Capacitor Miniaturizing 1970-2005
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A capacitor is a device that stores
electrical energy Electrical energy is energy related to forces on electrically charged particles and the movement of electrically charged particles (often electrons in wires, but not always). This energy is supplied by the combination of electric current and electr ...
in an
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
by virtue of accumulating
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
s on two close surfaces insulated from each other. It is a
passive Passive may refer to: * Passive voice, a grammatical voice common in many languages, see also Pseudopassive * Passive language, a language from which an interpreter works * Passivity (behavior), the condition of submitting to the influence of on ...
electronic component An electronic component is any basic discrete device or physical entity in an electronic system used to affect electrons or their associated fields. Electronic components are mostly industrial products, available in a singular form and are not ...
with two terminals. The effect of a capacitor is known as
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
. While some capacitance exists between any two electrical conductors in proximity in a circuit, a capacitor is a component designed to add capacitance to a circuit. The capacitor was originally known as the condenser, a term still encountered in a few compound names, such as the ''
condenser microphone A microphone, colloquially called a mic or mike (), is a transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, hearing aids, public address systems for concert halls and public ...
''. The physical form and construction of practical capacitors vary widely and many
types of capacitor Capacitors are manufactured in many styles, forms, dimensions, and from a large variety of materials. They all contain at least two electrical conductors, called ''plates'', separated by an insulator (electricity), insulating layer (''dielectric ...
are in common use. Most capacitors contain at least two
electrical conductor In physics and electrical engineering, a conductor is an object or type of material that allows the flow of charge (electric current) in one or more directions. Materials made of metal are common electrical conductors. Electric current is gener ...
s often in the form of metallic plates or surfaces separated by a
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
medium. A conductor may be a foil, thin film, sintered bead of metal, or an
electrolyte An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon dis ...
. The nonconducting dielectric acts to increase the capacitor's charge capacity. Materials commonly used as dielectrics include
glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
,
ceramic A ceramic is any of the various hard, brittle, heat-resistant and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcelain ...
,
plastic film Plastic film is a thin continuous polymeric material. Thicker plastic material is often called a "sheet". These thin plastic membranes are used to separate areas or volumes, to hold items, to act as barriers, or as printable surfaces. Plas ...
,
paper Paper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, rags, grasses or other vegetable sources in water, draining the water through fine mesh leaving the fibre evenly distributed ...
,
mica Micas ( ) are a group of silicate minerals whose outstanding physical characteristic is that individual mica crystals can easily be split into extremely thin elastic plates. This characteristic is described as perfect basal cleavage. Mica is ...
, air, and oxide layers. Capacitors are widely used as parts of
electrical circuit An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, ...
s in many common electrical devices. Unlike a
resistor A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active el ...
, an ideal capacitor does not dissipate energy, although real-life capacitors do dissipate a small amount (see Non-ideal behavior). When an
electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...
difference (a
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
) is applied across the terminals of a capacitor, for example when a capacitor is connected across a battery, an
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
develops across the dielectric, causing a net positive
charge Charge or charged may refer to: Arts, entertainment, and media Films * ''Charge, Zero Emissions/Maximum Speed'', a 2011 documentary Music * ''Charge'' (David Ford album) * ''Charge'' (Machel Montano album) * ''Charge!!'', an album by The Aqua ...
to collect on one plate and net negative charge to collect on the other plate. No current actually flows through the dielectric. However, there is a flow of charge through the source circuit. If the condition is maintained sufficiently long, the current through the source circuit ceases. If a time-varying voltage is applied across the leads of the capacitor, the source experiences an ongoing current due to the charging and discharging cycles of the capacitor. The earliest forms of capacitors were created in the 1740s, when European experimenters discovered that electric charge could be stored in water-filled glass jars that came to be known as
Leyden jar A Leyden jar (or Leiden jar, or archaically, sometimes Kleistian jar) is an electrical component that stores a high-voltage electric charge (from an external source) between electrical conductors on the inside and outside of a glass jar. It typi ...
s. Today, capacitors are widely used in
electronic circuit An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. It is a type of electrical ...
s for blocking
direct current Direct current (DC) is one-directional flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or even ...
while allowing
alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
to pass. In
analog filter Analogue filters are a basic building block of signal processing much used in electronics. Amongst their many applications are the separation of an audio signal before application to bass, mid-range, and tweeter loudspeakers; the combining and ...
networks, they smooth the output of
power supplies A power supply is an electrical device that supplies electric power to an electrical load. The main purpose of a power supply is to convert electric current from a source to the correct voltage, current, and frequency to power the load. As a res ...
. In resonant circuits they tune
radio Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmit ...
s to particular
frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
. In
electric power transmission Electric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation. The interconnected lines that facilitate this movement form a ''transmission network''. This is ...
systems, they stabilize voltage and power flow. The property of energy storage in capacitors was exploited as dynamic memory in early digital computers, and still is in modern
DRAM Dynamic random-access memory (dynamic RAM or DRAM) is a type of random-access semiconductor memory that stores each bit of data in a memory cell, usually consisting of a tiny capacitor and a transistor, both typically based on metal-oxid ...
.


History

In October 1745,
Ewald Georg von Kleist A member of the von Kleist family, Ewald was born in Wicewo (Wicewo) in Farther Pomerania. He studied jurisprudence at the University of Leipzig and the University of Leyden and may have started his interest in electricity at the latter universit ...
of
Pomerania Pomerania ( pl, Pomorze; german: Pommern; Kashubian: ''Pòmòrskô''; sv, Pommern) is a historical region on the southern shore of the Baltic Sea in Central Europe, split between Poland and Germany. The western part of Pomerania belongs to ...
, Germany, found that
charge Charge or charged may refer to: Arts, entertainment, and media Films * ''Charge, Zero Emissions/Maximum Speed'', a 2011 documentary Music * ''Charge'' (David Ford album) * ''Charge'' (Machel Montano album) * ''Charge!!'', an album by The Aqua ...
could be stored by connecting a high-voltage
electrostatic generator An electrostatic generator, or electrostatic machine, is an electrical generator that produces '' static electricity'', or electricity at high voltage and low continuous current. The knowledge of static electricity dates back to the earliest civi ...
by a wire to a volume of water in a hand-held glass jar. Von Kleist's hand and the water acted as conductors and the jar as a
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
(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 Pieter van Musschenbroek (14 March 1692 – 19 September 1761) was a Dutch scientist. He was a professor in Duisburg, Utrecht, and Leiden, where he held positions in mathematics, philosophy, medicine, and astronomy. He is credited with the inven ...
invented a similar capacitor, which was named the
Leyden jar A Leyden jar (or Leiden jar, or archaically, sometimes Kleistian jar) is an electrical component that stores a high-voltage electric charge (from an external source) between electrical conductors on the inside and outside of a glass jar. It typi ...
, after the
University of Leiden Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William, Prince of Orange, as a reward to the city of Le ...
where he worked. 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." Daniel Gralath was the first to combine several jars in parallel to increase the charge storage capacity.
Benjamin Franklin Benjamin Franklin ( April 17, 1790) was an American polymath who was active as a writer, scientist, inventor, statesman, diplomat, printer, publisher, and political philosopher. Encyclopædia Britannica, Wood, 2021 Among the leading inte ...
investigated the
Leyden jar A Leyden jar (or Leiden jar, or archaically, sometimes Kleistian jar) is an electrical component that stores a high-voltage electric charge (from an external source) between electrical conductors on the inside and outside of a glass jar. It typi ...
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", (denoting the increase of power with a row of similar units as in a battery of cannon), subsequently applied to clusters of electrochemical cells. 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. The earliest unit of capacitance was the
jar A jar is a rigid, cylindrical or slightly conical container, typically made of glass, ceramic, or plastic, with a wide mouth or opening that can be closed with a lid, screw cap, lug cap, cork stopper, roll-on cap, crimp-on cap, press-on c ...
, equivalent to about 1.11 nanofarads. 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 Wireless communication (or just wireless, when the context allows) is the transfer of information between two or more points without the use of an electrical conductor, optical fiber or other continuous guided medium for the transfer. The most ...
(
radio Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmit ...
) created a demand for standard capacitors, and the steady move to higher
frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
required capacitors with lower
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the ...
. More compact construction methods began to be used, such as a flexible dielectric sheet (like oiled paper) sandwiched between sheets of metal foil, rolled or folded into a small package. Early capacitors were known as ''condensers'', a term that is still occasionally used today, particularly in high power applications, such as automotive systems. The term was first used for this purpose by
Alessandro Volta Alessandro Giuseppe Antonio Anastasio Volta (, ; 18 February 1745 – 5 March 1827) was an Italian physicist, chemist and lay Catholic who was a pioneer of electricity and power who is credited as the inventor of the electric battery and the ...
in 1782, with reference to the device's ability to store a higher density of electric charge than was possible with an isolated conductor. The term became deprecated because of the ambiguous meaning of steam condenser, with ''capacitor'' becoming the recommended term in the UK from 1926, while the change occurred considerably later in the United States. In other countries, the term ''condensator'' has been in common use. Since the beginning of the study of
electricity Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...
, non-conductive materials like
glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
,
porcelain Porcelain () is a ceramic material made by heating substances, generally including materials such as kaolinite, in a kiln to temperatures between . The strength and translucence of porcelain, relative to other types of pottery, arises mainl ...
,
paper Paper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, rags, grasses or other vegetable sources in water, draining the water through fine mesh leaving the fibre evenly distributed ...
and
mica Micas ( ) are a group of silicate minerals whose outstanding physical characteristic is that individual mica crystals can easily be split into extremely thin elastic plates. This characteristic is described as perfect basal cleavage. Mica is ...
have been used as
insulators Insulator may refer to: * Insulator (electricity), a substance that resists electricity ** Pin insulator, a device that isolates a wire from a physical support such as a pin on a utility pole ** Strain insulator, a device that is designed to work ...
. Decades later, these materials were also well-suited for use as the dielectric for the first capacitors. Paper capacitors, made by sandwiching a strip of impregnated paper between strips of metal and rolling the result into a cylinder, were commonly used in the late 19th century; their manufacture started in 1876, and they were used from the early 20th century as
decoupling capacitor A decoupling capacitor is a capacitor used to decouple one part of an electrical network (circuit) from another. Noise caused by other circuit elements is shunted through the capacitor, reducing its effect on the rest of the circuit. For hig ...
s in
telephony Telephony ( ) is the field of technology involving the development, application, and deployment of telecommunication services for the purpose of electronic transmission of voice, fax, or data, between distant parties. The history of telephony is i ...
. Porcelain was used in the first
ceramic capacitor A ceramic capacitor is a fixed-value capacitor where the ceramic material acts as the dielectric. It is constructed of two or more alternating layers of ceramic and a metal layer acting as the electrodes. The composition of the ceramic material de ...
s. In the early years of Marconi's wireless transmitting apparatus, porcelain capacitors were used for high voltage and high frequency application in the
transmitter In electronics and telecommunications, a radio transmitter or just transmitter is an electronic device which produces radio waves with an antenna (radio), antenna. The transmitter itself generates a radio frequency alternating current, which i ...
s. On the receiver side, smaller mica capacitors were used for resonant circuits. Mica capacitors were invented in 1909 by William Dubilier. Prior to World War II, mica was the most common dielectric for capacitors in the United States. Charles Pollak (born
Karol Pollak Karol Franciszek Pollak (November 15, 1859 – December 17, 1928) was a Polish electrotechnician, inventor and businessman. Early life He was born in Sanok, Kingdom of Galicia and Lodomeria, part of the Austrian Empire . His father was Karol ...
), the inventor of the first
electrolytic capacitor An electrolytic capacitor is a polarized capacitor whose anode or positive plate is made of a metal that forms an insulating oxide layer through anodization. This oxide layer acts as the dielectric of the capacitor. A solid, liquid, or gel el ...
s, found out that the oxide layer on an aluminum anode remained stable in a neutral or alkaline
electrolyte An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon dis ...
, even when the power was switched off. In 1896 he was granted U.S. Patent No. 672,913 for an "Electric liquid capacitor with aluminum electrodes". Solid electrolyte
tantalum capacitor A tantalum electrolytic capacitor is an electrolytic capacitor, a passive component of electronic circuits. It consists of a pellet of porous tantalum metal as an anode, covered by an insulating oxide layer that forms the dielectric, surrounded ...
s were invented by
Bell Laboratories Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mult ...
in the early 1950s as a miniaturized and more reliable low-voltage support capacitor to complement their newly invented
transistor upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink). A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch e ...
. With the development of plastic materials by organic chemists during the
Second World War World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, the capacitor industry began to replace paper with thinner polymer films. One very early development in
film capacitor Film capacitors, plastic film capacitors, film dielectric capacitors, or polymer film capacitors, generically called film caps as well as power film capacitors, are electrical capacitors with an insulating plastic film as the dielectric, sometime ...
s was described in British Patent 587,953 in 1944. Electric double-layer capacitors (now
supercapacitor A supercapacitor (SC), also called an ultracapacitor, is a high-capacity capacitor, with a capacitance value much higher than other capacitors but with lower voltage limits. It bridges the gap between electrolytic capacitors and rechargeable ba ...
s) were invented in 1957 when H. Becker developed a "Low voltage electrolytic capacitor with porous carbon electrodes". He believed that the energy was stored as a charge in the carbon pores used in his capacitor as in the pores of the etched foils of electrolytic capacitors. Because the double layer mechanism was not known by him at the time, he wrote in the patent: "It is not known exactly what is taking place in the component if it is used for energy storage, but it leads to an extremely high capacity." The
metal–oxide–semiconductor The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...
capacitor (
MOS capacitor The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...
) originates from the
metal–oxide–semiconductor field-effect transistor The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...
(MOSFET) structure, where the MOS capacitor is flanked by two doped regions. The MOSFET structure was invented by
Mohamed M. Atalla Mohamed M. Atalla ( ar, محمد عطاالله; August 4, 1924 – December 30, 2009) was an Egyptian-American engineer, physicist, cryptographer, inventor and entrepreneur. He was a semiconductor pioneer who made important contributions to ...
and
Dawon Kahng Dawon Kahng ( ko, 강대원; May 4, 1931 – May 13, 1992) was a Korean-American electrical engineer and inventor, known for his work in solid-state electronics. He is best known for inventing the MOSFET (metal–oxide–semiconductor field-effe ...
at
Bell Labs Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mult ...
in 1959. The MOS capacitor was later widely adopted as a storage capacitor in
memory chip Semiconductor memory is a digital electronics, digital electronic semiconductor device used for digital data storage, such as computer memory. It typically refers to devices in which data is stored within metal–oxide–semiconductor (MOS) memo ...
s, and as the basic building block of the
charge-coupled device A charge-coupled device (CCD) is an integrated circuit containing an array of linked, or coupled, capacitors. Under the control of an external circuit, each capacitor can transfer its electric charge to a neighboring capacitor. CCD sensors are a ...
(CCD) in
image sensor An image sensor or imager is a sensor that detects and conveys information used to make an image. It does so by converting the variable attenuation of light waves (as they pass through or reflect off objects) into signals, small bursts of curr ...
technology. In dynamic
random-access memory Random-access memory (RAM; ) is a form of computer memory that can be read and changed in any order, typically used to store working Data (computing), data and machine code. A Random access, random-access memory device allows data items to b ...
(
DRAM Dynamic random-access memory (dynamic RAM or DRAM) is a type of random-access semiconductor memory that stores each bit of data in a memory cell, usually consisting of a tiny capacitor and a transistor, both typically based on metal-oxid ...
), each memory cell typically consists of a MOSFET and MOS capacitor.


