The term was first used for this purpose by Alessandro Volta in , with reference to the device's ability to store a higher density of electric charge than was possible with an isolated conductor. Since the beginning of the study of electricity non conductive materials like glass , porcelain , paper and mica have been used as insulators.
These materials some decades later were also well-suited for further 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 ,  and they were used from the early 20th century as decoupling capacitors in telecommunications telephony.
Porcelain was used in the first ceramic capacitors. In the early years of Marconi 's wireless transmitting apparatus porcelain capacitors were used for high voltage and high frequency application in the transmitters. On the receiver side smaller mica capacitors were used for resonant circuits. Mica dielectric capacitors were invented in by William Dubilier.
Charles Pollak born Karol Pollak , the inventor of the first electrolytic capacitors , found out that the oxide layer on an aluminum anode remained stable in a neutral or alkaline electrolyte , even when the power was switched off. In he was granted U. With the development of plastic materials by organic chemists during the Second World War , the capacitor industry began to replace paper with thinner polymer films. One very early development in film capacitors was described in British Patent , in Last but not least the electric double-layer capacitor now Supercapacitors were invented.
Becker developed a "Low voltage electrolytic capacitor with porous carbon electrodes". Because the double layer mechanism was not known by him at the time, he wrote in the patent: A capacitor consists of two conductors separated by a non-conductive region.
Examples of dielectric media are glass, air, paper, plastic, ceramic, and even a semiconductor depletion region chemically identical to the conductors. From Coulomb's law a charge on one conductor will exert a force on the charge carriers 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 C , in farads 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: A capacitance of one farad F means that one coulomb of charge on each conductor causes a voltage of one volt across the device.
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:. In the hydraulic analogy , charge carriers flowing through a wire are analogous to water flowing through a pipe. A capacitor is like a rubber membrane sealed inside a pipe.
Water molecules cannot pass through the membrane, but some water can move by stretching the membrane. The analogy clarifies a few aspects of capacitors:. 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. Therefore, in a capacitor the highest capacitance is achieved with a high permittivity dielectric material, large plate area, and small separation between the plates.
A parallel plate capacitor can only store a finite amount of energy before dielectric breakdown occurs. The maximum energy that the capacitor can store is therefore. The maximum energy is a function of dielectric volume, permittivity , and dielectric strength. 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. For some simple capacitor geometries this additional capacitance term can be calculated analytically. As shown to the figure on the right, the interleaved plates can be seen as parallel plates connected to each other. With the number of capacitor equal to the number of the spaces in between the plates. To increase the charge and voltage on a capacitor, work 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.
The energy is stored in the increased electric field between the plates. The total energy stored in a capacitor is equal to the total work done in establishing the electric field from an uncharged state.
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.
In this case the stored energy can be calculated from the electric field strength. 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. The current I t through any component in an electric circuit is defined as the rate of flow of a charge Q t passing through it, but actual charges—electrons—cannot pass through the dielectric layer of a capacitor.
Rather, 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 of the current as well as proportional to the voltage, as discussed above.
As with any antiderivative , a constant of integration is added to represent the initial voltage V t 0. This is the integral form of the capacitor equation: Taking the derivative of this and multiplying by C yields the derivative form: The dual of the capacitor is the inductor , which stores energy in a magnetic field rather than an electric field. A series circuit containing only a resistor , a capacitor, a switch and a constant DC source of voltage V 0 is known as a charging circuit.
Taking the derivative and multiplying by C , gives a first-order differential equation:. With this assumption, solving the differential equation yields. 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 V Ci replaces V 0. 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 allows any signal to be constructed from a spectrum of frequencies, whence the circuit's reaction to the various frequencies may be found. The reactance and impedance of a capacitor are respectively. Impedance decreases with increasing capacitance and increasing frequency. This implies that a higher-frequency signal or a larger capacitor results in a lower voltage amplitude per current amplitude—an AC "short circuit" or AC coupling.
Conversely, for very low frequencies, the reactance 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. A capacitor connected to a sinusoidal voltage source causes a displacement current to flow through it. The ratio of peak voltage to peak current is due to capacitive reactance denoted X C. If X C approaches 0, the capacitor resembles a short wire that strongly passes current at high frequencies.
If X C 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:.
When using the Laplace transform in circuit analysis, the impedance of an ideal capacitor with no initial charge is represented in the s domain by:. Capacitors deviate from the ideal capacitor equation in a number of ways.
