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| {{About|the electronic component|the physical phenomenon|capacitance|an overview of various kinds of capacitors|types of capacitor}}
| | Irwin Butts is what my wife enjoys to call me although I don't truly like becoming known as like that. One of the issues she enjoys most is to do aerobics and now she is attempting to make cash with it. Puerto Rico is where he and his wife live. Managing individuals is his occupation.<br><br>my blog - std testing at home ([http://www.ninfeta.tv/user/JVelasco click through the following document]) |
| {{Refimprove|date=June 2013}}
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| {{Infobox electronic component
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| | component = Capacitor
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| | photo = [[File:Photo-SMDcapacitors.jpg|250px]]
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| | invented =
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| | first_produced =
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| | photo_caption = Miniature low-voltage capacitors (next to a cm ruler)
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| | symbol = [[File:Types of capacitor.svg|IEC-style capacitor symbol|300px]]
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| }}
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| [[File:Condensador electrolitico 150 microF 400V.jpg|thumb|A typical [[electrolytic capacitor]]]]
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| [[File:Electrolytic capacitor.jpg|thumbnail|4 electrolytic capacitors of different voltages and capacitance]]
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| [[File:Tantalum capacitors.jpg|thumbnail|Solid-body, resin-dipped 10 μF 35 V [[tantalum capacitor]]s. The '''+''' sign indicates the positive lead.]]
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| A '''capacitor''' (originally known as a '''condenser''') is a [[passivity (engineering)|passive]] [[terminal (electronics)|two-terminal]] [[electronic component|electrical component]] used to store [[energy]] [[electrostatic]]ally in an [[electric field]]. The forms of practical capacitors vary widely, but all contain at least two [[electrical conductor]]s (plates) separated by a [[dielectric]] (i.e., [[insulator (electricity)|insulator]]). The conductors can be thin films of metal, aluminum foil or disks, etc. The 'nonconducting' dielectric acts to increase the capacitor's charge capacity. A dielectric can be glass, ceramic, plastic film, air, paper, mica, etc. Capacitors are widely used as parts of [[electrical circuit]]s in many common electrical devices. Unlike a [[resistor]], a capacitor does not dissipate energy. Instead, a capacitor stores [[energy]] in the form of an [[electric field|electrostatic field]] between its plates.
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| When there is a [[potential difference]] across the conductors (e.g., when a capacitor is attached across a battery), an [[electric field]] develops across the dielectric, causing positive charge (+Q) to collect on one plate and negative charge (-Q) to collect on the other plate. If a battery has been attached to a capacitor for a sufficient amount of time, no current can flow through the capacitor. However, if an accelerating or alternating voltage is applied across the leads of the capacitor, a [[displacement current]] can flow.
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| An ideal capacitor is characterized by a single constant value for its [[capacitance]]. Capacitance is expressed as the ratio of the [[electric charge]] (Q) on each conductor to the potential difference (V) between them. The [[SI]] unit of capacitance is the [[farad]] (F), which is equal to one [[coulomb]] per [[volt]] (1 C/V). Typical capacitance values range from about 1 pF (10<sup>-12</sup> F) to about 1 mF (10<sup>-3</sup> F).
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| The capacitance is greater when there is a narrower separation between conductors and when the conductors have a larger surface area. In practice, the dielectric between the plates passes a small amount of [[leakage (electronics)|leakage current]] and also has an electric field strength limit, known as the [[breakdown voltage]]. The conductors and [[Lead (electronics)|lead]]s introduce an undesired [[Equivalent series inductance|inductance]] and [[Equivalent series resistance|resistance]].
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| Capacitors are widely used in [[electronic circuit]]s for blocking [[direct current]] while allowing [[alternating current]] to pass. In [[analog filter]] networks, they smooth the output of [[power supply|power supplies]]. In [[LC circuit|resonant circuit]]s they tune [[radio]]s to particular [[frequency|frequencies]]. In [[electric power transmission]] systems they stabilize voltage and power flow.<ref>{{cite book |title=Electrical and Electronic Principles and Technology |last=Bird |first=John |url=http://books.google.com/books?id=A1tAHm_5sl0C&printsec=frontcover |year=2010 |publisher=Routledge |pages=63–76 |isbn=9780080890562 |accessdate=2013-03-17}}</ref>
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| ==History==
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| [[File:Leidse flessen Museum Boerhave december 2003 2.jpg|left|upright|thumb|Battery of four [[Leyden jar]]s in [[Museum Boerhaave]], [[Leiden]], the [[Netherlands]].]]
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| In October 1745, [[Ewald Georg von Kleist]] of [[Pomerania]] in Germany found that charge could be stored by connecting a high-voltage [[electrostatic generator]] by a wire to a volume of water in a hand-held glass jar.<ref>{{cite web |url=http://www.worldwideschool.org/library/books/sci/history/AHistoryofScienceVolumeII/chap49.html |title=A History of Science Volume II, Part VI: The Leyden Jar Discovered |last=Williams |first=Henry Smith |accessdate=2013-03-17}}</ref> Von Kleist's hand and the water acted as conductors, and the jar as a [[dielectric]] (although details of the mechanism were incorrectly identified at the time). Von Kleist found that touching the wire resulted in a powerful spark, much more painful than that obtained from an electrostatic machine. The following year, the Dutch physicist [[Pieter van Musschenbroek]] invented a similar capacitor, which was named the [[Leyden jar]], after the [[Leiden University|University of Leiden]] where he worked.<ref>{{cite book|title=The Story of Electrical and Magnetic Measurements: From 500 BC to the 1940s |last=Keithley |first=Joseph F. |url=http://books.google.com/?id=uwgNAtqSHuQC&printsec=frontcover&q |year=1999 |publisher=John Wiley & Sons |page=23 |isbn=9780780311930 |accessdate=2013-03-17}}</ref> He also was impressed by the power of the shock he received, writing, "I would not take a second shock for the kingdom of France."<ref>{{cite book |title=Electricity in Every-day Life |last=Houston |first=Edwin J. |url=http://books.google.com/?id=ko9BAAAAIAAJ&pg=PA71&dq=jar+%22von+Kleist%22 |year=1905 |publisher=P. F. Collier & Son |page=71 |accessdate=2013-03-17}}</ref>
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| [[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 came to the conclusion that the charge was stored on the glass, not in the water as others had assumed. He also adopted the term "battery",<ref>{{cite book |title=Benjamin Franklin: An American Life |last=Isaacson |first=Walter |authorlink=Walter Isaacson |url=http://books.google.com/?id=oIW915dDMBwC&lpg=PA135&dq=%22benjamin%20franklin%22%20leyden%20jar&pg=PA136#v=onepage |year=2003 |publisher=Simon and Schuster |page=136 |isbn=9780743260848 |accessdate=2013-03-17}}</ref><ref>{{cite web |title=Experiments & Observations on Electricity: Letter IV to Peter Collinson |url=http://www.chemteam.info/Chem-History/Franklin-1749/Franklin-1749-all.pdf |date=1749-04-29 |first=Benjamin |last=Franklin |page=28 |format=PDF |accessdate=2009-08-09}}</ref> (denoting the increasing of power with a row of similar units as in a [[Artillery battery|battery of cannon]]), subsequently applied to [[Battery (electricity)|clusters of electrochemical cells]].<ref>{{cite web |title=Franklin and Electrostatics—Ben Franklin as my Lab Partner |url=http://www.compadre.org/Repository/document/ServeFile.cfm?ID=3430&DocID=2402&DocFID=3925&Attachment=1 |last=Morse |first=Robert A. |page=23 |date=September 2004 |format=PDF |work=Wright Center for Science Education |publisher=Tufts University |quote=After Volta’s discovery of the electrochemical cell in 1800, the term was then applied to a group of electrochemical cells |accessdate=2009-08-10}}</ref> Leyden jars were later made by coating the inside and outside of jars with metal foil, leaving a space at the mouth to prevent arcing between the foils.{{Citation needed|date=December 2008}} The earliest unit of capacitance was the [[Jar (unit)|jar]], equivalent to about 1 [[Farad#Definition|nanofarad]].<ref>{{cite web |title=eFunda: Glossary: Units: Electric Capacitance: Jar |url=http://www.efunda.com/glossary/units/units--electric_capacitance--jar.cfm |publisher=eFunda |accessdate=2013-03-17}}</ref>
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| Leyden jars or more powerful devices employing flat glass plates alternating with foil conductors were used exclusively up until about 1900, when the invention of [[Wireless telegraphy|wireless]] ([[radio]]) created a demand for standard capacitors, and the steady move to higher [[frequency|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.