Theory of operation


Overview

A capacitor consists of two conductors separated by a non-conductive region. The non-conductive region can either be a
vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
or an electrical insulator material known as a
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
. Examples of dielectric media are glass, air, paper, plastic, ceramic, and even a
semiconductor A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
depletion region In semiconductor physics, the depletion region, also called depletion layer, depletion zone, junction region, space charge region or space charge layer, is an insulating region within a conductive, doped semiconductor material where the mobile ...
chemically identical to the conductors. From
Coulomb's law Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...
a charge on one conductor will exert a force on the
charge carrier In physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes. The term is used ...
s within the other conductor, attracting opposite polarity charge and repelling like polarity charges, thus an opposite polarity charge will be induced on the surface of the other conductor. The conductors thus hold equal and opposite charges on their facing surfaces, and the dielectric develops an electric field. An ideal capacitor is characterized by a constant
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
''C'', in
farad The farad (symbol: F) is the unit of electrical capacitance, the ability of a body to store an electrical charge, in the International System of Units (SI). It is named after the English physicist Michael Faraday (1791–1867). In SI base unit ...
s in the SI system of units, defined as the ratio of the positive or negative charge ''Q'' on each conductor to the voltage ''V'' between them: C= \frac A capacitance of one
farad The farad (symbol: F) is the unit of electrical capacitance, the ability of a body to store an electrical charge, in the International System of Units (SI). It is named after the English physicist Michael Faraday (1791–1867). In SI base unit ...
(F) means that one
coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant current in 1 second and to elementary char ...
of charge on each conductor causes a voltage of one
volt The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827). Defi ...
across the device. 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 when the conductors are separated, yielding a larger capacitance. In practical devices, charge build-up sometimes affects the capacitor mechanically, causing its capacitance to vary. In this case, capacitance is defined in terms of incremental changes: C= \frac


Hydraulic analogy

In the
hydraulic analogy The electronic–hydraulic analogy (derisively referred to as the drain-pipe theory by Oliver Lodge) is the most widely used analogy for "electron fluid" in a metal conductor. Since electric current is invisible and the processes in play in ...
, 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 pressure differential is analogous to voltage, while the rate of flow is analogous to electric current: * ''The
current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...
alters the
charge Charge or charged may refer to: Arts, entertainment, and media Films * ''Charge, Zero Emissions/Maximum Speed'', a 2011 documentary Music * ''Charge'' (David Ford album) * ''Charge'' (Machel Montano album) * ''Charge!!'', an album by The Aqua ...
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. * ''The more a capacitor is charged, the larger its
voltage drop Voltage drop is the decrease of electrical potential along the path of a current flowing in an electrical circuit. Voltage drops in the internal resistance of the source, across conductors, across contacts, and across connectors are undesirable ...
'': as the membrane stretches, allowing more water to flow in from the high pressure side, the membrane "pushes back" against the charging current, increasing the pressure differential between the two sides. * ''Charge can flow "through" a capacitor even though no individual electron can get from one side to the other.'' As more water flows into the high pressure side, the expanding membrane pushes an equal quantity of water out of the low pressure side. The flow cannot continue in the same direction forever; the capacitor experiences
dielectric breakdown Electrical breakdown or dielectric breakdown is a process that occurs when an electrical insulating material, subjected to a high enough voltage, suddenly becomes an electrical conductor and electric current flows through it. All insulating mate ...
, and analogously the membrane will eventually break. * The ''
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
'' describes how much charge can be stored on one plate of a capacitor for a given voltage drop. The
elasticity Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the cl ...
of the membrane is analogous to capacitance. A very stretchy, flexible membrane will expand more with a given pressure differential, allowing a greater volume of water to flow into the high pressure side. This corresponds to a higher capacitance than a stiff membrane. * A charged capacitor stores
potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potentia ...
, analogously to a stretched membrane.


Circuit equivalence at short-time limit and long-time limit

In a circuit, a capacitor can behave differently at different time instants. However, it is usually easy to think about the short-time limit and long-time limit: * In the long-time limit, after the charging/discharging current has saturated the capacitor, no current would come into (or get out of) either side of the capacitor; Therefore, the long-time equivalence of capacitor is an open circuit. * In the short-time limit, if the capacitor starts with a certain voltage V, since the voltage drop on the capacitor is known at this instant, we can replace it with an ideal voltage source of voltage V. Specifically, if V=0 (capacitor is uncharged), the short-time equivalence of a capacitor is a short circuit.


Parallel-plate capacitor

The simplest model of a capacitor consists of two thin parallel conductive plates each with an area of A separated by a uniform gap of thickness d filled with a dielectric with
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
\varepsilon. It is assumed the gap d is much smaller than the dimensions of the plates. This model applies well to many practical capacitors which are constructed of metal sheets separated by a thin layer of insulating dielectric, since manufacturers try to keep the dielectric very uniform in thickness to avoid thin spots which can cause failure of the capacitor. Since the separation between the plates is uniform over the plate area, the electric field between the plates E is constant, and directed perpendicularly to the plate surface, except for an area near the edges of the plates where the field decreases because the electric field lines "bulge" out of the sides of the capacitor. This "fringing field" area is approximately the same width as the plate separation, d, and assuming d is small compared to the plate dimensions, it is small enough to be ignored. Therefore, if a charge of +Q is placed on one plate and -Q on the other plate (the situation for unevenly charged plates is discussed below), the charge on each plate will be spread evenly in a
surface charge Surface charge is a two-dimensional surface with non-zero electric charge. These electric charges are constrained on this 2-D surface, and surface charge density, measured in coulombs per square meter (C•m−2), is used to describe the charge di ...
layer of constant
charge density In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in co ...
\sigma = \pm Q/A coulombs per square meter, on the inside surface of each plate. From
Gauss's law In physics and electromagnetism, Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating the distribution of electric charge to the resulting electric field. In its integral form, it sta ...
the magnitude of the electric field between the plates is E = \sigma / \varepsilon. The voltage(difference) V between the plates is defined as the
line integral In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms ''path integral'', ''curve integral'', and ''curvilinear integral'' are also used; ''contour integral'' is used as well, alt ...
of the electric field over a line (in the z-direction) from one plate to another V= \int_0^d E(z)\,\mathrmz = Ed = \fracd = \frac The capacitance is defined as C = Q/V. Substituting V above into this equation Therefore, in a capacitor the highest capacitance is achieved with a high
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
dielectric material, large plate area, and small separation between the plates. Since the area A of the plates increases with the square of the linear dimensions and the separation d increases linearly, the capacitance scales with the linear dimension of a capacitor (C \varpropto L), or as the cube root of the volume. A parallel plate capacitor can only store a finite amount of energy before
dielectric breakdown Electrical breakdown or dielectric breakdown is a process that occurs when an electrical insulating material, subjected to a high enough voltage, suddenly becomes an electrical conductor and electric current flows through it. All insulating mate ...
occurs. The capacitor's dielectric material has a
dielectric strength In physics, the term dielectric strength has the following meanings: *for a pure electrically insulating material, the maximum electric field that the material can withstand under ideal conditions without undergoing electrical breakdown and becom ...
''U''d which sets the capacitor's breakdown voltage at . The maximum energy that the capacitor can store is therefore E = \frac CV^2 = \frac \frac \left(U_d d\right)^2 = \frac \varepsilon A d U_d^2 The maximum energy is a function of dielectric volume,
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
, and
dielectric strength In physics, the term dielectric strength has the following meanings: *for a pure electrically insulating material, the maximum electric field that the material can withstand under ideal conditions without undergoing electrical breakdown and becom ...
. Changing the plate area and the separation between the plates while maintaining the same volume causes no change of the maximum amount of energy that the capacitor can store, so long as the distance between plates remains much smaller than both the length and width of the plates. 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 increase the effective capacitance of the capacitor. This is sometimes called
parasitic capacitance Parasitic capacitance is an unavoidable and usually unwanted capacitance that exists between the parts of an electronic component or circuit simply because of their proximity to each other. When two electrical conductors at different voltages a ...
. For some simple capacitor geometries this additional capacitance term can be calculated analytically. It becomes negligibly small when the ratios of plate width to separation and length to separation are large. For unevenly charged plates: * If one plate is charged with Q_1 while the other is charged with Q_2, and if both plates are separated from other materials in the environment, then the inner surface of the first plate will have \frac, and the inner surface of the second plated will have -\frac charge. Therefore, the voltage V between the plates is V = \frac. Note that the outer surface of both plates will have \frac, but those charges don't affect the voltage between the plates. * If one plate is charged with Q_1 while the other is charged with Q_2, and if the second plate is connected to ground, then the inner surface of the first plate will have Q_1, and the inner surface of the second plated will have -Q_1. Therefore, the voltage V between the plates is V = \frac C. Note that the outer surface of both plates will have zero charge.


