Capacitor

A capacitor is a passive electrical component that stores energy by separating electric charge. A conventional capacitor consists of two conductors, or electrodes, separated by an insulating dielectric. When a voltage is applied, opposite charges accumulate on the electrodes and energy is stored in the electric field between them. Capacitors are used for energy storage, power-supply stabilization, signal filtering, timing, and many other functions in electrical and electronic circuits. Their defining property is capacitance, which relates stored charge to the voltage across the component. (openstax.org)

Capacitance and physical principles

For an ideal linear capacitor,

where $Q$ is the magnitude of charge on either electrode, $V$ is the potential difference between the electrodes, and $C$ is the capacitance. The two electrodes ordinarily carry charges $+Q$ and $-Q$: charging separates charge rather than necessarily giving the capacitor as a whole a net charge. Capacitance is measured in farads, symbol F, in the International System of Units:

The C on the right denotes the coulomb, the unit of charge. Common component values are expressed in picofarads, nanofarads, and microfarads. (openstax.org)

For two parallel plates of area $A$, separated by a distance $d$ and filled with a uniform linear dielectric,

where $\varepsilon$ is the dielectric’s permittivity. This approximation neglects fringing fields at the plate edges and is most accurate when the separation is small compared with the plate dimensions. Greater electrode area, smaller separation, and higher permittivity increase capacitance. Practical capacitors use rolled foils, stacked layers, or enlarged electrode surfaces to achieve substantial capacitance in a compact volume. (openstax.org)

A dielectric responds to an applied field through the displacement or alignment of bound charges. This response allows more electrode charge to be stored at a given voltage than would be possible with the same geometry in vacuum. However, an insulating material can withstand only a finite field before electrical breakdown occurs; reducing dielectric thickness therefore creates a trade-off between capacitance and voltage withstand capability. (tdk.com)

Stored energy

The energy stored in an ideal capacitor with constant capacitance is

Charging requires work because additional charge must be moved against an increasing voltage. For a linear dielectric, the corresponding electric-field energy density is

where $E$ is the field magnitude. These expressions assume linear behavior; a nonlinear device requires an energy calculation based on its actual charge–voltage relation. (openstax.org)

Unlike a conventional battery, which stores energy principally through electrochemical changes, an ordinary dielectric capacitor stores energy through charge separation and dielectric response. Capacitors generally provide rapid charge and discharge but store less energy per unit mass or volume than batteries. Electrochemical supercapacitors occupy an intermediate technological category, and some of them also use reversible charge-transfer reactions. (murata.com)

Behavior in electrical circuits

Current and changing voltage

For constant capacitance, the current entering the positively referenced terminal is

Thus, current flows when the capacitor voltage changes. An ideal capacitor carrying finite current cannot undergo an instantaneous voltage change; its voltage depends on the accumulated charge. Under steady direct-current conditions, after charging is complete, it behaves as an open circuit. Real capacitors retain some leakage current. (openstax.org)

Charging and discharging

A capacitor connected to a constant source voltage $V_s$ through an electrical resistance $R$ forms an RC circuit. If initially uncharged,

If instead a capacitor initially at voltage $V_0$ discharges through the resistor,

The product

is the circuit’s time constant. After one time constant, charging reaches about 63.2% of its final voltage, or discharging falls to about 36.8% of its initial voltage. The exponential behavior underlies timing circuits and many filtering applications. During discharge through a resistor, the stored energy is converted into heat. (openstax.org)

Alternating current

In sinusoidal steady state, an ideal capacitor has impedance

where $j^2=-1$ and $\omega=2\pi f$. Its capacitive reactance has magnitude

Current leads voltage by $90^\circ$. Consequently, an ideal capacitor offers less opposition to higher-frequency alternating current than to lower-frequency current. This frequency dependence enables filtering and coupling between circuit stages. It does not mean that a real capacitor passes all high-frequency signals equally well, because parasitic inductance eventually becomes important. (openstax.org)

Series and parallel connections

Capacitors in parallel share the same voltage, and their capacitances add:

For capacitors in series,

In the usual ideal series arrangement with initially uncharged intermediate nodes, each capacitor carries the same charge magnitude. Its voltage is inversely proportional to its capacitance. Series connection therefore reduces equivalent capacitance, whereas parallel connection increases it. (openstax.org)

Main types

Ceramic capacitors

Ceramic capacitors use ceramic dielectrics. Multilayer ceramic capacitors, commonly abbreviated MLCCs, contain alternating dielectric and electrode layers connected to provide many capacitive sections in parallel. Their small size and high-frequency performance make them common in electronic equipment. (corporate.murata.com)

Two broad dielectric classes have different characteristics:

• Class 1, including C0G/NP0 types, emphasizes stability and low loss, generally at lower capacitance per unit volume.
• Class 2, including X7R and X5R types, provides higher capacitance density, but capacitance depends more strongly on temperature, applied voltage, and material history.