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| Early capacitors were also known as ''condensers'', a term that is still occasionally used today. The term was first used for this purpose by [[Alessandro Volta]] in 1782, with reference to the device's ability to store a higher density of electric charge than a normal isolated conductor.<ref>{{Cite journal |title=Sketch of Alessandro Volta |url=http://books.google.com/?id=eCADAAAAMBAJ&pg=PA117 |journal=The Popular Science Monthly |publisher=Bonnier Corporation |location=New York |pages=118–119 |issn=0161-7370 |date=May 1892}}</ref>
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| {{-}}
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| ==Theory of operation==
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| {{Main|Capacitance}}
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| ===Overview===
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| [[File:Capacitor schematic with dielectric.svg|thumb|left|Charge separation in a parallel-plate capacitor causes an internal electric field. A dielectric (orange) reduces the field and increases the capacitance.]]
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| [[File:Plattenkondensator hg.jpg|right|thumb|A simple demonstration of a parallel-plate capacitor]]
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| A capacitor consists of two [[Electrical conductor|conductor]]s separated by a non-conductive region.<ref name="Ulaby_p168">Ulaby, p.168</ref> The non-conductive region is called the [[dielectric]]. In simpler terms, the dielectric is just an [[Insulator (electrical)|electrical insulator]]. Examples of dielectric media are glass, air, paper, [[vacuum]], and even a [[semiconductor]] [[depletion region]] chemically identical to the conductors. A capacitor is assumed to be self-contained and isolated, with no net [[electric charge]] and no influence from any external electric field. The conductors thus hold equal and opposite charges on their facing surfaces,<ref name="Ulaby_p157">Ulaby, p.157</ref> and the dielectric develops an electric field. In [[SI]] units, a capacitance of one [[farad]] means that one [[coulomb]] of charge on each conductor causes a voltage of one [[volt]] across the device.<ref name="Ulaby_p169">Ulaby, p.169</ref>
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| An ideal capacitor is wholly characterized by a constant [[capacitance]] ''C'', defined as the ratio of charge ±''Q'' on each conductor to the voltage ''V'' between them:<ref name="Ulaby_p168" />
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| :<math>C= \frac{Q}{V}</math>
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| Because the conductors (or plates) are close together, the opposite charges on the conductors attract one another due to their electric fields, allowing the capacitor to store more charge for a given voltage than if the conductors were separated, giving the capacitor a large capacitance.
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| Sometimes charge build-up affects the capacitor mechanically, causing its capacitance to vary. In this case, capacitance is defined in terms of incremental changes:
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| :<math>C= \frac{\mathrm{d}Q}{\mathrm{d}V}</math>
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| ===Hydraulic analogy===
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| [[File:CapacitorHydraulicAnalogyAnimation.gif|thumb|In the [[hydraulic analogy]], a capacitor is analogous to a rubber membrane sealed inside a pipe. This animation illustrates a membrane being repeatedly stretched and un-stretched by the flow of water, which is analogous to a capacitor being repeatedly charged and discharged by the flow of charge.]]
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| In the [[hydraulic analogy]], charge carriers flowing through a wire are analogous to water flowing through a pipe. A capacitor is like a rubber membrane sealed inside a pipe. Water molecules cannot pass through the membrane, but some water can move by stretching the membrane. The analogy clarifies a few aspects of capacitors:
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| *''The [[electric current|current]] alters the [[electric charge|charge]] on a capacitor'', just as the flow of water changes the position of the membrane. More specifically, the effect of an electric current is to increase the charge of one plate of the capacitor, and decrease the charge of the other plate by an equal amount. This is just as when water flow moves the rubber membrane, it increases the amount of water on one side of the membrane, and decreases the amount of water on the other side.
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| *''The more a capacitor is charged, the larger its [[voltage drop]]''; i.e., the more it "pushes back" against the charging current. This is analogous to the fact that the more a membrane is stretched, the more it pushes back on the water.
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| *''Charge can flow "through" a capacitor even though no individual electron can get from one side to the other.'' This is analogous to the fact that water can flow through the pipe even though no water molecule can pass through the rubber membrane. Of course, the flow cannot continue in the same direction forever; the capacitor will experience [[dielectric breakdown]], and analogously the membrane will eventually break.
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| *The ''[[capacitance]]'' describes how much charge can be stored on one plate of a capacitor for a given "push" (voltage drop). A very stretchy, flexible membrane corresponds to a higher capacitance than a stiff membrane.
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| *A charged-up capacitor is storing [[potential energy]], analogously to a stretched membrane.
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| ===Energy of electric field===
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| [[Work (thermodynamics)|Work]] must be done by an external influence to "move" charge between the conductors in a capacitor. When the external influence is removed, the charge separation persists in the electric field and energy is stored to be released when the charge is allowed to return to its equilibrium position. The work done in establishing the electric field, and hence the amount of energy stored, is<ref>{{cite book |title=Electromagnetism for Engineers: An Introductory Course |last=Hammond |first=Percy |series=The Commonwealth and International Library of Science, Technology, Engineering and Liberal Studies. Applied Electricity and Electronics Division |volume=3 |year=1964 |publisher=Pergamon Press |pages=44–45 |accessdate=2013-03-17}}</ref>
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| :<math>W = \int_0^Q V \mathrm{d}q = \int_0^Q \frac{q}{C} \mathrm{d}q = {1 \over 2} {Q^2 \over C} = {1 \over 2} C V^2 = {1 \over 2} VQ</math>
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| Here ''Q'' is the charge stored in the capacitor, ''V'' is the voltage across the capacitor, and ''C'' is the capacitance.
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| In the case of a fluctuating voltage ''V''(''t''), the stored energy also fluctuates and hence [[power (physics)|power]] must flow into or out of the capacitor. This power can be found by taking the [[time derivative]] of the stored energy:
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| :<math>P = \frac{\mathrm{d}W}{\mathrm{d}t} = \frac{\mathrm{d}}{\mathrm{d}t}\left(\frac{1}{2} CV^2\right) = C V(t) \frac{\mathrm{d}V}{\mathrm{d}t}</math>
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| ===Current–voltage relation===
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| The current ''I''(''t'') through any component in an electric circuit is defined as the rate of flow of a charge ''Q''(''t'') passing through it, but actual charges—electrons—cannot pass through the dielectric layer of a capacitor. Rather, an electron accumulates on the negative plate for each one that leaves the positive plate, resulting in an electron depletion and consequent positive charge on one electrode that is equal and opposite to the accumulated negative charge on the other. Thus the charge on the electrodes is equal to the [[integral]] of the current as well as proportional to the voltage, as discussed above. As with any [[antiderivative]], a [[constant of integration]] is added to represent the initial voltage ''V''(''t''<sub>0</sub>). This is the integral form of the capacitor equation:<ref name="Dorf_p263">Dorf, p.263</ref>
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| :<math>V(t) = \frac{Q(t)}{C} = \frac{1}{C}\int_{t_0}^t I(\tau) \mathrm{d}\tau + V(t_0)</math>
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| Taking the derivative of this and multiplying by ''C'' yields the derivative form:<ref name="Dorf_p260">Dorf, p.260</ref>
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| :<math>I(t) = \frac{\mathrm{d}Q(t)}{\mathrm{d}t} = C\frac{\mathrm{d}V(t)}{\mathrm{d}t}</math>
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| The [[duality (electrical circuits)|dual]] of the capacitor is the [[inductor]], which stores energy in a [[magnetic field]] rather than an electric field. Its current-voltage relation is obtained by exchanging current and voltage in the capacitor equations and replacing ''C'' with the inductance ''L''.