Interleaved capacitor

For n number of plates in a capacitor, the total capacitance would be C = \varepsilon_o\frac (n-1) where C = \varepsilon_o A / d is the capacitance for a single plate and n is the number of interleaved plates. As shown to the figure on the right, the interleaved plates can be seen as parallel plates connected to each other. Every pair of adjacent plates acts as a separate capacitor; the number of pairs is always one less than the number of plates, hence the (n-1) multiplier.


Energy stored in a capacitor

To increase the charge and voltage on a capacitor,
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal tr ...
must be done by an external power source to move charge from the negative to the positive plate against the opposing force of the electric field. If the voltage on the capacitor is V, the work dW required to move a small increment of charge dq from the negative to the positive plate is dW = Vdq. The energy is stored in the increased electric field between the plates. The total energy W stored in a capacitor (expressed in
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
s) is equal to the total work done in establishing the electric field from an uncharged state. W = \int_0^Q V(q) \, \mathrmq = \int_0^Q \frac \, \mathrmq = \frac \frac = \frac VQ = \frac C V^2 where Q is the charge stored in the capacitor, V is the voltage across the capacitor, and C is the capacitance. This potential energy will remain in the capacitor until the charge is removed. If charge is allowed to move back from the positive to the negative plate, for example by connecting a circuit with resistance between the plates, the charge moving under the influence of the electric field will do work on the external circuit. If the gap between the capacitor plates d is constant, as in the parallel plate model above, the electric field between the plates will be uniform (neglecting fringing fields) and will have a constant value E = V/d. In this case the stored energy can be calculated from the electric field strength W = \fracCV^2 = \frac\frac\left(Ed\right)^2 = \frac \varepsilon AdE^2 = \frac \varepsilon E^2 (\text) The last formula above is equal to the energy density per unit volume in the electric field multiplied by the volume of field between the plates, confirming that the energy in the capacitor is stored in its electric field.


Current–voltage relation

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. Actual charges – electrons – cannot pass through the dielectric layer of a capacitor. Rather, one 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 In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ...
of the current as well as proportional to the voltage, as discussed above. As with any
antiderivative In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function . This can be stated symbolically ...
, a
constant of integration In calculus, the constant of integration, often denoted by C (or c), is a constant term added to an antiderivative of a function f(x) to indicate that the indefinite integral of f(x) (i.e., the set of all antiderivatives of f(x)), on a connected ...
is added to represent the initial voltage ''V''(''t''0). This is the integral form of the capacitor equation: V(t) = \frac = V(t_0) + \frac\int_^t I(\tau) \, \mathrm\tau Taking the derivative of this and multiplying by ''C'' yields the derivative form: I(t) = \frac = C\frac for independent of time, voltage and electric charge. The
dual Dual or Duals may refer to: Paired/two things * Dual (mathematics), a notion of paired concepts that mirror one another ** Dual (category theory), a formalization of mathematical duality *** see more cases in :Duality theories * Dual (grammatical ...
of the capacitor is the
inductor An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
, which stores energy in a
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
rather than an electric field. Its current-voltage relation is obtained by exchanging current and voltage in the capacitor equations and replacing with the inductance .


DC circuits

A series circuit containing only a
resistor A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active el ...
, a capacitor, a switch and a constant DC source of voltage is known as a ''charging circuit''. If the capacitor is initially uncharged while the switch is open, and the switch is closed at , it follows from
Kirchhoff's voltage law Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchho ...
that V_0 = v_\text(t) + v_\text(t) = i(t) R + \frac \int_^t i(\tau) \, \mathrm\tau Taking the derivative and multiplying by ''C'', gives a
first-order differential equation In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast ...
: RC \frac + i(t) = 0 At , the voltage across the capacitor is zero and the voltage across the resistor is ''V''0. The initial current is then . With this assumption, solving the differential equation yields \begin I(t) &= \frac e^ \\ V(t) &= V_0 \left( 1 - e^\right) \\ Q(t) &= C V_0 \left( 1 - e^\right) \end where is the ''
time constant In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system.Concretely, a first-order LTI system is a sy ...
'' of the system. As the capacitor reaches equilibrium with the source voltage, the voltages across the resistor and the current through the entire circuit decay exponentially. In the case of a ''discharging'' capacitor, the capacitor's initial voltage () replaces . The equations become \begin I(t) &= \frac e^ \\ V(t) &= V_ \, e^ \\ Q(t) &= C \, V_ \, e^ \end


AC circuits

Impedance, the vector sum of reactance and resistance, describes the phase difference and the ratio of amplitudes between sinusoidally varying voltage and sinusoidally varying current at a given frequency.
Fourier analysis In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Josep ...
allows any signal to be constructed from a
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
of frequencies, whence the circuit's reaction to the various frequencies may be found. The reactance and impedance of a capacitor are respectively \begin X &= -\frac = -\frac \\ Z &= \frac = -\frac = -\frac \end where is the
imaginary unit The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition an ...
and is the
angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
of the sinusoidal signal. The phase indicates that the AC voltage 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. 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 Capacitive coupling is the transfer of energy within an electrical network or between distant networks by means of displacement current between circuit(s) nodes, induced by the electric field. This coupling can have an intentional or accidental ...
. Conversely, for very low frequencies, the reactance is high, so that a capacitor is nearly an open circuit in AC analysis – those frequencies have been "filtered out". Capacitors are different from resistors and inductors in that the impedance is ''inversely'' proportional to the defining characteristic; i.e.,
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
. A capacitor connected to a sinusoidal voltage source causes a displacement current to flow through it. In the case that the voltage source is ''V''0cos(ωt), the displacement current can be expressed as: I = C \frac = -\omega \sin(\omega t) At , the capacitor has a maximum (or peak) current whereby . The ratio of peak voltage to peak current is due to
capacitive reactance In electrical circuits, reactance is the opposition presented to alternating current by inductance or capacitance. Greater reactance gives smaller current for the same applied voltage. Reactance is similar to resistance in this respect, but doe ...
(denoted XC). X_C = \frac = \frac = \frac XC approaches zero as approaches infinity. If XC approaches 0, the capacitor resembles a short wire that strongly passes current at high frequencies. XC approaches infinity as ω approaches zero. If XC approaches infinity, the capacitor resembles an open circuit that poorly passes low frequencies. The current of the capacitor may be expressed in the form of cosines to better compare with the voltage of the source: I = - I_0 \sin() = I_0 \cos( + ) In this situation, the current is out of
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
with the voltage by +π/2 radians or +90 degrees, i.e. the current leads the voltage by 90°.


Laplace circuit analysis (s-domain)

When using the
Laplace transform In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform In mathematics, an integral transform maps a function from its original function space into another function space via integra ...
in circuit analysis, the impedance of an ideal capacitor with no initial charge is represented in the domain by: Z(s) = \frac where * is the capacitance, and * is the complex frequency.


Circuit analysis

;For capacitors in parallel :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. C_\mathrm= \sum_ C_i = C_1 + C_2 + \cdots + C_n ;For capacitors in series :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. \frac = \sum_ \frac = \frac + \frac + \cdots + \frac :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 does not apply too much voltage to the other series capacitors. :Series connection is also sometimes used to adapt polarized
electrolytic capacitor An electrolytic capacitor is a polarized capacitor whose anode or positive plate is made of a metal that forms an insulating oxide layer through anodization. This oxide layer acts as the dielectric of the capacitor. A solid, liquid, or gel el ...
s for bipolar AC use. ;Voltage distribution in parallel-to-series networks. :To model the distribution of voltages from a single charged capacitor \left( A \right) connected in parallel to a chain of capacitors in series \left( B_\text \right) : \begin \text A_\mathrm &= A\left(1 - \frac\right) \\ \text B_\text &= \frac \left(1 - \frac\right) \\ A - B &= 0 \end :Note: This is only correct if all capacitance values are equal. :The power transferred in this arrangement is: P = \frac \cdot \frac A_\text \left( A_\text + B_\text \right)


Non-ideal behavior

In practice, capacitors deviate from the ideal capacitor equation in several aspects. Some of these, such as leakage current and parasitic effects are linear, or can be analyzed as nearly linear, and can be accounted for by adding virtual components to the
equivalent circuit In electrical engineering and science, an equivalent circuit refers to a theoretical circuit that retains all of the electrical characteristics of a given circuit. Often, an equivalent circuit is sought that simplifies calculation, and more broadly ...
of an ideal capacitor. The usual methods of
network analysis Network analysis can refer to: * Network theory, the analysis of relations through mathematical graphs ** Social network analysis, network theory applied to social relations * Network analysis (electrical circuits) See also *Network planning and ...
can then be applied. In other cases, such as with breakdown voltage, the effect is non-linear and ordinary (normal, e.g., linear) network analysis cannot be used, the effect must be considered separately. Yet another group of artifacts may exist, including temperature dependence, that may be linear but invalidates the assumption in the analysis that capacitance is a constant. Finally, combined parasitic effects such as inherent inductance, resistance, or dielectric losses can exhibit non-uniform behavior at varying frequencies of operation.


Breakdown voltage

Above a particular electric field strength, known as the dielectric strength ''Eds'', 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, V_= E_ d 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 In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It is sometimes confused with energy per unit mass which is properly called specific energy or . Often only the ''useful'' or extract ...
, to the extent that the dielectric dominates their volume. For air dielectric capacitors the breakdown field strength is of the order 2–5 MV/m (or kV/mm); for
mica Micas ( ) are a group of silicate minerals whose outstanding physical characteristic is that individual mica crystals can easily be split into extremely thin elastic plates. This characteristic is described as perfect basal cleavage. Mica is ...
the breakdown is 100–300 MV/m; for oil, 15–25 MV/m; it can be much less when other materials are used for the dielectric. 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 The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
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 and causing a short (or relatively low resistance) circuit. The results can be explosive, as the short in the capacitor draws current from the surrounding circuitry and dissipates the energy. However, in capacitors with particular dielectrics and thin metal electrodes shorts are not formed after breakdown. It happens because a metal melts or evaporates in a breakdown vicinity, isolating it from the rest of the capacitor. 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 Avalanche breakdown (or avalanche effect) is a phenomenon that can occur in both insulating and semiconducting materials. It is a form of electric current multiplication that can allow very large currents within materials which are otherwise good ...
as seen in semi-conductor devices. Breakdown voltage is also affected by pressure, humidity and temperature.


