stretched and un-stretched *y the flow of water, which is analogous to a capacitor *eing repeatedly charged and discharged *y

the flow of charge

/n the hydraulic analogy, charge carriers flowing through a wire are analogous to waterflowing through a pipe A capacitor is like a ru**er mem*rane sealed inside a pipe Watermolecules cannot pass through the mem*rane, *ut some water can move *y stretching themem*rane he analogy clarifies a few aspects of capacitors

•

The current  alters the charge on a capacitor , Gust as the flow of water changes theposition of the mem*rane More specifically, the effect of an electric current is toincrease the charge of one plate of the capacitor, and decrease the charge of the otherplate *y an e3ual amount his is Gust as when water flow moves the ru**er mem*rane,it increases the amount of water on one side of the mem*rane, and decreases theamount of water on the other side

• The more a capacitor is charged, the larger its voltage dropJ ie, the more it 6pushes

*ack6 against the charging current his is analogous to the fact that the more amem*rane is stretched, the more it pushes *ack on the water

• Charge can flow "through" a capacitor even though no individual electron can get from

one side to the other. his is analogous to the fact that water can flow through the pipeeven though no water molecule can pass through the ru**er mem*rane 9f course, the

flow cannot continue in the same direction foreverJ the capacitor will experiencedielectric*reakdown, and analogously the mem*rane will eventually *reak

• he capacitance descri*es how much charge can *e stored on one plate of a capacitor

for a given 6push6 (voltage drop) A very stretchy, flexi*le mem*rane corresponds to ahigher capacitance than a stiff mem*rane

•  A charged-up capacitor is storing potential energy, analogously to a stretched

mem*rane

Energy of electric field[edit]

Work must *e done *y an external influence to 6move6 charge *etween the conductors in a

capacitor When the external influence is removed, the charge separation persists in theelectric field and energy is stored to *e released when the charge is allowed to return to itse3uili*rium position he work done in esta*lishing the electric field, and hence the amountof energy stored, is 7"=8

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2ere Q is the charge stored in the capacitor, V  is the voltage across the capacitor,and C  is the capacitance

/n the case of a fluctuating voltage V (t ), the stored energy also fluctuates andhence power  must flow into or out of the capacitor his power can *e found *y takingthe time derivative of the stored energy

Current–voltage relation[edit]

he current  (t ) through any component in an electric circuit is defined as the rate offlow of a charge Q(t ) passing through it, *ut actual chargesOelectronsOcannotpass through the dielectric layer of a capacitor ather, one electron accumulates onthe negative plate for each one that leaves the positive plate, resulting in an electrondepletion and conse3uent positive charge on one electrode that is e3ual andopposite to the accumulated negative charge on the other hus the charge on theelectrodes is e3ual to the integral of the current as well as proportional to thevoltage, as discussed a*ove As with any antiderivative, a constant of integration isadded to represent the initial voltage V (t #) his is the integral form of the capacitore3uation7">8

aking the derivative of this and multiplying *y C  yields the derivative form 7"@8

he dual of the capacitor is the inductor , which stores energy in a magnetic

field rather than an electric field /ts current-voltage relation is o*tained *yexchanging current and voltage in the capacitor e3uations andreplacing C  with the inductance #

DC circuits[edit]$ee also! %C circuit 

 A simple resistor-capacitor circuit demonstrates charging of a capacitor

 A series circuit containing only a resistor , a capacitor, a switch and aconstant < source of voltage V # is known as a charging circuit 7"B8 /f thecapacitor is initially uncharged while the switch is open, and the switch isclosed at t & , it follows from Iirchhoffs voltage law that

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aking the derivative and multiplying *y C , gives a first-order differentiale3uation

 At t  P #, the voltage across the capacitor is +ero and the voltageacross the resistor is V &  he initial current is then  (#) PV #4%  Withthis assumption, solving the differential e3uation yields

where Q# P %C  is the time constant  of the system As thecapacitor reaches e3uili*rium with the source voltage, thevoltages across the resistor and the current through the entirecircuit decay exponentially he case of discharging  a chargedcapacitor likewise demonstrates exponential decay, *ut with theinitial capacitor voltage replacing V # and the final voltage *eing+ero

AC circuits[edit]$ee also! reactance 'electronics( and electrical impedance )

*eriving the device+specific impedances

/mpedance, the vector sum of reactance and resistance,descri*es the phase difference and the ratio of amplitudes*etween sinusoidally varying voltage and sinusoidally varyingcurrent at a given fre3uency Fourier analysis allows any signalto *e constructed from a spectrum of fre3uencies, whence thecircuits reaction to the various fre3uencies may *e found hereactance and impedance of a capacitor are respectively

where   is the imaginary unit and R is the angularfre3uency of the sinusoidal signal he 1   phase indicatesthat the A voltage V  P -  lags the A current *y B#S thepositive current phase corresponds to increasing voltageas the capacitor chargesJ +ero current corresponds toinstantaneous constant voltage, etc

/mpedance decreases with increasing capacitance andincreasing fre3uency his implies that a higher-fre3uency