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| ===DC circuits===
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| {{See also|RC circuit}}
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| [[File:RC switch.svg|A simple resistor-capacitor circuit demonstrates charging of a capacitor.|thumb]]
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| A series circuit containing only a [[resistor]], a capacitor, a switch and a constant DC source of voltage ''V''<sub>0</sub> is known as a ''charging circuit''.<ref name="ChargingCircuit">{{cite web |title=Capacitor charging and discharging |url=http://www.allaboutcircuits.com/vol_6/chpt_3/17.html |work=All About Circuits |accessdate=2009-02-19}}</ref> If the capacitor is initially uncharged while the switch is open, and the switch is closed at ''t<sub>0</sub>'', it follows from [[Kirchhoff's voltage law]] that
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| :<math>V_0 = v_\text{resistor}(t) + v_\text{capacitor}(t) = i(t)R + \frac{1}{C}\int_{t_0}^t i(\tau) \mathrm{d}\tau</math>
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| Taking the derivative and multiplying by ''C'', gives a [[first-order differential equation]]:
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| :<math>RC\frac{\mathrm{d}i(t)}{\mathrm{d}t} + i(t) = 0</math>
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| At ''t'' = 0, the voltage across the capacitor is zero and the voltage across the resistor is ''V<sub>0</sub>''. The initial current is then ''I''(0) =''V''<sub>0</sub>/''R''. With this assumption, solving the differential equation yields
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| :<math>\begin{align}
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| I(t) &= \frac{V_0}{R} e^{-\frac{t}{\tau_0}} \\
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| V(t) &= V_0 \left( 1 - e^{-\frac{t}{\tau_0}}\right)
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| \end{align}</math>
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| where τ<sub>0</sub> = ''RC'' is the ''[[time constant]]'' of the system. As the capacitor reaches equilibrium with the source voltage, the voltages across the resistor and the current through the entire circuit [[exponential decay|decay exponentially]]. The case of ''discharging'' a charged capacitor likewise demonstrates exponential decay, but with the initial capacitor voltage replacing ''V''<sub>0</sub> and the final voltage being zero.
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| ===AC circuits===
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| {{See also|reactance (electronics)|electrical impedance#Deriving the device specific impedances}}
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| [[Electrical impedance|Impedance]], the vector sum of [[Electrical reactance|reactance]] and [[Electrical resistance|resistance]], describes the phase difference and the ratio of amplitudes between sinusoidally varying voltage and sinusoidally varying current at a given frequency. [[Fourier analysis]] allows any signal to be constructed from a [[spectrum]] of frequencies, whence the circuit's reaction to the various frequencies may be found. The reactance and impedance of a capacitor are respectively
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| :<math>\begin{align}
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| X &= -\frac{1}{\omega C} = -\frac{1}{2\pi f C} \\
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| Z &= \frac{1}{j\omega C} = -\frac{j}{\omega C} = -\frac{j}{2\pi f C}
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| \end{align}</math>
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| where ''j'' is the [[imaginary unit]] and ω is the [[angular frequency]] of the sinusoidal signal. The −''j'' phase indicates that the AC voltage ''V'' = ''ZI'' lags the AC current by 90°: the positive current phase corresponds to increasing voltage as the capacitor charges; zero current corresponds to instantaneous constant voltage, etc.
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| Impedance decreases with increasing capacitance and increasing frequency. This implies that a higher-frequency signal or a larger capacitor results in a lower voltage amplitude per current amplitude—an AC "short circuit" or [[AC coupling]]. Conversely, for very low frequencies, the reactance will be high, so that a capacitor is nearly an open circuit in AC analysis—those frequencies have been "filtered out".
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| Capacitors are different from resistors and inductors in that the impedance is ''inversely'' proportional to the defining characteristic; i.e., [[capacitance]].
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| A capacitor connected to a sinusoidal voltage source will cause a displacement current to flow through it. In the case that the voltage source is V<sub>0</sub>cos(ωt), the displacement current can be expressed as:
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| :<math> I = C \frac{dV}{dt} = -\omega {C}{V_\text{0}}\sin(\omega t)</math>
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| At sin(ωt) = -1, the capacitor has a maximum (or peak) current whereby I<sub>0</sub> = ωCV<sub>0</sub>. The ratio of peak voltage to peak current is due to [[Electrical reactance#Capacitive reactance|capacitive reactance]] (denoted X<sub>C</sub>).
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| <math> X_C = \frac{V_\text{0}}{I_\text{0}} = \frac{V_\text{0}}{{\omega C}}{V_\text{0}} = \frac{1}{\omega C} </math>
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| X<sub>C</sub> approaches zero as ω approaches infinity. If X<sub>C</sub> approaches 0, the capacitor resembles a short wire that strongly passes current at high frequencies. X<sub>C</sub> approaches infinity as ω approaches zero. If X<sub>C</sub> approaches infinity, the capacitor resembles an open circuit that poorly passes low frequencies.
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| The current of the capacitor may be expressed in the form of cosines to better compare with the voltage of the source:
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| :<math> I = - {I_\text{0}}{\sin({\omega t}}) = {I_\text{0}}{\cos({\omega t} + {90^\circ})}</math>
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| In this situation, the current is out of [[Phase (waves)|phase]] with the voltage by +π/2 radians or +90 degrees (i.e., the current will lag the voltage by 90°).
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| ===Laplace circuit analysis (s-domain)===
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| When using the [[Laplace transform]] in circuit analysis, the impedance of an ideal capacitor with no initial charge is represented in the ''s'' domain by:
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| :<math>Z(s) = \frac{1}{sC}</math>
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| where
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| * ''C'' is the capacitance, and
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| * ''s'' is the complex frequency.
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| ===Parallel-plate model===
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| [[File:Parallel plate capacitor.svg|thumb|left|Dielectric is placed between two conducting plates, each of area ''A'' and with a separation of ''d'']]
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| The simplest capacitor consists of two parallel conductive plates separated by a dielectric with [[permittivity]] ε (such as air). The model may also be used to make qualitative predictions for other device geometries. The plates are considered to extend uniformly over an area ''A'' and a charge density ±ρ = ±''Q''/''A'' exists on their surface. Assuming that the width of the plates is much greater than their separation ''d'', the electric field near the centre of the device will be uniform with the magnitude ''E'' = ρ/ε. The voltage is defined as the [[line integral]] of the electric field between the plates
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| :<math>V= \int_0^d E\,\mathrm{d}z = \int_0^d \frac{\rho}{\varepsilon}\,\mathrm{d}z = \frac{\rho d}{\varepsilon} = \frac{Qd}{\varepsilon A}</math>
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| Solving this for ''C'' = ''Q''/''V'' reveals that capacitance increases with area and decreases with separation
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| :<math>C = \frac{\varepsilon A}{d}</math>
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| The capacitance is therefore greatest in devices made from materials with a high permittivity, large plate area, and small distance between plates.