Equivalent circuit

An ideal capacitor only stores and releases electrical energy, without dissipation. In practice, all capacitors have imperfections within the capacitor's materials that permit leakage current, and represent resistance. This is specified as the ''
equivalent series resistance Practical capacitors and inductors as used in electric circuits are not ideal components with only capacitance or inductance. However, they can be treated, to a very good degree of approximation, as being ideal capacitors and inductors in series ...
'' (ESR) of the device. It add a
real-valued In mathematics, value may refer to several, strongly related notions. In general, a mathematical value may be any definite mathematical object. In elementary mathematics, this is most often a number – for example, a real number such as or an i ...
component to the impedance: Z_\text= Z + R_\text = \frac + R_\text As frequency approaches infinity, the capacitive impedance (reactance) approaches zero and the ESR becomes significant. As the reactance becomes negligible, power dissipation approaches ''P''RMS = ''V''RMS2 /''R''ESR. Similarly to ESR, the capacitor's leads add ''
equivalent series inductance Equivalent series inductance (ESL) is an effective inductance that is used to describe the inductive part of the impedance of certain electrical components. Overview The theoretical treatment of devices such as capacitors and resistors tends to ...
'' (ESL) to the component. This is usually significant only at relatively high frequencies. As inductive reactance is positive and increases with frequency, capacitance is canceled by inductance above a certain frequency. High-frequency engineering involves accounting for the inductance of all connections and components. 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, and slowly discharges over time, which may vary greatly depending on the capacitor material and quality.


Q factor

The
quality factor In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy los ...
(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 capacitor. The Q factor of a capacitor can be found through the following formula: Q = \frac=\frac where \omega is
angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
, C is the capacitance, X_C is the
capacitive reactance In electrical circuits, reactance is the opposition presented to alternating current by inductance or capacitance. Greater reactance gives smaller current for the same applied voltage. Reactance is similar to resistance in this respect, but doe ...
, and R is the equivalent series resistance (ESR) of the capacitor.


Ripple current

Ripple Ripple may refer to: Science and technology * Capillary wave, commonly known as ripple, a wave traveling along the phase boundary of a fluid ** Ripple, more generally a disturbance, for example of spacetime in gravitational waves * Ripple (electri ...
current is the AC component of an applied source (often a
switched-mode power supply A switched-mode power supply (switching-mode power supply, switch-mode power supply, switched power supply, SMPS, or switcher) is an electronic power supply that incorporates a switching regulator to convert electrical power efficiently. Lik ...
) 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. Some
types of capacitor Capacitors are manufactured in many styles, forms, dimensions, and from a large variety of materials. They all contain at least two electrical conductors, called ''plates'', separated by an insulator (electricity), insulating layer (''dielectric ...
s, primarily
tantalum Tantalum is a chemical element with the symbol Ta and atomic number 73. Previously known as ''tantalium'', it is named after Tantalus, a villain in Greek mythology. Tantalum is a very hard, ductile, lustrous, blue-gray transition metal that is ...
and
aluminum Aluminium (aluminum in American and Canadian English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately one third that of steel. It has ...
electrolytic capacitor An electrolytic capacitor is a polarized capacitor whose anode or positive plate is made of a metal that forms an insulating oxide layer through anodization. This oxide layer acts as the dielectric of the capacitor. A solid, liquid, or gel el ...
s, as well as some
film capacitor Film capacitors, plastic film capacitors, film dielectric capacitors, or polymer film capacitors, generically called film caps as well as power film capacitors, are electrical capacitors with an insulating plastic film as the dielectric, sometime ...
s have a specified rating value for maximum ripple current. * 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. * Aluminum 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. *
Ceramic capacitor A ceramic capacitor is a fixed-value capacitor where the ceramic material acts as the dielectric. It is constructed of two or more alternating layers of ceramic and a metal layer acting as the electrodes. The composition of the ceramic material de ...
s generally have no ripple current limitation and have some of the lowest ESR ratings. *
Film capacitor Film capacitors, plastic film capacitors, film dielectric capacitors, or polymer film capacitors, generically called film caps as well as power film capacitors, are electrical capacitors with an insulating plastic film as the dielectric, sometime ...
s have very low ESR ratings but exceeding rated ripple current may cause degradation failures.


Capacitance instability

The capacitance of certain capacitors decreases as the component ages. In
ceramic capacitor A ceramic capacitor is a fixed-value capacitor where the ceramic material acts as the dielectric. It is constructed of two or more alternating layers of ceramic and a metal layer acting as the electrodes. The composition of the ceramic material de ...
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 usually has a smaller effect, i.e., usual capacitor design is to minimize voltage coefficient. The aging process may be reversed by heating the component above the
Curie point In physics and materials science, the Curie temperature (''T''C), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Cur ...
. Aging is fastest near the beginning of life of the component, and the device stabilizes over time. Electrolytic capacitors age as the electrolyte evaporates. In contrast with ceramic capacitors, this occurs towards the end of life of the component. 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. Capacitors, especially ceramic capacitors, and older designs such as paper capacitors, can absorb sound waves resulting in a
microphonic Microphonics, microphony, or microphonism describes the phenomenon wherein certain components in electronic devices transform mechanical vibrations into an undesired electrical signal (noise). The term comes from analogy with a microphone, which ...
effect. Vibration moves the plates, causing the capacitance to vary, in turn inducing AC current. Some dielectrics also generate
piezoelectricity Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word ''p ...
. 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.


Current and voltage reversal

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 is usually less than 100%, often in the range of 0 to 90%, whereas AC circuits experience 100% reversal. In DC circuits and pulsed circuits, current and voltage reversal are affected by the
damping Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples incl ...
of the system. Voltage reversal is encountered in
RLC circuits An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the constituent components ...
that are
underdamped Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples incl ...
. The current and voltage reverse direction, forming a
harmonic oscillator In classical mechanics, a harmonic oscillator is a system that, when displaced from its Mechanical equilibrium, equilibrium position, experiences a restoring force ''F'' Proportionality (mathematics), proportional to the displacement ''x'': \v ...
between the
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the ...
and capacitance. The current and voltage tends 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 Ringing may mean: Vibrations * Ringing (signal), unwanted oscillation of a signal, leading to ringing artifacts * Vibration of a harmonic oscillator ** Bell ringing * Ringing (telephony), the sound of a telephone bell * Ringing (medicine), a ri ...
. In comparison,
critically damped Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples incl ...
or
overdamped Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples incl ...
systems usually do not experience a voltage reversal. Reversal is also encountered in AC circuits, where the peak current is equal in each direction. For maximum life, capacitors usually need to be able to handle the maximum amount of reversal that a system may experience. An AC circuit experiences 100% voltage reversal, while underdamped DC circuits 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 often affect the design considerations for the capacitor, from the choice of dielectric materials and voltage ratings to the types of internal connections used.


Dielectric absorption

Capacitors made with any type of dielectric material show some level of "
dielectric absorption Dielectric absorption is the name given to the effect by which a capacitor, that has been charged for a long time, discharges only incompletely when briefly discharged. Although an ideal capacitor would remain at zero volts after being discharged, r ...
" 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 is objectionable in applications such as precision
sample and hold In electronics, a sample and hold (also known as sample and follow) circuit is an analog device that samples (captures, takes) the voltage of a continuously varying analog signal and holds (locks, freezes) its value at a constant level for a ...
circuits or timing circuits. The level of absorption depends on many factors, from design considerations to charging time, since the absorption is a time-dependent process. However, the primary factor is the type of dielectric material. Capacitors such as tantalum electrolytic or
polysulfone Polysulfones are a family of high performance thermoplastics. These polymers are known for their toughness and stability at high temperatures. Technically used polysulfones contain an aryl- SO2-aryl subunit. Due to the high cost of raw material ...
film exhibit relatively high absorption, while
polystyrene Polystyrene (PS) is a synthetic polymer made from monomers of the aromatic hydrocarbon styrene. Polystyrene can be solid or foamed. General-purpose polystyrene is clear, hard, and brittle. It is an inexpensive resin per unit weight. It is a ...
or
Teflon Polytetrafluoroethylene (PTFE) is a synthetic fluoropolymer of tetrafluoroethylene that has numerous applications. It is one of the best-known and widely applied PFAS. The commonly known brand name of PTFE-based composition is Teflon by Chemou ...
allow very small levels of absorption. In some capacitors where dangerous voltages and energies exist, such as in
flashtube A flashtube (flashlamp) is an electric arc lamp designed to produce extremely intense, incoherent, full-spectrum white light for a very short time. A flashtube is a glass tube with an electrode at each end and is filled with a gas that, when tr ...
s,
television set A television set or television receiver, more commonly called the television, TV, TV set, telly, tele, or tube, is a device that combines a tuner, display, and loudspeakers, for the purpose of viewing and hearing television broadcasts, or using ...
s,
microwave ovens A microwave oven (commonly referred to as a microwave) is an electric oven that heats and cooks food by exposing it to electromagnetic radiation in the microwave frequency range. This induces polar molecules in the food to rotate and produce th ...
and
defibrillator Defibrillation is a treatment for life-threatening cardiac arrhythmias, specifically ventricular fibrillation (V-Fib) and non-perfusing ventricular tachycardia (V-Tach). A defibrillator delivers a dose of electric current (often called a ''coun ...
s, the dielectric absorption can recharge the capacitor to hazardous voltages after it has been shorted or discharged. Any capacitor containing over 10 joules of energy is generally considered hazardous, while 50 joules or higher is potentially lethal. A capacitor may regain anywhere from 0.01 to 20% of its original charge over a period of several minutes, allowing a seemingly safe capacitor to become surprisingly dangerous.


Leakage

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.


Electrolytic failure from disuse

Aluminum electrolytic capacitor Aluminum electrolytic capacitors are polarized electrolytic capacitors whose anode electrode (+) is made of a pure aluminum foil with an etched surface. The aluminum forms a very thin insulating layer of aluminum oxide by anodization that acts ...
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. Sometimes they fail with a short circuit when next operated.