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signal or a larger capacitor results in a lower voltageamplitude per current amplitudeOan A 6short circuit6or A coupling onversely, for very low fre3uencies, thereactance will *e high, so that a capacitor is nearly an opencircuit in A analysisOthose fre3uencies have *een6filtered out6

apacitors are different from resistors and inductors in thatthe impedance is inversely  proportional to the definingcharacteristicJ ie, capacitance

 A capacitor connected to a sinusoidal voltage source willcause a displacement current to flow through it /n the casethat the voltage source is '#cos(Rt), the displacementcurrent can *e expressed as

 At sin(Rt) P -", the capacitor has a maximum (or peak)

current where*y /# P R'# he ratio of peak voltage topeak current is due to capacitive reactance (denotedT)

T approaches +ero as R approaches infinity /fT approaches #, the capacitor resem*les a short wirethat strongly passes current at high fre3uenciesT approaches infinity as R approaches +ero /fT approaches infinity, the capacitor resem*les anopen circuit that poorly passes low fre3uencies

he current of the capacitor may *e expressed in theform of cosines to *etter compare with the voltage ofthe source

/n this situation, the current is out of phase with thevoltage *y 0U45 radians or 0B# degrees (ie, thecurrent will lead the voltage *y B#S)

Laplace circuit analysis (sdo!ain"[edit]

When using the ?aplace transform in circuitanalysis, the impedance of an ideal capacitor withno initial charge is represented in the s domain *y

where

• C  is the capacitance, and

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• s is the complex fre3uency

#arallelplate !odel[edit]

<ielectric is placed *etween two conducting plates, each of

area  and with a separation of d 

he simplest model capacitor consists of twothin parallel conductive plates separated *y adielectric with permittivity V his model mayalso *e used to make 3ualitative predictionsfor other device geometries he plates areconsidered to extend uniformly over anarea  and a charge density N P NQ4 existson their surface Assuming that the length andwidth of the plates are much greater than theirseparation d , the electric field near the centreof the device will *e uniform with themagnitude /  P 4V he voltage is defined asthe line integral of the electric field *etweenthe plates

!olving this for C  P Q4V  reveals thatcapacitance increases with area of theplates, and decreases as separation*etween plates increases

he capacitance is therefore greatestin devices made from materials with ahigh permittivity, large plate area, andsmall distance *etween plates

 A parallel plate capacitor can onlystore a finite amount of energy*efore dielectric *reakdown occurshe capacitors dielectric material has

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a dielectric strength 0 d which setsthe capacitors *reakdownvoltage at V  P V *d P 0 dd  he maximumenergy that the capacitor can store istherefore

he maximum energy is a functionof dielectric volume, permittivity, and dielectric strength hangingthe plate area and the separation*etween the plates whilemaintaining the same volumecauses no change of themaximum amount of energy thatthe capacitor can store, so long asthe distance *etween plates

remains much smaller than *oththe length and width of the plates/n addition, these e3uationsassume that the electric field isentirely concentrated in thedielectric *etween the plates /nreality there are fringing fieldsoutside the dielectric, for example*etween the sides of the capacitor plates, which will increase theeffective capacitance of thecapacitor his is sometimescalled parasitic capacitance For

some simple capacitor geometriesthis additional capacitance termcan *e calculated analytically75#8 /t*ecomes negligi*ly small whenthe ratios of plate width toseparation and length toseparation are large

!everal capacitors in parallel

$etwor%s[edit]

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$ee also! $eries and parallel

circuits

&or capacitors in parallel

apacitors in a parallel configuration each have the same applied voltage heir

capacitances add up harge is apportioned among them *y si+e .sing the schematic

diagram to visuali+e parallel plates, it is apparent that each capacitor contri*utes to the total

surface area

&or capacitors in series

!everal capacitors in series

onnected in series, the schematic diagram reveals that the separation distance,not the

plate area, adds up he capacitors each store instantaneous charge *uild-up e3ual to thatof every other capacitor in the series he total voltage difference from end to end isapportioned to each capacitor according to the inverse of its capacitance he entire seriesacts as a capacitor smaller  than any of its components

apacitors are com*ined in series to achieve a higher working voltage, for example for

smoothing a high voltage power supply he voltage ratings, which are *ased on plate

separation, add up, if capacitance and leakage currents for each capacitor are identical /n

such an application, on occasion, series strings are connected in parallel, forming a matrix

he goal is to maximi+e the energy storage of the network without overloading any capacitor

For high-energy storage with capacitors in series, some safety considerations must *e

applied to ensure one capacitor failing and leaking current will not apply too much voltage to

the other series capacitors

!eries connection is also sometimes used to adapt polari+ed electrolytic capacitors for

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$ote* his is only correct if all capacitance values are e3ual

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more of a pair of plates, the circuit capacitance increases !3uee+ing the dielectric can

change a capacitor at a few tens of *ar pressure sufficiently that it can *e used as a pressure

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microphones, where one plate is moved *y air pressure, relative to the fixed position of the

other plate !omeaccelerometers use M:M! capacitors etched on a chip to measure the

magnitude and direction of the acceleration vector hey are used to detect changes in

acceleration, in tilt sensors, or to detect free fall, as sensors triggering air*ag deployment,

and in many other applications !ome fingerprint sensors use capacitors Additionally, a user

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