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| A parallel plate capacitor can only store a finite amount of energy before [[dielectric breakdown]] occurs. The capacitor's dielectric material has a [[dielectric strength]] ''U''<sub>d</sub> which sets the [[Capacitor#Breakdown voltage|capacitor's breakdown voltage]] at ''V'' = ''V''<sub>bd</sub> = ''U''<sub>d</sub>''d''. The maximum energy that the capacitor can store is therefore
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| :<math>E = \frac{1}{2}CV^2=\frac{1}{2} \frac{\varepsilon A}{d} (U_d d)^2 = \frac{1}{2} \varepsilon A d U_d^2</math>
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| We see that the maximum energy is a function of dielectric volume, [[permittivity]], and [[dielectric strength]] per distance. So increasing the plate area while decreasing the separation between the plates while maintaining the same volume has no change on the amount of energy the capacitor can store. Care must be taken when increasing the plate separation so that the above assumption of the distance between plates being much smaller than the area of the plates is still valid for these equations to be accurate. In addition, these equations assume that the electric field is entirely concentrated in the dielectric between the plates. In reality there are fringing fields outside the dielectric, for example between the sides of the capacitor plates, which will increase the effective capacitance of the capacitor. This could be seen as a form of [[parasitic capacitance]]. For some simple capacitor geometries this additional capacitance term can be calculated analytically.<ref name=Pillai1970>{{Cite doi|10.1049/piee.1970.0232}}</ref> It becomes negligibly small when the ratio of plate area to separation is large.
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| [[File:capacitors in parallel.svg|right|thumb|Several capacitors in parallel.]]
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| ===Networks===
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| {{See also|Series and parallel circuits}}
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| ;For capacitors in parallel
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| :Capacitors in a parallel configuration each have the same applied voltage. Their capacitances add up. Charge is apportioned among them by size. Using the schematic diagram to visualize parallel plates, it is apparent that each capacitor contributes to the total surface area.
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| :: <math>C_\mathrm{eq}= C_1 + C_2 + \cdots + C_n</math>
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| {{Clear}}
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| ;For capacitors in series
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| [[File:capacitors in series.svg|right|thumb|Several capacitors in series.]]
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| :Connected in series, the schematic diagram reveals that the separation distance, not the plate area, adds up. The capacitors each store instantaneous charge build-up equal to that of every other capacitor in the series. The total voltage difference from end to end is apportioned to each capacitor according to the inverse of its capacitance. The entire series acts as a capacitor ''smaller'' than any of its components.
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| :: <math>\frac{1}{C_\mathrm{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}</math>
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| {{Clear}}
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| :Capacitors are combined in series to achieve a higher working voltage, for example for smoothing a high voltage power supply. The voltage ratings, which are based on plate separation, add up, if capacitance and leakage currents for each capacitor are identical. In such an application, on occasion series strings are connected in parallel, forming a matrix. The goal is to maximize the energy storage of the network without overloading any capacitor. For high-energy storage with capacitors in series, some safety considerations must be applied to ensure one capacitor failing and leaking current will not apply too much voltage to the other series capacitors.
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| ;Voltage distribution in parallel-to-series networks.
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| :To model the distribution of voltages from a single charged capacitor <math> \left( A \right)</math> connected in parallel to a chain of capacitors in series <math> \left( B_\text{n} \right) </math> :
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| :: <math>\begin{align}
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| (volts) A_\mathrm{eq} &= A\left(1 - \frac{1}{n + 1}\right) \\
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| (volts) B_\text{1..n} &= \frac{A}{n} \left(1 - \frac{1}{n + 1}\right) \\
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| A - B &= 0
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| \end{align}</math>
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| :'''Note:''' This is only correct if all capacitance values are equal.
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| :The power transferred in this arrangement is:
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| :: <math>P = \frac{1}{R} \cdot \frac{1}{n + 1} A_\text{volts} \left( A_\text{farads} + B_\text{farads} \right)</math>
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| :Series connection is also sometimes used to adapt polarized [[electrolytic capacitor]]s for bipolar AC use. Two identical polarized electrolytic capacitors are connected back to back to form a bipolar capacitor with half the nominal capacitance of either.<ref>{{cite web |title=Application Guide, Aluminum Electrolytic Capacitors |url=http://electrochem.cwru.edu/encycl/misc/c04-appguide.pdf |publisher=Cornell Dubilier |format=PDF |accessdate=2013-05-27}}</ref> However, the anode film can only withstand a small reverse voltage.<ref>{{cite book |title=Discrete electronic components |url=http://books.google.com/books?id=3qk8AAAAIAAJ |last=Mazda |first=F. F. |year=1981 |publisher=CUP Archive |page=71 |isbn=9780521234702 |accessdate=2013-03-17}}</ref> This arrangement can lead to premature failure as the anode film is broken down during the reverse-conduction phase and partially rebuilt during the forward phase.<ref>{{cite web |title=Application Guide, Aluminum Electrolytic Capacitors |url=http://electrochem.cwru.edu/encycl/misc/c04-appguide.pdf |publisher=Cornell Dubilier |format=PDF |accessdate=2011-10-28}}</ref> A factory-made non-polarized electrolytic capacitor has both plates anodized so that it can withstand rated voltage in both directions; such capacitors also have about half the capacitance per unit volume of polarized capacitors.
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| ==Non-ideal behavior==
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| {{anchor|Non-ideal behavior}}
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| <!-- NB. Section header used in various redirects to this page -->
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| Capacitors deviate from the ideal capacitor equation in a number of ways. Some of these, such as leakage current and parasitic effects are linear, or can be assumed to be linear, and can be dealt with by adding virtual components to the [[equivalent circuit]] of the capacitor. The usual methods of [[network analysis (electrical circuits)|network analysis]] can then be applied. In other cases, such as with breakdown voltage, the effect is non-linear and normal (i.e., linear) network analysis cannot be used, the effect must be dealt with separately. There is yet another group, which may be linear but invalidate the assumption in the analysis that capacitance is a constant. Such an example is temperature dependence. Finally, combined parasitic effects such as inherent inductance, resistance, or dielectric losses can exhibit non-uniform behavior at variable frequencies of operation.