Lifespan

All capacitors have varying lifespans, depending upon their construction, operational conditions, and environmental conditions. Solid-state ceramic capacitors generally have very long lives under normal use, which has little dependency on factors such as vibration or ambient temperature, but factors like humidity, mechanical stress, and
fatigue Fatigue describes a state of tiredness that does not resolve with rest or sleep. In general usage, fatigue is synonymous with extreme tiredness or exhaustion that normally follows prolonged physical or mental activity. When it does not resolve ...
play a primary role in their failure. Failure modes may differ. Some capacitors may experience a gradual loss of capacitance, increased leakage or an increase in
equivalent series resistance Practical capacitors and inductors as used in electric circuits are not ideal components with only capacitance or inductance. However, they can be treated, to a very good degree of approximation, as being ideal capacitors and inductors in series ...
(ESR), while others may fail suddenly or even catastrophically. For example, metal-film capacitors are more prone to damage from stress and humidity, but will self-heal when a breakdown in the dielectric occurs. The formation of a
glow discharge A glow discharge is a plasma formed by the passage of electric current through a gas. It is often created by applying a voltage between two electrodes in a glass tube containing a low-pressure gas. When the voltage exceeds a value called the str ...
at the point of failure prevents arcing by vaporizing the metallic film in that spot, neutralizing any short circuit with minimal loss in capacitance. When enough pinholes accumulate in the film, a total failure occurs in a metal-film capacitor, generally happening suddenly without warning. Electrolytic capacitors generally have the shortest lifespans. Electrolytic capacitors are affected very little by vibration or humidity, but factors such as ambient and operational temperatures play a large role in their failure, which gradually occur as an increase in ESR (up to 300%) and as much as a 20% decrease in capacitance. The capacitors contain electrolytes which will eventually diffuse through the seals and evaporate. An increase in temperature also increases internal pressure, and increases the reaction rate of the chemicals. Thus, the life of an electrolytic capacitor is generally defined by a modification of the
Arrhenius equation In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 18 ...
, which is used to determine chemical-reaction rates: L = B e^ Manufacturers often use this equation to supply an expected lifespan, in hours, for electrolytic capacitors when used at their designed operating temperature, which is affected by both ambient temperature, ESR, and ripple current. However, these ideal conditions may not exist in every use. The rule of thumb for predicting lifespan under different conditions of use is determined by: L_a = L_0 2^ This says that the capacitor's life decreases by half for every 10 degrees Celsius that the temperature is increased, where: * L_0 is the rated life under rated conditions, e.g. 2000 hours * T_0 is the rated max/min operational temperature * T_a is the average operational temperature * L_a is the expected lifespan under given conditions


Capacitor types

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. 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
supercapacitors A supercapacitor (SC), also called an ultracapacitor, is a high-capacity capacitor, with a capacitance value much higher than other capacitors but with lower voltage limits. It bridges the gap between electrolytic capacitors and Rechargeable ba ...
. Above approximately 1 microfarad electrolytic capacitors are usually used because of their small size and low cost compared with other types, unless their relatively poor stability, life and polarised nature make them unsuitable. Very high capacity supercapacitors use a porous carbon-based electrode material.


Dielectric materials

Most capacitors have a dielectric spacer, which increases their capacitance compared to air or a vacuum. In order to maximise the charge that a capacitor can hold, the dielectric material needs to have as high a
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
as possible, while also having as high a
breakdown voltage The breakdown voltage of an insulator is the minimum voltage that causes a portion of an insulator to experience electrical breakdown and become electrically conductive. For diodes, the breakdown voltage is the minimum reverse voltage that mak ...
as possible. The dielectric also needs to have as low a loss with frequency as possible. However, low value capacitors are available with a vacuum between their plates to allow extremely high voltage operation and low losses.
Variable capacitor A variable capacitor is a capacitor whose capacitance may be intentionally and repeatedly changed mechanically or electronically. Variable capacitors are often used in L/C circuits to set the resonance frequency, e.g. to tune a radio (therefo ...
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 the plates. Several solid dielectrics are available, including
paper Paper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, rags, grasses or other vegetable sources in water, draining the water through fine mesh leaving the fibre evenly distributed ...
,
plastic Plastics are a wide range of synthetic or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adaptab ...
,
glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
,
mica Micas ( ) are a group of silicate minerals whose outstanding physical characteristic is that individual mica crystals can easily be split into extremely thin elastic plates. This characteristic is described as perfect basal cleavage. Mica is ...
and
ceramic A ceramic is any of the various hard, brittle, heat-resistant and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcelain ...
. Paper was used extensively in older capacitors and offers relatively high voltage performance. However, paper absorbs moisture, and has been largely replaced by plastic
film capacitor Film capacitors, plastic film capacitors, film dielectric capacitors, or polymer film capacitors, generically called film caps as well as power film capacitors, are electrical capacitors with an insulating plastic film as the dielectric, sometime ...
s. Most of the plastic films now used offer better stability and ageing performance than such older dielectrics such as oiled paper, which makes them useful in timer circuits, although they may be limited to relatively low
operating temperature An operating temperature is the allowable temperature range of the local ambient environment at which an electrical or mechanical device operates. The device will operate effectively within a specified temperature range which varies based on the de ...
s and frequencies, because of the limitations of the plastic film being used. Large plastic film capacitors are used extensively in suppression circuits, motor start circuits, and
power-factor correction In electrical engineering, the power factor of an AC power system is defined as the ratio of the '' real power'' absorbed by the load to the ''apparent power'' flowing in the circuit. Real power is the average of the instantaneous product of v ...
circuits. Ceramic capacitors are generally small, cheap and useful for high frequency applications, although their capacitance varies strongly with voltage and temperature and they age poorly. They can also suffer from the piezoelectric effect. Ceramic capacitors are broadly categorized as class 1 dielectrics, which have predictable variation of capacitance with temperature or class 2 dielectrics, which can operate at higher voltage. Modern multilayer ceramics are usually quite small, but some types have inherently wide value tolerances, microphonic issues, and are usually physically brittle. Glass and mica capacitors are extremely reliable, stable and tolerant to high temperatures and voltages, but are too expensive for most mainstream applications. Electrolytic capacitors and
supercapacitor A supercapacitor (SC), also called an ultracapacitor, is a high-capacity capacitor, with a capacitance value much higher than other capacitors but with lower voltage limits. It bridges the gap between electrolytic capacitors and rechargeable ba ...
s are used to store small and larger amounts of energy, respectively, ceramic capacitors are often used in
resonators A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator ...
, and
parasitic capacitance Parasitic capacitance is an unavoidable and usually unwanted capacitance that exists between the parts of an electronic component or circuit simply because of their proximity to each other. When two electrical conductors at different voltages a ...
occurs in circuits wherever the simple conductor-insulator-conductor structure is formed unintentionally by the configuration of the circuit layout.
Electrolytic capacitor An electrolytic capacitor is a polarized capacitor whose anode or positive plate is made of a metal that forms an insulating oxide layer through anodization. This oxide layer acts as the dielectric of the capacitor. A solid, liquid, or gel el ...
s use an
aluminum Aluminium (aluminum in American and Canadian English) is a chemical element with the symbol Al and atomic number 13. Aluminium has a density lower than those of other common metals, at approximately one third that of steel. It has ...
or
tantalum Tantalum is a chemical element with the symbol Ta and atomic number 73. Previously known as ''tantalium'', it is named after Tantalus, a villain in Greek mythology. Tantalum is a very hard, ductile, lustrous, blue-gray transition metal that is ...
plate with an oxide dielectric layer. The second electrode is a liquid
electrolyte An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon dis ...
, 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. 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 suffer from self-degradation 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 example, in older equipment, this may cause arcing in rectifier tubes. They can be restored before use by gradually applying the operating voltage, often performed on antique
vacuum tube A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied. The type kn ...
equipment over a period of thirty minutes by using a variable transformer to supply AC power. 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. Tantalum capacitors offer better frequency and temperature characteristics than aluminum, but higher
dielectric absorption Dielectric absorption is the name given to the effect by which a capacitor, that has been charged for a long time, discharges only incompletely when briefly discharged. Although an ideal capacitor would remain at zero volts after being discharged, r ...
and leakage.
Polymer capacitor A polymer capacitor, or more accurately a polymer electrolytic capacitor, is an electrolytic capacitor (e-cap) with a solid conductive polymer electrolyte. There are four different types: * Polymer tantalum capacitor, tantalum electrolytic capac ...
s (OS-CON, OC-CON, KO, AO) use solid conductive polymer (or polymerized organic semiconductor) as electrolyte and offer longer life and lower ESR at higher cost than standard electrolytic capacitors. A
feedthrough capacitor A feedthrough is a Conductor (material), conductor used to carry a signal through an enclosure or printed circuit board. Like any conductor, it has a small amount of capacitance. A "feedthrough capacitor" has a guaranteed minimum value of bui ...
is a component that, while not serving as its main use, has capacitance and is used to conduct signals through a conductive sheet. Several other types of capacitor are available for specialist applications.
Supercapacitor A supercapacitor (SC), also called an ultracapacitor, is a high-capacity capacitor, with a capacitance value much higher than other capacitors but with lower voltage limits. It bridges the gap between electrolytic capacitors and rechargeable ba ...
s store large amounts of energy. Supercapacitors made from carbon
aerogel Aerogels are a class of synthetic porous ultralight material derived from a gel, in which the liquid component for the gel has been replaced with a gas, without significant collapse of the gel structure. The result is a solid with extremely low ...
, carbon nanotubes, or highly porous electrode materials, offer extremely high capacitance (up to 5 kF ) and can be used in some applications instead of
rechargeable batteries A rechargeable battery, storage battery, or secondary cell (formally a type of energy accumulator), is a type of electrical battery which can be charged, discharged into a load, and recharged many times, as opposed to a disposable or prima ...
.
Alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
capacitors are specifically designed to work on line (mains) voltage AC power circuits. They are commonly used in
electric motor An electric motor is an Electric machine, electrical machine that converts electrical energy into mechanical energy. Most electric motors operate through the interaction between the motor's magnetic field and electric current in a Electromagneti ...
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 Direct current (DC) is one-directional flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or even ...
breakdown voltages of at least five times the maximum AC voltage.


Voltage-dependent capacitors

The dielectric constant for a number of very useful dielectrics changes as a function of the applied electrical field, for example
ferroelectric Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. All ferroelectrics are also piezoelectric and pyroelectric, with the add ...
materials, so the capacitance for these devices is more complex. For example, in charging such a capacitor the differential increase in voltage with charge is governed by: dQ = C(V) \, dV where the voltage dependence of capacitance, , suggests that the capacitance is a function of the electric field strength, which in a large area parallel plate device is given by . This field polarizes the dielectric, which polarization, in the case of a ferroelectric, is a nonlinear ''S''-shaped function of the electric field, which, in the case of a large area parallel plate device, translates into a capacitance that is a nonlinear function of the voltage. Corresponding to the voltage-dependent capacitance, to charge the capacitor to voltage an integral relation is found: Q = \int_0^V C(V) \, dV which agrees with only when does not depend on voltage . By the same token, the energy stored in the capacitor now is given by dW = Q \, dV =\left \int_0^V dV' \, C(V') \rightdV \, . Integrating: W = \int_0^V dV \int_0^V dV' \, C(V') = \int_0^V dV' \int_^V dV \, C(V') = \int_0^V dV' \left(V-V'\right) C(V') \, , where interchange of the
order of integration In statistics, the order of integration, denoted ''I''(''d''), of a time series is a summary statistic, which reports the minimum number of differences required to obtain a covariance-stationary series. Integration of order ''d'' A time seri ...
is used. The nonlinear capacitance of a microscope probe scanned along a ferroelectric surface is used to study the domain structure of ferroelectric materials. Another example of voltage dependent capacitance occurs in
semiconductor devices A semiconductor device is an electronic component that relies on the electronic properties of a semiconductor material (primarily silicon, germanium, and gallium arsenide, as well as organic semiconductors) for its function. Its conductivity li ...
such as semiconductor
diode A diode is a two-terminal electronic component that conducts current primarily in one direction (asymmetric conductance); it has low (ideally zero) resistance in one direction, and high (ideally infinite) resistance in the other. A diode ...
s, where the voltage dependence stems not from a change in dielectric constant but in a voltage dependence of the spacing between the charges on the two sides of the capacitor. This effect is intentionally exploited in diode-like devices known as
varicap In electronics, a varicap diode, varactor diode, variable capacitance diode, variable reactance diode or tuning diode is a type of diode designed to exploit the voltage-dependent capacitance of a reverse-biased p–n junction. Applications Vara ...
s.