For Class 2 devices, the effective capacitance under DC bias may be substantially below the nominal value measured under specified test conditions. (murata.com)

Film capacitors

Film capacitors use thin plastic films, such as polypropylene or polyester, with separate metal foils or deposited metal electrodes. Their characteristics depend on the polymer and construction. Polypropylene types are particularly associated with low dielectric loss and high insulation resistance. Film capacitors serve in pulse circuits, power conversion, and AC applications. (tdk.com)

Many metallized-film capacitors are self-healing: a localized dielectric breakdown vaporizes nearby metallization, electrically isolating the defective region. This restores insulation around the fault, although repeated events can progressively reduce capacitance. Self-healing is a construction-dependent property, not a feature of every film capacitor. (tdk-electronics.tdk.com)

Electrolytic capacitors

Electrolytic capacitors use a thin oxide dielectric formed on a metal electrode, together with an electrolyte or another conducting cathode system. Aluminum electrolytic capacitors provide large capacitance in a relatively compact package; other families include tantalum and conductive-polymer types. (openstax.org)

Most electrolytic capacitors are polarized: correct operation depends on the specified terminal polarity. Reverse voltage can damage the oxide dielectric. Their capacitance, losses, frequency response, and lifetime characteristics differ substantially among technologies, so “electrolytic” does not describe a single uniform performance class. (openstax.org)

Supercapacitors

Supercapacitors, also called ultracapacitors, achieve high capacitance through electrode–electrolyte interfaces and, in some designs, reversible faradaic processes. Principal categories include:

• Electric double-layer capacitors, which store charge through interfacial charge separation.
• Pseudocapacitors, which use rapid, reversible charge-transfer processes.
• Hybrid electrochemical capacitors, which combine different storage mechanisms.

They are useful where rapid response, high power output, and repeated cycling matter. Compared with batteries, their limitations generally include lower energy density and appreciable self-discharge. (energy.gov)

Variable and integrated capacitors

Variable capacitors permit adjustment of capacitance for tuning or calibration. Adjustment may be mechanical or electronic; some devices provide digitally selectable capacitance values. Capacitors can also be fabricated as silicon-based components or incorporated into integrated passive structures. (murata.com)

Applications

Capacitors perform several distinct circuit functions:

• Power-supply smoothing and decoupling: supplying or absorbing transient charge to limit voltage fluctuations, including near integrated circuits.
• Signal coupling: transferring changing signals between stages while blocking their steady DC voltage difference.
• Filtering: directing selected frequency components through different paths, a basic operation in signal processing.
• Timing: producing controlled charging and discharging intervals in RC networks.
• Tuning and resonance: interacting with an inductor to select frequencies in resonant circuits.
• Pulse-energy storage: accumulating energy for rapid release, including photographic flashes and defibrillator circuits.
• Power-system functions: supporting power-factor correction, power converters, and the operation of certain AC motors. (murata.com)

Real behavior, limitations, and failure

An ideal capacitor is lossless and has constant capacitance. Real components depart from this model in several important ways:

Leakage. Finite insulation resistance allows a small current under steady voltage and gradually reduces stored charge. Leakage is especially significant in high-impedance circuits and applications that must retain a voltage for long periods. (analog.com)

Equivalent series resistance. Equivalent series resistance (ESR) represents dissipative effects associated with electrodes, dielectric losses, and other parts of the component. It produces heating and limits performance under alternating or ripple current. ESR is generally frequency-dependent. (article.murata.com)

Equivalent series inductance. Electrode geometry, terminals, and leads contribute parasitic inductance. Together with capacitance, it produces a self-resonant frequency. Above that frequency, the component’s impedance can become predominantly inductive rather than capacitive. (article.murata.com)

Dielectric absorption. Dielectric absorption is a memory effect in which some terminal voltage reappears after a charged capacitor has been briefly discharged and then left open-circuit. It can introduce errors in precision integrators and circuits that hold sampled analog voltages. (analog.com)

Environmental and operating dependence. Capacitance and losses can change with temperature, applied voltage, aging, and mechanical conditions. Ceramic capacitors can develop internal cracks under mechanical or thermal stress; cracks reaching the electrode region may lead to leakage or short-circuit failure. (analog.com)

A capacitor’s nominal capacitance alone therefore does not fully describe it. Voltage rating, capacitance tolerance, temperature behavior, leakage, ESR, frequency characteristics, construction, and expected service conditions are also relevant specifications. Capacitors may retain substantial stored energy after their external power source is disconnected, and dielectric absorption can cause voltage to return after an initial discharge. (murata.com)

Historical development

An early practical charge-storage device was the Leyden jar, developed in the mid-1740s. In its familiar form, conducting layers on the inside and outside of a glass vessel act as electrodes, while the glass serves as the dielectric. Such devices made it possible to accumulate charge for experiments in electrostatics. (collection.sciencemuseumgroup.org.uk)

Later capacitor technologies replaced bulky vessels with compact layered or wound structures. Thin plastic films enabled low-loss film capacitors; oxide dielectrics supported high-capacitance electrolytic devices; and multilayer ceramic construction combined miniaturization with high-frequency performance. These different construction principles remain distinct because they address different combinations of capacitance, voltage, loss, stability, and physical size. (tdk.com)

References

1. 1 Capacitors and Capacitance — University Physics Volume 2openstax.org
2. 2 Capacitors in Series and in Parallel — University Physics Volume 2openstax.org
3. 3 Energy Stored in a Capacitor — University Physics Volume 2openstax.org
4. 5 RC Circuits — University Physics Volume 2openstax.org
5. 11 Reactance, Inductive and Capacitive — College Physics 2eopenstax.org
6. 3 RLC Series Circuits with AC — University Physics Volume 2openstax.org
7. Basics of Ceramic Capacitors — Muratamurata.com
8. Capacitor Selection Guide — Muratamurata.com
9. High Reliability and High Performance Enabled by Murata’s Multilayer Ceramic Capacitor (MLCC) Lineupcorporate.murata.com
10. Film Capacitors (Part 5, Vol. 2): Structure & Features — TDKtdk.com
11. Film Capacitors — General Technical Information — TDKtdk-electronics.tdk.com