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| ===Breakdown voltage===
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| {{Main|Breakdown voltage}}
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| Above a particular electric field, known as the dielectric strength ''E<sub>ds</sub>'', the dielectric in a capacitor becomes conductive. The voltage at which this occurs is called the breakdown voltage of the device, and is given by the product of the dielectric strength and the separation between the conductors,<ref name="Ulaby_p170">Ulaby, p.170</ref>
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| :<math>V_{\text{bd}}= E_{\text{ds}} d</math>
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| The maximum energy that can be stored safely in a capacitor is limited by the breakdown voltage. 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.<ref>{{cite book |title=Introduction to High Power Pulse Technology |url=http://books.google.com/?id=spZ_H4nwIN0C&pg=PA47&dq=breakdown+field+energy-density+dielectric |last1=Pai |first1=S. T. |last2=Qi Zhang |publisher=World Scientific |year=1995 |series=Advanced Series in Electrical and Computer Engineering |volume=10 |isbn=9789810217143 |accessdate=2013-03-17}}</ref>
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| For air dielectric capacitors the breakdown field strength is of the order 2 to 5 MV/m; for [[mica]] the breakdown is 100 to 300 MV/m, for oil 15 to 25 MV/m, and can be much less when other materials are used for the dielectric.<ref>{{cite book |title=Wiley Survey of Instrumentation and Measurement |url=http://books.google.com/books?id=Wr6l42rEizUC |last=Dyer |first=Stephen A. |year=2004 |publisher=John Wiley & Sons |isbn=9780471221654 |page=397 |accessdate=2013-03-17}}</ref> The dielectric is used in very thin layers and so absolute breakdown voltage of capacitors is limited. Typical ratings for capacitors used for general [[electronics]] applications range from a few volts to 1 kV. As the voltage increases, the dielectric must be thicker, making high-voltage capacitors larger per capacitance than those rated for lower voltages. The breakdown voltage is critically affected by factors such as the geometry of the capacitor conductive parts; sharp edges or points increase the electric field strength at that point and can lead to a local breakdown. Once this starts to happen, the breakdown quickly tracks through the dielectric until it reaches the opposite plate, leaving carbon behind causing a short circuit.<ref>{{cite book |title=Practical Electronics for Inventors |edition=2nd |url=http://books.google.com/books?id=C9pL3iL6eSMC |last=Scherz |first=Paul |year=2006 |publisher=McGraw Hill Professional |page=100 |isbn=9780071776448 |accessdate=2013-03-17}}</ref>
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| The usual breakdown route is that the field strength becomes large enough to pull electrons in the dielectric from their atoms thus causing conduction. Other scenarios are possible, such as impurities in the dielectric, and, if the dielectric is of a crystalline nature, imperfections in the crystal structure can result in an [[avalanche breakdown]] as seen in semi-conductor devices. Breakdown voltage is also affected by pressure, humidity and temperature.<ref>{{cite book |title=Electrical Circuit Theory and Technology |url=http://books.google.com/books?id=Q9zpWdgQeM4C |last=Bird |first=John |year=2007 |publisher=Routledge |page=501 |isbn=9780750681391 |accessdate=2013-03-17}}</ref>
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| ===Equivalent circuit===
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| [[File:Capacitor equivalent circuits.svg|thumb|Two different circuit models of a real capacitor]]
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| An ideal capacitor only stores and releases electrical energy, without dissipating any. In reality, all capacitors have imperfections within the capacitor's material that create resistance. This is specified as the ''[[equivalent series resistance]]'' or '''ESR''' of a component. This adds a real component to the impedance:
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| :<math>R_\text{C}= Z + R_\text{ESR} = \frac{1}{j\omega C} + R_\text{ESR}</math>
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| As frequency approaches infinity, the capacitive impedance (or reactance) approaches zero and the ESR becomes significant. As the reactance becomes negligible, power dissipation approaches ''P''<sub>RMS</sub> = ''V''<sub>RMS</sub>² /''R''<sub>ESR</sub>.
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| Similarly to ESR, the capacitor's leads add ''[[equivalent series inductance]]'' or '''ESL''' to the component. This is usually significant only at relatively high frequencies. As inductive reactance is positive and increases with frequency, above a certain frequency capacitance will be canceled by inductance. High-frequency engineering involves accounting for the inductance of all connections and components.
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| If the conductors are separated by a material with a small conductivity rather than a perfect dielectric, then a small leakage current flows directly between them. The capacitor therefore has a finite parallel resistance,<ref name="Ulaby_p169" /> and slowly discharges over time (time may vary greatly depending on the capacitor material and quality).
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| ===Q factor===
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| The [[Q factor|quality factor]] (or ''Q'') of a capacitor is the ratio of its reactance to its resistance at a given frequency, and is a measure of its efficiency. The higher the Q factor of the capacitor, the closer it approaches the behavior of an ideal, lossless, capacitor.
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| The Q factor of a capacitor can be found through the following formula:
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| :<math>Q = \frac{X_C}{R_C}=\frac{1}{\omega C R_C}</math>
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| Where:
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| * <math>\omega</math> is frequency in radians per second,
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| * <math>C</math> is the capacitance,
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| * <math>X_C</math> is the [[Electrical reactance#Capacitive reactance|capacitive reactance]], and
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| * <math>R_C</math> is the series resistance of the capacitor.
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| ===Ripple current===
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| Ripple current is the AC component of an applied source (often a [[switched-mode power supply]]) whose frequency may be constant or varying. Ripple current causes heat to be generated within the capacitor due to the dielectric losses caused by the changing field strength together with the current flow across the slightly resistive supply lines or the electrolyte in the capacitor. The equivalent series resistance (ESR) is the amount of internal series resistance one would add to a perfect capacitor to model this.
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| Some [[types of capacitor]]s, primarily [[tantalum]] and [[aluminum]] [[electrolytic capacitor]]s, as well as some [[film capacitor]]s have a specified rating value for maximum ripple current.
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| * Tantalum electrolytic capacitors with solid manganese dioxide electrolyte are limited by ripple current and generally have the highest ESR ratings in the capacitor family. Exceeding their ripple limits can lead to shorts and burning parts.
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| * Aluminium electrolytic capacitors, the most common type of electrolytic, suffer a shortening of life expectancy at higher ripple currents. If ripple current exceeds the rated value of the capacitor, it tends to result in explosive failure.
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| * [[Ceramic capacitor]]s generally have no ripple current limitation and have some of the lowest ESR ratings.
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| * [[Film capacitor]]s have very low ESR ratings but exceeding rated ripple current may cause degradation failures.
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| ===Capacitance instability===
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| The capacitance of certain capacitors decreases as the component ages. In [[ceramic capacitor]]s, this is caused by degradation of the dielectric. The type of dielectric, ambient operating and storage temperatures are the most significant aging factors, while the operating voltage has a smaller effect. The aging process may be reversed by heating the component above the [[Curie point]]. Aging is fastest near the beginning of life of the component, and the device stabilizes over time.<ref>{{cite web |url=http://www.johansondielectrics.com/technicalnotes/age |title=Ceramic Capacitor Aging Made Simple |publisher=Johanson Dielectrics |date=2012-05-21 |accessdate=2013-03-17}}</ref> Electrolytic capacitors age as the [[Electrolytic capacitor#Electrical behavior of electrolytics|electrolyte evaporates]]. In contrast with ceramic capacitors, this occurs towards the end of life of the component.
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| Temperature dependence of capacitance is usually expressed in parts per million (ppm) per °C. It can usually be taken as a broadly linear function but can be noticeably non-linear at the temperature extremes. The temperature coefficient can be either positive or negative, sometimes even amongst different samples of the same type. In other words, the spread in the range of temperature coefficients can encompass zero. See the data sheet in the leakage current section above for an example.
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| Capacitors, especially ceramic capacitors, and older designs such as paper capacitors, can absorb sound waves resulting in a [[microphonic]] effect. Vibration moves the plates, causing the capacitance to vary, in turn inducing AC current. Some dielectrics also generate [[piezoelectricity]]. The resulting interference is especially problematic in audio applications, potentially causing feedback or unintended recording. In the reverse microphonic effect, the varying electric field between the capacitor plates exerts a physical force, moving them as a speaker. This can generate audible sound, but drains energy and stresses the dielectric and the electrolyte, if any.
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| ===Current and voltage reversal===
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| Current reversal occurs when the current changes direction. Voltage reversal is the change of polarity in a circuit. Reversal is generally described as the percentage of the maximum rated voltage that reverses polarity. In DC circuits, this will usually be less than 100% (often in the range of 0 to 90%), whereas AC circuits experience 100% reversal.
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| In DC circuits and pulsed circuits, current and voltage reversal are affected by the [[damping]] of the system. Voltage reversal is encountered in [[RLC circuits]] that are [[dampening#Under-damping (0 ≤ ζ < 1)|under-damped]]. The current and voltage reverse direction, forming a [[harmonic oscillator]] between the [[inductance]] and capacitance. The current and voltage will tend to oscillate and may reverse direction several times, with each peak being lower than the previous, until the system reaches an equilibrium. This is often referred to as [[ringing (signal)|ringing]]. In comparison, [[damping#Critical damping (ζ = 1)|critically damped]] or [[Damping#Over-damping (ζ > 1)|over-damped]] systems usually do not experience a voltage reversal. Reversal is also encountered in AC circuits, where the peak current will be equal in each direction.