Frequency-dependent capacitors

If a capacitor is driven with a time-varying voltage that changes rapidly enough, at some frequency the polarization of the dielectric cannot follow the voltage. As an example of the origin of this mechanism, the internal microscopic dipoles contributing to the dielectric constant cannot move instantly, and so as frequency of an applied alternating voltage increases, the dipole response is limited and the dielectric constant diminishes. A changing dielectric constant with frequency is referred to as
dielectric dispersion In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mater ...
, and is governed by
dielectric relaxation In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mater ...
processes, such as
Debye relaxation In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mater ...
. Under transient conditions, the displacement field can be expressed as (see
electric susceptibility In electricity (electromagnetism), the electric susceptibility (\chi_; Latin: ''susceptibilis'' "receptive") is a dimensionless proportionality constant that indicates the degree of polarization of a dielectric material in response to an applie ...
): \boldsymbol=\varepsilon_0\int_^t \varepsilon_r (t-t') \boldsymbol E (t')\, dt' , indicating the lag in response by the time dependence of , calculated in principle from an underlying microscopic analysis, for example, of the dipole behavior in the dielectric. See, for example,
linear response function A linear response function describes the input-output relationship of a signal transducer such as a radio turning electromagnetic waves into music or a neuron turning synaptic input into a response. Because of its many applications in information ...
. The integral extends over the entire past history up to the present time. A
Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
in time then results in: \boldsymbol D(\omega) = \varepsilon_0 \varepsilon_r(\omega) \boldsymbol E (\omega)\, , where ''ε''r(''ω'') is now a
complex function Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...
, with an imaginary part related to absorption of energy from the field by the medium. See
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...
. The capacitance, being proportional to the dielectric constant, also exhibits this frequency behavior. Fourier transforming Gauss's law with this form for displacement field: \begin I(\omega) &= j\omega Q(\omega) = j\omega \oint_ \boldsymbol D (\boldsymbol r , \omega)\cdot d \boldsymbol \\ &=\left G(\omega) + j \omega C(\omega)\rightV(\omega) = \frac \, , \end where is the
imaginary unit The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition an ...
, is the voltage component at angular frequency , is the ''real'' part of the current, called the ''conductance'', and determines the ''imaginary'' part of the current and is the ''capacitance''. is the complex impedance. When a parallel-plate capacitor is filled with a dielectric, the measurement of dielectric properties of the medium is based upon the relation: \varepsilon_r(\omega) = \varepsilon '_r(\omega) - j \varepsilon ''_r(\omega) = \frac = \frac \, , where a single ''prime'' denotes the real part and a double ''prime'' the imaginary part, is the complex impedance with the dielectric present, is the so-called ''complex'' capacitance with the dielectric present, and is the capacitance without the dielectric. (Measurement "without the dielectric" in principle means measurement in
free space A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
, an unattainable goal inasmuch as even the
quantum vacuum In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. The word zero-point field is sometimes used as ...
is predicted to exhibit nonideal behavior, such as
dichroism In optics, a dichroic material is either one which causes visible light to be split up into distinct beams of different wavelengths (colours) (not to be confused with dispersion), or one in which light rays having different polarizations are abs ...
. For practical purposes, when measurement errors are taken into account, often a measurement in terrestrial vacuum, or simply a calculation of ''C''0, is sufficiently accurate.) Using this measurement method, the dielectric constant may exhibit a
resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
at certain frequencies corresponding to characteristic response frequencies (excitation energies) of contributors to the dielectric constant. These resonances are the basis for a number of experimental techniques for detecting defects. The ''conductance method'' measures absorption as a function of frequency. Alternatively, the time response of the capacitance can be used directly, as in ''
deep-level transient spectroscopy Deep-level transient spectroscopy (DLTS) is an experimental tool for studying electrically active defects (known as charge carrier traps) in semiconductors. DLTS establishes fundamental defect parameters and measures their concentration in the mater ...
''. Another example of frequency dependent capacitance occurs with MOS capacitors, where the slow generation of minority carriers means that at high frequencies the capacitance measures only the majority carrier response, while at low frequencies both types of carrier respond. At optical frequencies, in semiconductors the dielectric constant exhibits structure related to the band structure of the solid. Sophisticated modulation spectroscopy measurement methods based upon modulating the crystal structure by pressure or by other stresses and observing the related changes in absorption or reflection of light have advanced our knowledge of these materials.


Styles

The arrangement of plates and dielectric has many variations in different styles 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
paper Paper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, rags, grasses or other vegetable sources in water, draining the water through fine mesh leaving the fibre evenly distributed ...
or plasticthese 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. The assembly is encased to prevent moisture entering the dielectricearly radio equipment used a cardboard tube sealed with wax. Modern paper or film dielectric capacitors are dipped in a hard thermoplastic. Large capacitors for high-voltage use may have the roll form compressed to fit into a rectangular metal case, with bolted terminals and bushings for connections. The dielectric in larger capacitors is often impregnated with a liquid to improve its properties. Capacitors may have their connecting leads arranged in many configurations, for example axially or radially. "Axial" means that the leads are on a common axis, typically the axis of the capacitor's cylindrical bodythe leads extend from opposite ends. Radial leads are rarely aligned along radii of the body's circle, so the term is conventional. 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. Small, cheap discoidal
ceramic capacitor A ceramic capacitor is a fixed-value capacitor where the ceramic material acts as the dielectric. It is constructed of two or more alternating layers of ceramic and a metal layer acting as the electrodes. The composition of the ceramic material de ...
s have existed from the 1930s onward, and remain in widespread use. After the 1980s,
surface mount Surface-mount technology (SMT), originally called planar mounting, is a method in which the electrical components are mounted directly onto the surface of a printed circuit board (PCB). An electrical component mounted in this manner is referred ...
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 A printed circuit board (PCB; also printed wiring board or PWB) is a medium used in electrical and electronic engineering to connect electronic components to one another in a controlled manner. It takes the form of a laminated sandwich struct ...
. Surface mount components avoid undesirable high-frequency effects due to the leads and simplify automated assembly, although manual handling is made difficult due to their small size. Mechanically controlled variable capacitors allow the plate spacing to be adjusted, for example by rotating or sliding a set of movable plates into alignment with a set of stationary plates. Low cost variable capacitors squeeze together alternating layers of aluminum and plastic with a
screw A screw and a bolt (see '' Differentiation between bolt and screw'' below) are similar types of fastener typically made of metal and characterized by a helical ridge, called a ''male thread'' (external thread). Screws and bolts are used to fa ...
. Electrical control of capacitance is achievable with
varactor In electronics, a varicap diode, varactor diode, variable capacitance diode, variable reactance diode or tuning diode is a type of diode designed to exploit the voltage-dependent capacitance of a reverse-biased p–n junction. Applications Vara ...
s (or varicaps), which are reverse-biased
semiconductor diode A diode is a two-terminal electronic component that conducts current primarily in one direction (asymmetric conductance); it has low (ideally zero) resistance in one direction, and high (ideally infinite) resistance in the other. A diode ...
s whose depletion region width varies with applied voltage. They are used in phase-locked loops, amongst other applications.


Capacitor markings


Marking codes for larger parts

Most capacitors have designations printed on their bodies to indicate their electrical characteristics. Larger capacitors, such as electrolytic types usually display the capacitance as value with explicit unit, for example, ''220 μF''. For typographical reasons, some manufacturers print ''MF'' on capacitors to indicate microfarads (μF).


Three-/four-character marking code for small capacitors

Smaller capacitors, such as ceramic types, often use a shorthand-notation consisting of three digits and an optional letter, where the digits (''XYZ'') denote the capacitance in
picofarad The farad (symbol: F) is the unit of electrical capacitance, the ability of a body to store an electrical charge, in the International System of Units (SI). It is named after the English physicist Michael Faraday (1791–1867). In SI base units ...
(pF), calculated as ''XY'' × 10''Z'', and the letter indicating the tolerance. Common tolerances are ±5%, ±10%, and ±20%, denotes as J, K, and M, respectively. A capacitor may also be labeled with its working voltage, temperature, and other relevant characteristics. Example: A capacitor labeled or designated as ''473K 330V'' has a capacitance of = 47 nF (±10%) with a maximum working voltage of 330 V. The working voltage of a capacitor is nominally the highest voltage that may be applied across it without undue risk of breaking down the dielectric layer.


Two-character marking code for small capacitors

For capacitances following the E3, E6, E12 or
E24 series The E series is a system of preferred numbers (also called preferred values) derived for use in electronic components. It consists of the E3, E6, E12, E24, E48, E96 and E192 series, where the number after the 'E' designates the quantity of ...
of preferred values, the former ANSI/EIA-198-D:1991, ANSI/EIA-198-1-E:1998 and ANSI/EIA-198-1-F:2002 as well as the amendment IEC 60062:2016/AMD1:2019 to IEC 60062 define a ''special two-character marking code for capacitors'' for very small parts which leave no room to print the above mentioned three-/four-character code onto them. The code consists of an uppercase letter denoting the two significant digits of the value followed by a digit indicating the multiplier. The EIA standard also defines a number of lowercase letters to specify a number of values not found in E24.


RKM code

The notation to state a capacitor's value in a circuit diagram varies. The
RKM code The RKM code, also referred to as "letter and numeral code for resistance and capacitance values and tolerances", "letter and digit code for resistance and capacitance values and tolerances", or informally as "R notation" is a notation to specif ...
following
IEC 60062 The RKM code, also referred to as "letter and numeral code for resistance and capacitance values and tolerances", "letter and digit code for resistance and capacitance values and tolerances", or informally as "R notation" is a notation to specif ...
and
BS 1852 The RKM code, also referred to as "letter and numeral code for resistance and capacitance values and tolerances", "letter and digit code for resistance and capacitance values and tolerances", or informally as "R notation" is a notation to specif ...
avoids using a
decimal separator A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The cho ...
and replaces the decimal separator with the SI prefix symbol for the particular value (and the letter for weight 1). The code is also used for part markings. Example: for 4.7 nF or for 2.2 F.


Historical

In texts prior to the 1960s and on some capacitor packages until more recently, obsolete capacitance units were utilized in electronic books, magazines, and electronics catalogs. The old units "mfd" and "mf" meant ''microfarad'' (μF); and the old units "mmfd", "mmf", "uuf", "μμf", "pfd" meant ''picofarad'' (pF); but they are rarely used any more. Also, "Micromicrofarad" or "micro-microfarad" are obsolete units that are found in some older texts that is equivalent to ''picofarad'' (pF). Summary of obsolete capacitance units: (upper/lower case variations aren't shown) * μF (microfarad) = mf, mfd * pF (picofarad) = mmf, mmfd, pfd, μμF


Applications


Energy storage

A capacitor can store electric energy when disconnected from its charging circuit, so it can be used like a temporary
battery Battery most often refers to: * Electric battery, a device that provides electrical power * Battery (crime), a crime involving unlawful physical contact Battery may also refer to: Energy source *Automotive battery, a device to provide power t ...
, or like other types of
rechargeable energy storage system A rechargeable battery, storage battery, or secondary cell (formally a type of Accumulator (energy), energy accumulator), is a type of electrical battery which can be charged, discharged into a load, and recharged many times, as opposed to ...
. Capacitors are commonly used in electronic devices to maintain power supply while batteries are being changed. (This prevents loss of information in volatile memory.) A capacitor can facilitate conversion of kinetic energy of charged particles into electric energy and store it. Conventional capacitors provide less than 360
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
s per kilogram of
specific energy Specific energy or massic energy is energy per unit mass. It is also sometimes called gravimetric energy density, which is not to be confused with energy density, which is defined as energy per unit volume. It is used to quantify, for example, sto ...
, whereas a conventional
alkaline battery An alkaline battery (IEC code: L) is a type of primary battery where the electrolyte (most commonly potassium hydroxide) has a pH value above 7. Typically these batteries derive energy from the reaction between zinc metal and manganese dioxide, ...
has a density of 590 kJ/kg. There is an intermediate solution:
supercapacitor A supercapacitor (SC), also called an ultracapacitor, is a high-capacity capacitor, with a capacitance value much higher than other capacitors but with lower voltage limits. It bridges the gap between electrolytic capacitors and rechargeable ba ...
s, which can accept and deliver charge much faster than batteries, and tolerate many more charge and discharge cycles than rechargeable batteries. They are, however, 10 times larger than conventional batteries for a given charge. On the other hand, it has been shown that the amount of charge stored in the dielectric layer of the thin film capacitor can be equal to, or can even exceed, the amount of charge stored on its plates. In
car audio Vehicle audio is equipment installed in a car or other vehicle to provide in-car entertainment and information for the vehicle occupants. Until the 1950s it consisted of a simple AM radio. Additions since then have included FM radio (1952), 8 ...
systems, large capacitors store energy for the
amplifier An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost the v ...
to use on demand. Also, for a
flash tube Flash, flashes, or FLASH may refer to: Arts, entertainment, and media Fictional aliases * Flash (DC Comics character), several DC Comics superheroes with super speed: ** Flash (Barry Allen) ** Flash (Jay Garrick) ** Wally West, the first Kid F ...
, a capacitor is used to hold the
high voltage High voltage electricity refers to electrical potential large enough to cause injury or damage. In certain industries, ''high voltage'' refers to voltage above a certain threshold. Equipment and conductors that carry high voltage warrant spec ...
.