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| For maximum life, capacitors usually need to be able to handle the maximum amount of reversal that a system will experience. An AC circuit will experience 100% voltage reversal, while under-damped DC circuits will experience less than 100%. Reversal creates excess electric fields in the dielectric, causes excess heating of both the dielectric and the conductors, and can dramatically shorten the life expectancy of the capacitor. Reversal ratings will often affect the design considerations for the capacitor, from the choice of dielectric materials and voltage ratings to the types of internal connections used.<ref>{{cite web |url=http://www.ga-esi.com/support/ep/tech-bulletins/voltage-reversal.pdf |title=The Effect of Reversal on Capacitor Life |publisher=Sorrento Electronics |work=Engineering Bulletin 96-004 |date=November 2003 |format=PDF |accessdate=2013-03-17}}</ref>
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| ===Dielectric absorption===
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| Capacitors made with some types of dielectric material show "[[dielectric absorption]]" or "soakage". On discharging a capacitor and disconnecting it, after a short time it may develop a voltage due to hysteresis in the dielectric. This effect can be objectionable in applications such as precision [[sample and hold]] circuits.
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| ===Leakage===
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| Leakage is equivalent to a resistor in parallel with the capacitor. Constant exposure to heat can cause dielectric breakdown and excessive leakage, a problem often seen in older vacuum tube circuits, particularly where oiled paper and foil capacitors were used. In many vacuum tube circuits, interstage coupling capacitors are used to conduct a varying signal from the plate of one tube to the grid circuit of the next stage. A leaky capacitor can cause the grid circuit voltage to be raised from its normal bias setting, causing excessive current or signal distortion in the downstream tube. In power amplifiers this can cause the plates to glow red, or current limiting resistors to overheat, even fail. Similar considerations apply to component fabricated solid-state (transistor) amplifiers, but owing to lower heat production and the use of modern polyester dielectric barriers this once-common problem has become relatively rare.
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| ===Electrolytic failure from disuse===
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| [[Electrolytic capacitor]]s are ''conditioned'' when manufactured by applying a voltage sufficient to initiate the proper internal chemical state. This state is maintained by regular use of the equipment. If a system using electrolytic capacitors is unused for a long period of time it can lose its conditioning, and will generally fail with a short circuit when next operated, permanently damaging the capacitor. To prevent this in tube equipment, the voltage can be slowly brought up using a variable transformer (variac) on the mains, over a twenty or thirty minute interval. Transistor equipment is more problematic as such equipment ''may'' be sensitive to low voltage ("brownout") conditions, with excessive currents due to improper bias in some circuits.{{citation needed|date=November 2012}}
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| ==Capacitor types==
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| {{Main|Types of capacitor}}
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| Practical capacitors are available commercially in many different forms. The type of internal dielectric, the structure of the plates and the device packaging all strongly affect the characteristics of the capacitor, and its applications.
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| Values available range from very low (picofarad range; while arbitrarily low values are in principle possible, stray (parasitic) capacitance in any circuit is the limiting factor) to about 5 kF [[Electric double-layer capacitor|supercapacitors]].
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| Above approximately 1 microfarad electrolytic capacitors are usually used because of their small size and low cost compared with other technologies, unless their relatively poor stability, life and polarised nature make them unsuitable. Very high capacity supercapacitors use a porous carbon-based electrode material.
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| ===Dielectric materials===
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| [[File:Condensators.JPG|thumb|Capacitor materials. From left: multilayer ceramic, ceramic disc, multilayer polyester film, tubular ceramic, polystyrene, metalized polyester film, aluminum electrolytic. Major scale divisions are in centimetres.]]
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| Most types of capacitor include a dielectric spacer, which increases their capacitance. These dielectrics are most often insulators. However, low capacitance devices are available with a vacuum between their plates, which allows extremely high voltage operation and low losses. [[Variable capacitor]]s with their plates open to the atmosphere were commonly used in radio tuning circuits. Later designs use polymer foil dielectric between the moving and stationary plates, with no significant air space between them.
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| In order to maximise the charge that a capacitor can hold, the dielectric material needs to have as high a [[permittivity]] as possible, while also having as high a [[breakdown voltage]] as possible.
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| 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 capacitor]]s. Plastics offer better stability and aging performance, which makes them useful in timer circuits, although they may be limited to low [[operating temperature]]s 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 [[EIA Class 1 dielectric|class 1 dielectrics]], which have predictable variation of capacitance with temperature or [[EIA Class 2 dielectric|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.
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| Electrolytic capacitors and [[supercapacitor]]s are used to store small and larger amounts of energy, respectively, ceramic capacitors are often used in [[LC circuit|resonator]]s, and [[parasitic capacitance]] occurs in circuits wherever the simple conductor-insulator-conductor structure is formed unintentionally by the configuration of the circuit layout.
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| Electrolytic capacitors use an [[aluminum]] or [[tantalum]] plate with an oxide dielectric layer. The second electrode is a liquid [[electrolyte]], connected to the circuit by another foil plate. 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. [[Capacitor plague|Poor quality capacitors]] may leak electrolyte, which is harmful to printed circuit boards. 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. Electrolytic capacitors will self-degrade if unused for a period (around a year), and when full power is applied may short circuit, permanently damaging the capacitor and usually blowing a fuse or causing failure of rectifier diodes (for instance, in older equipment, arcing in rectifier tubes). They can be restored before use (and damage) by gradually applying the operating voltage, often done on antique [[vacuum tube]] equipment over a period of 30 minutes by using a variable transformer to supply AC power. Unfortunately, the use of this technique may be less satisfactory for some solid state equipment, which may be damaged by operation below its normal power range, requiring that the power supply first be isolated from the consuming circuits. Such remedies may not be applicable to modern high-frequency power supplies as these produce full output voltage even with reduced input.
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| Tantalum capacitors offer better frequency and temperature characteristics than aluminum, but higher [[dielectric absorption]] and leakage.<ref>{{cite web |url=http://www.analog.com/library/analogDialogue/Anniversary/21.html |title=Ask The Applications Engineer – 21 |last=Guinta |first=Steve |publisher=Analog Devices |accessdate=2013-03-17}}</ref>
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| '''[[Polymer capacitor]]s''' (OS-CON, OC-CON, KO, AO) use solid conductive polymer (or polymerized organic semiconductor) as electrolyte and offer longer life and lower [[equivalent series resistance|ESR]] at higher cost than standard electrolytic capacitors.
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| A [[Feedthrough]] is a component that, while not serving as its main use, has capacitance and is used to conduct signals through a circuit board.
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| Several other types of capacitor are available for specialist applications. [[Supercapacitor]]s store large amounts of energy. Supercapacitors made from carbon [[aerogel]], carbon nanotubes, or highly porous electrode materials, offer extremely high capacitance (up to 5 kF {{As of|2010|lc=on}}) and can be used in some applications instead of [[rechargeable battery|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 are designed with [[direct current]] breakdown voltages of at least five times the maximum AC voltage.
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| ===Structure===
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| [[File:Photo-SMDcapacitors.jpg|thumb|left|Capacitor packages: [[Surface-mount technology|SMD]] ceramic at top left; SMD tantalum at bottom left; [[through-hole]] tantalum at top right; through-hole electrolytic at bottom right. Major scale divisions are cm.]]
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| The arrangement of plates and dielectric has many variations depending on the desired ratings of the capacitor. For small values of capacitance (microfarads and less), ceramic disks use metallic coatings, with wire leads bonded to the coating. Larger values can be made by multiple stacks of plates and disks. Larger value capacitors usually use a metal foil or metal film layer deposited on the surface of a dielectric film to make the plates, and a dielectric film of impregnated [[Electrical insulation paper|paper]] or plastic{{spaced ndash}}these are rolled up to save space. To reduce the series resistance and inductance for long plates, the plates and dielectric are staggered so that connection is made at the common edge of the rolled-up plates, not at the ends of the foil or metalized film strips that comprise the plates.
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| The assembly is encased to prevent moisture entering the dielectric{{spaced ndash}}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.