Digital memory

In the 1930s,
John Atanasoff John Vincent Atanasoff, , (October 4, 1903 – June 15, 1995) was an American physicist and inventor from mixed Bulgarian-Irish origin, best known for being credited with inventing the first electronic digital computer. Atanasoff invented the ...
applied the principle of energy storage in capacitors to construct dynamic digital memories for the first binary computers that used electron tubes for logic.


Pulsed power and weapons

Groups of large, specially constructed, low-inductance high-voltage capacitors (''capacitor banks'') are used to supply huge pulses of current for many
pulsed power Pulsed power is the science and technology of accumulating energy over a relatively long period of time and releasing it instantly, thus increasing the instantaneous power. They can be used in some applications such as food processing, water treatme ...
applications. These include
electromagnetic forming Electromagnetic forming (EM forming or magneforming) is a type of high-velocity, cold forming process for electrically conductive metals, most commonly copper and aluminium. The workpiece is reshaped by high-intensity pulsed magnetic fields tha ...
,
Marx generator A Marx generator is an electrical circuit first described by Erwin Otto Marx in 1924. Its purpose is to generate a high-voltage pulse from a low-voltage DC supply. Marx generators are used in high-energy physics experiments, as well as to simulat ...
s, pulsed
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
s (especially
TEA laser A TEA laser is a gas laser energized by a high voltage electrical discharge in a gas mixture generally at or above atmospheric pressure. The most common types are carbon dioxide lasers and excimer lasers, both used extensively in industry and res ...
s),
pulse forming network A pulse-forming network (PFN) is an electric circuit that accumulates electrical energy over a comparatively long time, and then releases the stored energy in the form of a relatively square pulse of comparatively brief duration for various puls ...
s,
radar Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
,
fusion Fusion, or synthesis, is the process of combining two or more distinct entities into a new whole. Fusion may also refer to: Science and technology Physics *Nuclear fusion, multiple atomic nuclei combining to form one or more different atomic nucl ...
research, and
particle accelerator A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle ...
s. Large capacitor banks (reservoir) are used as energy sources for the
exploding-bridgewire detonator The exploding-bridgewire detonator (EBW, also known as exploding wire detonator) is a type of detonator used to initiate the detonation reaction in explosive materials, similar to a blasting cap because it is fired using an electric current. EB ...
s or
slapper detonator A slapper detonator, also called exploding foil initiator (EFI), is a relatively recent kind of a detonator developed by Lawrence Livermore National Laboratory, US Patent No. 4,788,913. It is an improvement of the earlier exploding-bridgewire det ...
s in
nuclear weapon A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission bomb) or a combination of fission and fusion reactions ( thermonuclear bomb), producing a nuclear explosion. Both bom ...
s and other specialty weapons. Experimental work is under way using banks of capacitors as power sources for electromagnetic armour and electromagnetic
railgun A railgun or rail gun is a linear motor device, typically designed as a weapon, that uses Electromagnet, electromagnetic force to launch high velocity projectiles. The projectile normally does not contain explosives, instead relying on the proj ...
s and
coilgun A coilgun, also known as a Gauss rifle, is a type of mass driver consisting of one or more coils used as electromagnets in the configuration of a linear motor that accelerate a ferromagnetic or conducting projectile to high velocity. In almost ...
s.


Power conditioning

Reservoir capacitor A rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction. The reverse operation (converting DC to AC) is performed by an inver ...
s are used in
power supplies A power supply is an electrical device that supplies electric power to an electrical load. The main purpose of a power supply is to convert electric current from a source to the correct voltage, current, and frequency to power the load. As a res ...
where they smooth the output of a full or half wave
rectifier A rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction. The reverse operation (converting DC to AC) is performed by an Power ...
. They can also be used in
charge pump A charge pump is a kind of DC-to-DC converter that uses capacitors for energetic charge storage to raise or lower voltage. Charge-pump circuits are capable of high efficiencies, sometimes as high as 90–95%, while being electrically simple c ...
circuits as the energy storage element in the generation of higher voltages than the input voltage. Capacitors are connected in parallel with the power circuits of most electronic devices and larger systems (such as factories) to shunt away and conceal current fluctuations from the primary power source to provide a "clean" power supply for signal or control circuits. Audio equipment, for example, uses several capacitors in this way, to shunt away power line hum before it gets into the signal circuitry. The capacitors act as a local reserve for the DC power source, and bypass AC currents from the power supply. This is used in car audio applications, when a stiffening capacitor compensates for the inductance and resistance of the leads to the lead-acid
car battery An automotive battery or car battery is a rechargeable battery that is used to start a motor vehicle. Its main purpose is to provide an electric current to the electric-powered starting motor, which in turn starts the chemically-powered intern ...
.


Power-factor correction

In electric power distribution, capacitors are used for
power-factor correction In electrical engineering, the power factor of an AC power system is defined as the ratio of the '' real power'' absorbed by the load to the ''apparent power'' flowing in the circuit. Real power is the average of the instantaneous product of v ...
. Such capacitors often come as three capacitors connected as a
three phase Three-phase electric power (abbreviated 3φ) is a common type of alternating current used in electricity generation, transmission, and distribution. It is a type of polyphase system employing three wires (or four including an optional neutral r ...
load Load or LOAD may refer to: Aeronautics and transportation *Load factor (aeronautics), the ratio of the lift of an aircraft to its weight *Passenger load factor, the ratio of revenue passenger miles to available seat miles of a particular transpo ...
. Usually, the values of these capacitors are not given in farads but rather as a
reactive power Reactive may refer to: *Generally, capable of having a reaction (disambiguation) *An adjective abbreviation denoting a bowling ball coverstock made of reactive resin *Reactivity (chemistry) *Reactive mind *Reactive programming See also *Reactanc ...
in volt-amperes reactive (var). The purpose is to counteract inductive loading from devices like
electric motors An electric motor is an electrical machine that converts electrical energy into mechanical energy. Most electric motors operate through the interaction between the motor's magnetic field and electric current in a wire winding to generate force ...
and
transmission line In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
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 substation.


Suppression and coupling


Signal coupling

Because capacitors pass AC but block DC
signals In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
(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 is small at the signal frequency, is employed.


Decoupling

A
decoupling capacitor A decoupling capacitor is a capacitor used to decouple one part of an electrical network (circuit) from another. Noise caused by other circuit elements is shunted through the capacitor, reducing its effect on the rest of the circuit. For hig ...
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. An alternative name is ''
bypass capacitor A decoupling capacitor is a capacitor used to decouple one part of an electrical network (circuit) from another. Noise caused by other circuit elements is shunted through the capacitor, reducing its effect on the rest of the circuit. For hig ...
'' as it is used to bypass the power supply or other high impedance component of a circuit. Decoupling capacitors need not always be discrete components. Capacitors used in these applications may be built into a
printed circuit board A printed circuit board (PCB; also printed wiring board or PWB) is a medium used in Electrical engineering, electrical and electronic engineering to connect electronic components to one another in a controlled manner. It takes the form of a L ...
, between the various layers. These are often referred to as embedded capacitors. The layers in the board contributing to the capacitive properties also function as power and ground planes, and have a dielectric in between them, enabling them to operate as a parallel plate capacitor.


High-pass and low-pass filters


Noise suppression, spikes, and snubbers

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 may generate a spark, causing the contact points to oxidize, deteriorate, or sometimes weld together, or destroying a solid-state switch. A
snubber A snubber is a device used to suppress ("snub") a phenomenon such as voltage transients in electrical systems, pressure transients in fluid systems (caused by for example water hammer) or excess force or rapid movement in mechanical systems. Ele ...
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 A contact breaker (or "points") is a type of electrical switch, found in the ignition systems of spark-ignition internal combustion engines. The switch is automatically operated by a cam driven by the engine. The timing of operation of the switch ...
ignition system An ignition system generates a spark or heats an electrode to a high temperature to ignite a fuel-air mixture in spark ignition internal combustion engines, oil-fired and gas-fired boilers, rocket engines, etc. The widest application for spark ig ...
s, for instance. Similarly, in smaller scale circuits, the spark may not be enough to damage the switch but may still radiate undesirable
radio frequency interference Electromagnetic interference (EMI), also called radio-frequency interference (RFI) when in the radio frequency spectrum, is a disturbance generated by an external source that affects an electrical circuit by electromagnetic induction, electrost ...
(RFI), which a
filter capacitor Capacitors have many uses in electronic and electrical systems. They are so ubiquitous that it is rare that an electrical product does not include at least one for some purpose. Energy storage A capacitor can store electric energy when it is c ...
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. Capacitors are also used in parallel with interrupting units of a high-voltage
circuit breaker A circuit breaker is an electrical safety device designed to protect an electrical circuit from damage caused by an overcurrent or short circuit. Its basic function is to interrupt current flow to protect equipment and to prevent the risk ...
to equally distribute the voltage between these units. These are called "grading capacitors". In schematic diagrams, a capacitor used primarily for DC charge storage is often drawn vertically in circuit diagrams with the lower, more negative, plate drawn as an arc. The straight plate indicates the positive terminal of the device, if it is polarized (see
electrolytic capacitor An electrolytic capacitor is a polarized capacitor whose anode or positive plate is made of a metal that forms an insulating oxide layer through anodization. This oxide layer acts as the dielectric of the capacitor. A solid, liquid, or gel el ...
).


Motor starters

In single phase 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. 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. Motor-starting capacitors are typically non-polarized electrolytic types, while running capacitors are conventional paper or plastic film dielectric types.


Signal processing

The energy stored in a capacitor can be used to represent
information Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
, either in binary form, as in
DRAM Dynamic random-access memory (dynamic RAM or DRAM) is a type of random-access semiconductor memory that stores each bit of data in a memory cell, usually consisting of a tiny capacitor and a transistor, both typically based on metal-oxid ...
s, or in analogue form, as in
analog sampled filter An analog sampled filter an electronic filter that is a hybrid between an analog and a digital filter. The input is an analog signal, and usually stored in capacitors. The time domain is discrete, however. Distinct analog samples are shifted th ...
s and CCDs. Capacitors can be used in
analog circuit Analogue electronics ( en-US, analog electronics) are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two levels. The term "analogue" describes the proportional relati ...
s as components of integrators or more complex filters and in
negative feedback Negative feedback (or balancing feedback) occurs when some function (Mathematics), function of the output of a system, process, or mechanism is feedback, fed back in a manner that tends to reduce the fluctuations in the output, whether caused by ...
loop stabilization. Signal processing circuits also use capacitors to integrate a current signal.


Tuned circuits

Capacitors and inductors are applied together in tuned circuits to select information in particular frequency bands. For example,
radio receiver In radio communications, a radio receiver, also known as a receiver, a wireless, or simply a radio, is an electronic device that receives radio waves and converts the information carried by them to a usable form. It is used with an antenna. Th ...
s rely on variable capacitors to tune the station frequency. Speakers use passive analog
crossovers Crossover may refer to: Entertainment Albums and songs * ''Cross Over'' (Dan Peek album) * ''Crossover'' (Dirty Rotten Imbeciles album), 1987 * ''Crossover'' (Intrigue album) * ''Crossover'' (Hitomi Shimatani album) * ''Crossover'' (Yoshino ...
, and analog equalizers use capacitors to select different audio bands. The
resonant frequency Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
''f'' of a tuned circuit is a function of the inductance (''L'') and capacitance (''C'') in series, and is given by: f = \frac where is in
henries The henry (symbol: H) is the unit of electrical inductance in the International System of Units (SI). If a current of 1 ampere flowing through a coil produces flux linkage of 1 weber turn, that coil has a self inductance of 1 henry.‌ The unit ...
and is in farads.


Sensing

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
sense A sense is a biological system used by an organism for sensation, the process of gathering information about the world through the detection of Stimulus (physiology), stimuli. (For example, in the human body, the brain which is part of the cen ...
those factors. ;Changing the dielectric: :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 An airplane or aeroplane (informally plane) is a fixed-wing aircraft that is propelled forward by thrust from a jet engine, propeller, or rocket engine. Airplanes come in a variety of sizes, shapes, and wing configurations. The broad spe ...
s; as the fuel covers more of a pair of plates, the circuit capacitance increases. Squeezing the dielectric can change a capacitor at a few tens of bar pressure sufficiently that it can be used as a pressure sensor. A selected, but otherwise standard, polymer dielectric capacitor, when immersed in a compatible gas or liquid, can work usefully as a very low cost pressure sensor up to many hundreds of bar. ;Changing the distance between the plates: :Capacitors with a flexible plate can be used to measure strain or pressure. Industrial pressure transmitters used for
process control An industrial process control in continuous production processes is a discipline that uses industrial control systems to achieve a production level of consistency, economy and safety which could not be achieved purely by human manual control. I ...
use pressure-sensing diaphragms, which form a capacitor plate of an oscillator circuit. Capacitors are used as the
sensor A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon. In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
in
condenser microphone A microphone, colloquially called a mic or mike (), is a transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, hearing aids, public address systems for concert halls and public ...
s, where one plate is moved by air pressure, relative to the fixed position of the other plate. Some
accelerometer An accelerometer is a tool that measures proper acceleration. Proper acceleration is the acceleration (the rate of change of velocity) of a body in its own instantaneous rest frame; this is different from coordinate acceleration, which is accele ...
s use
MEMS Microelectromechanical systems (MEMS), also written as micro-electro-mechanical systems (or microelectronic and microelectromechanical systems) and the related micromechatronics and microsystems constitute the technology of microscopic devices, ...
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 An airbag is a vehicle occupant-restraint system using a bag designed to inflate extremely quickly, then quickly deflate during a collision. It consists of the airbag cushion, a flexible fabric bag, an inflation module, and an impact sensor. Th ...
deployment, and in many other applications. Some fingerprint sensors use capacitors. Additionally, a user can adjust the pitch of a
theremin The theremin (; originally known as the ætherphone/etherphone, thereminophone or termenvox/thereminvox) is an electronic musical instrument controlled without physical contact by the performer (who is known as a thereminist). It is named afte ...
musical instrument by moving their hand since this changes the effective capacitance between the user's hand and the antenna. ;Changing the effective area of the plates: :Capacitive
touch switch A touch switch is a type of switch In electrical engineering, a switch is an electrical component that can disconnect or connect the conducting path in an electrical circuit, interrupting the electric current or diverting it from one conductor ...
es are now used on many consumer electronic products.


Oscillators

A capacitor can possess spring-like qualities in an oscillator circuit. In the image example, a capacitor acts to influence the biasing voltage at the npn transistor's base. The resistance values of the voltage-divider resistors and the capacitance value of the capacitor together control the oscillatory frequency.


Producing light

A light-emitting capacitor is made from a dielectric that uses
phosphorescence Phosphorescence is a type of photoluminescence related to fluorescence. When exposed to light (radiation) of a shorter wavelength, a phosphorescent substance will glow, absorbing the light and reemitting it at a longer wavelength. Unlike fluo ...
to produce light. If one of the conductive plates is made with a transparent material, the light is visible. Light-emitting capacitors are used in the construction of electroluminescent panels, for applications such as backlighting for laptop computers. In this case, the entire panel is a capacitor used for the purpose of generating light.


Hazards and safety

The hazards posed by a capacitor are usually determined, foremost, by the amount of energy stored, which is the cause of things like electrical burns or heart
fibrillation Fibrillation is the rapid, irregular, and unsynchronized contraction of muscle fibers. An important occurrence is with regard to the heart. Cardiology There are two major classes of cardiac fibrillation: atrial fibrillation and ventricular fib ...
. Factors such as voltage and chassis material are of secondary consideration, which are more related to how easily a shock can be initiated rather than how much damage can occur. Under certain conditions, including conductivity of the surfaces, preexisting medical conditions, the humidity of the air, or the pathways it takes through the body (i.e.: shocks that travel across the core of the body and, especially, the heart are more dangerous than those limited to the extremities), shocks as low as one joule have been reported to cause death, although in most instances they may not even leave a burn. Shocks over ten joules will generally damage skin, and are usually considered hazardous. Any capacitor that can store 50 joules or more should be considered potentially lethal. Capacitors may retain a charge long after power is removed from a circuit; this charge can cause dangerous or even potentially fatal 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, has a capacitor which may contain over 15 joules of energy and 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 shorted, as protection from potentially dangerous voltages due to
dielectric absorption Dielectric absorption is the name given to the effect by which a capacitor, that has been charged for a long time, discharges only incompletely when briefly discharged. Although an ideal capacitor would remain at zero volts after being discharged, r ...
or from transient voltages the capacitor may pick up from static charges or passing weather events. Some old, large oil-filled paper or plastic film capacitors contain
polychlorinated biphenyl Polychlorinated biphenyls (PCBs) are highly carcinogenic chemical compounds, formerly used in industrial and consumer products, whose production was banned in the United States by the Toxic Substances Control Act in 1979 and internationally by t ...
s (PCBs). It is known that waste PCBs can leak into
groundwater Groundwater is the water present beneath Earth's surface in rock and soil pore spaces and in the fractures of rock formations. About 30 percent of all readily available freshwater in the world is groundwater. A unit of rock or an unconsolidate ...
under
landfill A landfill site, also known as a tip, dump, rubbish dump, garbage dump, or dumping ground, is a site for the disposal of waste materials. Landfill is the oldest and most common form of waste disposal, although the systematic burial of the waste ...
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 A fluorescent lamp, or fluorescent tube, is a low-pressure mercury-vapor gas-discharge lamp that uses fluorescence to produce visible light. An electric current in the gas excites mercury vapor, which produces short-wave ultraviolet lig ...
ballasts, and other applications. Capacitors may catastrophically fail when subjected to voltages or currents beyond their rating, or as they reach their normal end of life. Dielectric or metal interconnection failures may create arcing that vaporizes the dielectric fluid, resulting in case bulging, rupture, or even an
explosion An explosion is a rapid expansion in volume associated with an extreme outward release of energy, usually with the generation of high temperatures and release of high-pressure gases. Supersonic explosions created by high explosives are known ...
. Capacitors used in RF or sustained high-current applications can overheat, especially in the center of the capacitor rolls. Capacitors used within high-energy capacitor banks can violently explode when a short in one capacitor causes sudden dumping of energy stored in the rest of the bank into the failing unit. High voltage vacuum capacitors can generate soft X-rays even during normal operation. Proper containment, fusing, and preventive maintenance can help to minimize these hazards. High-voltage capacitors may benefit from a
pre-charge Pre-charge of the powerline voltages in a high voltage DC application is a preliminary mode which limits the inrush current during the power up procedure. A high-voltage system with a large capacitive load can be exposed to high electric curren ...
to limit in-rush currents at power-up of high voltage direct current (HVDC) circuits. This extends the life of the component and may mitigate high-voltage hazards. File:Defekte Kondensatoren.jpg, Swollen electrolytic capacitors – the special design of the capacitor tops allows them to vent instead of bursting violently. File:High-energy capacitor from a defibrillator 42 MFD @ 5000 VDC.jpg, This high-energy capacitor from a
defibrillator Defibrillation is a treatment for life-threatening cardiac arrhythmias, specifically ventricular fibrillation (V-Fib) and non-perfusing ventricular tachycardia (V-Tach). A defibrillator delivers a dose of electric current (often called a ''coun ...
has a resistor connected between the terminals for safety, to dissipate stored energy. File:Exploded Electrolytic Capacitor.jpg, Catastrophic failure of a capacitor has scattered fragments of paper and metallic foil


See also

*
Capacitance meter A capacitance meter is a piece of electronic test equipment used to measure capacitance, mainly of discrete capacitors. Depending on the sophistication of the meter, it may display the capacitance only, or it may also measure a number of other p ...
*
Capacitor plague The capacitor plague was a problem related to a higher-than-expected failure rate of non-solid aluminium electrolytic capacitors, between 1999 and 2007, especially those from some Taiwanese manufacturers, due to faulty electrolyte composition t ...
*
Electric displacement field In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in ...
*
Electroluminescence Electroluminescence (EL) is an optical phenomenon, optical and electrical phenomenon, in which a material emits light in response to the passage of an electric current or to a strong electric field. This is distinct from black body light emissi ...
* List of capacitor manufacturers


Notes


References


Bibliography

* * Philosophical Transactions of the Royal Society LXXII, Appendix 8, 1782 (Volta coins the word ''condenser'') * * *


Further reading

* ''Tantalum and Niobium-Based Capacitors – Science, Technology, and Applications''; 1st Ed; Yuri Freeman; Springer; 120 pages; 2018; . * ''Capacitors''; 1st Ed; R. P. D. Eshpande; McGraw-Hill; 342 pages; 2014; . * ''The Capacitor Handbook''; 1st Ed; Cletus Kaiser; Van Nostrand Reinhold; 124 pages; 1993; . * ''Understanding Capacitors and their Uses''; 1st Ed; William Mullin; Sams Publishing; 96 pages; 1964. (archive)
/small> * ''Fixed and Variable Capacitors''; 1st Ed; G. W. A. Dummer and Harold Nordenberg; Maple Press; 288 pages; 1960. (archive)
/small> * ''The Electrolytic Capacitor''; 1st Ed; Alexander Georgiev; Murray Hill Books; 191 pages; 1945. (archive)
/small>


External links


The First Condenser – A Beer Glass
– SparkMuseum

– Howstuffworks

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