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| [[File:Axial electrolytic capacitors.jpg|thumb|right|Several axial-lead [[electrolytic capacitor]]s]]Capacitors may have their connecting leads arranged in many configurations, for example axially or radially. "Axial" means that the leads are on a common axis, typically the axis of the capacitor's cylindrical body{{spaced ndash}}the leads extend from opposite ends. Radial leads might more accurately be referred to as tandem; they are rarely actually aligned along radii of the body's circle, so the term is inexact, although universal. The leads (until bent) are usually in planes parallel to that of the flat body of the capacitor, and extend in the same direction; they are often parallel as manufactured.
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| Small, cheap discoidal [[ceramic capacitor]]s 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.
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| 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 [[trimmer (electronics)|screw]]. Electrical control of capacitance is achievable with [[varactor]]s (or varicaps), which are [[reverse-biased]] [[semiconductor diode]]s whose depletion region width varies with applied voltage. They are used in [[Phase locked loop|phase-locked loops]], amongst other applications.
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| ==Capacitor markings==
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| Most capacitors have numbers printed on their bodies to indicate their electrical characteristics. Larger capacitors like electrolytics usually display the actual capacitance together with the unit (for example, '''220 μF'''). Smaller capacitors like ceramics, however, use a shorthand consisting of three numbers and a letter, where the numbers show the capacitance in [[picofarad|pF]] (calculated as XY × 10<sup>Z</sup> for the numbers XYZ) and the letter indicates the tolerance (J, K or M for ±5%, ±10% and ±20% respectively).
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| Additionally, the capacitor may show its working voltage, temperature and other relevant characteristics.
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| ===Example===
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| A capacitor with the text '''473K 330V''' on its body has a capacitance of 47 × 10<sup>3</sup> pF = 47 nF (±10%) with a working voltage of 330 V. The working voltage of a capacitor is the highest voltage that can be applied across it without undue risk of breaking down the dielectric layer.
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| ==Applications==
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| {{Main|Applications of capacitors}}
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| [[File:Mylar-film oil-filled low-inductance capacitor 6.5 MFD @ 5000 VDC.jpg|right|thumb|This mylar-film, oil-filled capacitor has very low inductance and low resistance, to provide the high-power (70 megawatt) and high speed (1.2 microsecond) discharge needed to operate a [[dye laser]].]]
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| ===Energy storage===
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| A capacitor can store electric energy when disconnected from its charging circuit, so it can be used like a temporary [[Battery (electricity)|battery]], or like other types of [[rechargeable energy storage system]].<ref>Miller, Charles. ''[http://books.google.com/books?id=RSsJAAAAQBAJ&pg=PA445 Illustrated Guide to the National Electrical Code]'', p. 445 (Cengage Learning 2011).</ref> Capacitors are commonly used in electronic devices to maintain power supply while batteries are being changed. (This prevents loss of information in volatile memory.)
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| Conventional capacitors provide less than 360 [[joule]]s per kilogram of [[energy density]], whereas a conventional [[alkaline battery]] has a density of 590 kJ/kg.
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| In [[car audio]] systems, large capacitors store energy for the [[amplifier]] to use on demand. Also for a [[flash tube]] a capacitor is used to hold the [[high voltage]].
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| ===Pulsed power and weapons===
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| Groups of large, specially constructed, low-inductance high-voltage capacitors (''capacitor banks'') are used to supply huge pulses of current for many [[pulsed power]] applications. These include [[electromagnetic forming]], [[Marx generator]]s, pulsed [[laser]]s (especially [[TEA laser]]s), [[pulse forming network]]s, [[radar]], [[Z machine|fusion research]], and [[particle accelerator]]s.
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| Large capacitor banks (reservoir) are used as energy sources for the [[exploding-bridgewire detonator]]s or [[slapper detonator]]s in [[nuclear weapon]]s and other specialty weapons. Experimental work is under way using banks of capacitors as power sources for [[Electromagnetism|electromagnetic]] [[Vehicle armour|armour]] and electromagnetic [[railgun]]s and [[coilgun]]s.
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| ===Power conditioning===
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| [[File:Capacitor.jpg|thumb|A 10 [[millifarad]] capacitor in an amplifier power supply]]
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| [[Reservoir capacitor]]s are used in [[Power supply|power supplies]] where they smooth the output of a full or half wave [[rectifier]]. They can also be used in [[charge pump]] circuits as the energy storage element in the generation of higher voltages than the input voltage.
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| 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 batteries|lead-acid]] [[car battery]].
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| ====Power factor correction====
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| [[File:Condensor bank 150kV - 75MVAR.jpg|thumb|left|upright|A high-voltage capacitor bank used for power factor correction on a power transmission system.]]
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| In electric power distribution, capacitors are used for [[power factor correction]]. Such capacitors often come as three capacitors connected as a [[three phase]] [[Electrical load|load]]. Usually, the values of these capacitors are given not in farads but rather as a [[reactive power]] in volt-amperes reactive (var). The purpose is to counteract inductive loading from devices like [[Induction motor|electric motors]] and [[transmission line]]s to make the load appear to be mostly resistive. Individual motor or lamp loads may have capacitors for power factor correction, or larger sets of capacitors (usually with automatic switching devices) may be installed at a load center within a building or in a large utility [[electrical substation|substation]].
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| ===Suppression and coupling===
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| ====Signal coupling====
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| {{Main|capacitive coupling}}
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| [[File:Polyester film capacitor.jpg|thumb|right|Polyester [[film capacitor]]s are frequently used as coupling capacitors.]]
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| Because capacitors pass AC but block DC [[Signal (information theory)|signals]] (when charged up to the applied dc voltage), they are often used to separate the AC and DC components of a signal. This method is known as ''AC coupling'' or "capacitive coupling". Here, a large value of capacitance, whose value need not be accurately controlled, but whose [[Reactance (electronics)|reactance]] is small at the signal frequency, is employed.
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| ====Decoupling====
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| {{Main|decoupling capacitor}}
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| A [[decoupling capacitor]] is a capacitor used to protect one part of a circuit from the effect of another, for instance to suppress noise or transients. Noise caused by other circuit elements is shunted through the capacitor, reducing the effect they have on the rest of the circuit. It is most commonly used between the power supply and ground.
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| An alternative name is ''bypass capacitor'' as it is used to bypass the power supply or other high impedance component of a circuit.
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| ====Noise filters and snubbers====
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| When an inductive circuit is opened, the current through the inductance collapses quickly, creating a large voltage across the open circuit of the switch or relay. If the inductance is large enough, the energy will generate a spark, causing the contact points to oxidize, deteriorate, or sometimes weld together, or destroying a solid-state switch. A [[snubber]] capacitor across the newly opened circuit creates a path for this impulse to bypass the contact points, thereby preserving their life; these were commonly found in [[contact breaker]] [[ignition system]]s, for instance. Similarly, in smaller scale circuits, the spark may not be enough to damage the switch but will still [[Spark-gap transmitter|radiate]] undesirable [[radio frequency interference]] (RFI), which a [[filter capacitor]] absorbs. Snubber capacitors are usually employed with a low-value resistor in series, to dissipate energy and minimize RFI. Such resistor-capacitor combinations are available in a single package.
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| 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.
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| 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]]).
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| ===Motor starters===
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| {{Main|motor capacitor}}
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| In single phase [[Squirrel-cage rotor|squirrel cage]] motors, the primary winding within the motor housing is not capable of starting a rotational motion on the rotor, but is capable of sustaining one. To start the motor, a secondary "start" winding has a series non-polarized ''[[starting capacitor]]'' to introduce a lead in the sinusoidal current. When the secondary (start) winding is placed at an angle with respect to the primary (run) winding, a rotating electric field is created. The force of the rotational field is not constant, but is sufficient to start the rotor spinning. When the rotor comes close to operating speed, a centrifugal switch (or current-sensitive relay in series with the main winding) disconnects the capacitor. The start capacitor is typically mounted to the side of the motor housing. These are called capacitor-start motors, that have relatively high starting torque. Typically they can have up-to four times as much starting torque than a split-phase motor and are used on applications such as compressors, pressure washers and any small device requiring high starting torques.
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| Capacitor-run induction motors have a permanently connected phase-shifting capacitor in series with a second winding. The motor is much like a two-phase induction motor.
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| Motor-starting capacitors are typically non-polarized electrolytic types, while running capacitors are conventional paper or plastic film dielectric types.
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| ===Signal processing===
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| The energy stored in a capacitor can be used to represent [[information]], either in binary form, as in [[DRAM]]s, or in analogue form, as in [[analog sampled filter]]s and [[Charge-coupled device|CCD]]s. Capacitors can be used in [[analog circuit]]s as components of integrators or more complex filters and in [[negative feedback]] loop stabilization. Signal processing circuits also use capacitors to [[integral|integrate]] a current signal.
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| ====Tuned circuits====
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| Capacitors and inductors are applied together in [[RLC circuit|tuned circuits]] to select information in particular frequency bands. For example, [[radio receiver]]s rely on variable capacitors to tune the station frequency. Speakers use passive analog [[Audio crossover|crossovers]], and analog equalizers use capacitors to select different audio bands.
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| The [[resonant frequency]] ''f'' of a tuned circuit is a function of the inductance (''L'') and capacitance (''C'') in series, and is given by:
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| :<math>f = \frac{1}{2 \pi \sqrt{LC}}</math>
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| where ''L'' is in [[henry (unit)|henries]] and ''C'' is in farads.
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| ===Sensing===
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| : {{main|capacitive sensing}}
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| : {{main|Capacitive displacement sensor}}
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| Most capacitors are designed to maintain a fixed physical structure. However, various factors can change the structure of the capacitor, and the resulting change in capacitance can be used to [[Sensor|sense]] those factors.
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| Changing the dielectric:<br />
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| :The effects of varying the characteristics of the '''dielectric''' can be used for sensing purposes. 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 [[airplane]]s; as the fuel covers more of a pair of plates, the circuit capacitance increases.
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| Changing the distance between the plates:<br />
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| :Capacitors with a flexible plate can be used to measure strain or pressure. Industrial pressure transmitters used for [[process control]] use pressure-sensing diaphragms, which form a capacitor plate of an oscillator circuit. Capacitors are used as the [[sensor]] in [[condenser microphone]]s, where one plate is moved by air pressure, relative to the fixed position of the other plate. Some [[accelerometer]]s 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, in tilt sensors, or to detect free fall, as sensors triggering [[airbag]] deployment, and in many other applications. Some [[Fingerprint authentication#Fingerprint sensors|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.
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| Changing the effective area of the plates:<br />
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| :Capacitive [[touch switch]]es are now used on many consumer electronic products.
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| ==Hazards and safety==
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| Capacitors may retain a charge long after power is removed from a circuit; this charge can cause dangerous or even potentially fatal [[Electric shock|shocks]] or damage 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, for instance using a [[Brinkley stick]]. 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 [[short circuit|shorted]], as protection from potentially dangerous voltages due to [[Permittivity#Lossy medium|dielectric absorption]].
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| Some old, large oil-filled paper or plastic film capacitors contain [[polychlorinated biphenyl]]s (PCBs). It is known that waste PCBs can leak into [[groundwater]] under [[landfill]]s. Capacitors containing PCB were labelled as containing "Askarel" and several other trade names. PCB-filled paper capacitors are found in very old (pre-1975) [[fluorescent lamp]] ballasts, and other applications.
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| Capacitors may [[catastrophic failure|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 the dielectric fluid, resulting in case bulging, rupture, or even an [[explosion]]. Capacitors used in [[Radio frequency|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.
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| High-voltage capacitors can benefit from a [[pre-charge]] to limit in-rush currents at power-up of high voltage direct current (HVDC) circuits. This will extend the life of the component and may mitigate high-voltage hazards.
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| <gallery widths="180px" heights="120px" perrow="3">
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| File:Defekte Kondensatoren.jpg|Swollen caps of electrolytic capacitors – special design of semi-cut caps prevents capacitors from bursting
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| File:High-energy capacitor from a defibrillator 42 MFD @ 5000 VDC.jpg|This high-energy capacitor from a [[defibrillator]] can deliver over 500 joules of energy. A resistor is connected between the terminals for safety, to allow the stored energy to be released.
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| File:Exploded Electrolytic Capacitor.jpg|Catastrophic failure
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| </gallery>
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| ==See also==
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| {{Portal|Electronics}}
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| {{Columns-list|2|
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| *[[Capacitance meter]]
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| *[[Circuit design]]
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| *[[Electric displacement field]]
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| *[[Electroluminescence]]
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| *[[Electronic oscillator]]
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| *[[Vacuum variable capacitor]]
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| }}
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| ==References==
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| {{Reflist|35em}}
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| ==Bibliography==
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| *{{cite book |title=Introduction to Electric Circuits |url=http://books.google.com/books?id=l-weAQAAIAAJ |last=Dorf |first=Richard C. |last2=Svoboda |first2=James A. |edition=5th |publisher=John Wiley & Sons |location=New York |year=2001 |isbn=9780471386896}}
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| *Philosophical Transactions of the Royal Society LXXII, Appendix 8, 1782 (Volta coins the word ''condenser'')
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| *{{cite book |title=Fundamentals of Applied Electromagnetics |url=http://books.google.com/books?id=a_C8QgAACAAJ |last=Ulaby |first=Fawwaz Tayssir |publisher=Prentice Hall |year=1999 |location=Upper Saddle River, New Jersey |isbn=9780130115546}}
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| *{{cite journal |title=Super Charged: A Tiny South Korean Company is Out to Make Capacitors Powerful enough to Propel the Next Generation of Hybrid-Electric Cars |last=Zorpette |first=Glenn |year=2005 |journal=[[IEEE Spectrum]] |volume=42 |issue=1 |pages=32 |edition=North American |doi=10.1109/MSPEC.2005.1377872}}
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| ==External links==
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| {{Wikibooks
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| |1=Electronics
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| |2=Capacitors
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| |3=Capacitors
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| }}
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| {{Wiktionary}}
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| {{Commons category|Capacitors}}
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| *{{cite web |url=http://www.acmi.net.au/AIC/VON_KLEIST_BIO.html |title=Adventures in Cybersound – Ewald Christian von Kleist |last=Currier |first=Dean P. |year=2000 |archiveurl=http://web.archive.org/web/20080625014024/http://www.acmi.net.au/AIC/VON_KLEIST_BIO.html |archivedate=2008-06-25}}
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| *{{cite web |url=http://www.sparkmuseum.com/BOOK_LEYDEN.HTM |title=The First Condenser – A Beer Glass |publisher=SparkMuseum}}
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| *[http://electronics.howstuffworks.com/capacitor.htm/printable Howstuffworks.com: How Capacitors Work]
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| *[http://my.execpc.com/~endlr/ CapSite 2009: Introduction to Capacitors]
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| *[http://www.sentex.ca/~mec1995/gadgets/caps/caps.html Capacitor Tutorial] – Includes how to read capacitor temperature codes
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| * [http://www.robotplatform.com/electronics/capacitor/capacitor.html Introduction to Capacitor and Capacitor codes]
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| * [http://www.capacitorlab.com/low-esr-capacitor-manufacturers/ Low ESR Capacitor Manufacturers]
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| * [http://freecircuits.org/2012/01/capacitors-basics-working/ How Capacitor Works – Capacitor Markings and Color Codes]
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| {{Electronic component}}
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| [[Category:Capacitors| ]]
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