Some of these, such as leakage current and parasitic effects are linear, or can be analyzed as nearly linear, and can be dealt with by adding virtual components to the equivalent circuit of an ideal capacitor. The usual methods of network analysis can then be applied. In other cases, such as with breakdown voltage, the effect is non-linear and ordinary normal, e.
There is yet another group, which may be linear but invalidate the assumption in the analysis that capacitance is a constant. Such an example is temperature dependence. Finally, combined parasitic effects such as inherent inductance, resistance, or dielectric losses can exhibit non-uniform behavior at variable frequencies of operation.
Above a particular electric field, known as the dielectric strength E ds , 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, . The maximum energy that can be stored safely in a capacitor is limited by the breakdown voltage.
Due to the scaling of capacitance and breakdown voltage with dielectric thickness, all capacitors made with a particular dielectric have approximately equal maximum energy density , to the extent that the dielectric dominates their volume. 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. 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 as seen in semi-conductor devices.
Breakdown voltage is also affected by pressure, humidity and temperature. An ideal capacitor only stores and releases electrical energy, without dissipating any. In reality, all capacitors have imperfections within the capacitor's material that create resistance.
This is specified as the equivalent series resistance or ESR of a component. This adds a real component to the impedance:. As frequency approaches infinity, the capacitive impedance or reactance approaches zero and the ESR becomes significant. This is usually significant only at relatively high frequencies.
As inductive reactance is positive and increases with frequency, above a certain frequency capacitance is canceled by inductance. 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 time may vary greatly depending on the capacitor material and quality. The quality factor or Q of a capacitor is the ratio of its reactance to its resistance at a given frequency, and is a measure of its efficiency. The higher the Q factor of the capacitor, the closer it approaches the behavior of an ideal capacitor. Ripple current is the AC component of an applied source often a switched-mode power supply whose frequency may be constant or varying.
Ripple current causes heat to be generated within the capacitor due to the dielectric losses caused by the changing field strength together with the current flow across the slightly resistive supply lines or the electrolyte in the capacitor. The equivalent series resistance ESR is the amount of internal series resistance one would add to a perfect capacitor to model this. Some types of capacitors , primarily tantalum and aluminum electrolytic capacitors , as well as some film capacitors have a specified rating value for maximum ripple current.
The capacitance of certain capacitors decreases as the component ages. In ceramic capacitors , this is caused by degradation of the dielectric. The type of dielectric, ambient operating and storage temperatures are the most significant aging factors, while the operating voltage has a smaller effect. The aging process may be reversed by heating the component above the Curie point. Aging is fastest near the beginning of life of the component, and the device stabilizes over time.
In contrast with ceramic capacitors, this occurs towards the end of life of the component. 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 effect.
Vibration moves the plates, causing the capacitance to vary, in turn inducing AC current. Some dielectrics also generate piezoelectricity. The resulting interference is especially problematic in audio applications, potentially causing feedback or unintended recording. In the reverse microphonic effect, the varying electric field between the capacitor plates exerts a physical force, moving them as a speaker.
This can generate audible sound, but drains energy and stresses the dielectric and the electrolyte, if any. 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 and pulsed circuits, current and voltage reversal are affected by the damping of the system. Voltage reversal is encountered in RLC circuits that are underdamped. The current and voltage reverse direction, forming a harmonic oscillator between the inductance 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. In comparison, critically damped or overdamped 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. 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.
Capacitors made with any type of dielectric material show some level of " dielectric absorption " or "soakage".
On discharging a capacitor and disconnecting it, after a short time it may develop a voltage due to hysteresis in the dielectric. This effect is objectionable in applications such as precision sample and hold 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 film exhibit relatively high absorption, while polystyrene or Teflon allow very small levels of absorption. 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. 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. Aluminum electrolytic capacitors 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.
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. 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. 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 as possible, while also having as high a breakdown voltage 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 capacitors 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 , plastic , glass , mica and ceramic. 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 capacitors. 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 temperatures 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 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 supercapacitors are used to store small and larger amounts of energy, respectively, ceramic capacitors are often used in resonators , and parasitic capacitance occurs in circuits wherever the simple conductor-insulator-conductor structure is formed unintentionally by the configuration of the circuit layout.
Electrolytic capacitors use an aluminum or tantalum plate with an oxide dielectric layer. The second electrode is a liquid electrolyte , connected to the circuit by another foil plate. Electrolytic capacitors offer very high capacitance but suffer from poor tolerances, high instability, gradual loss of capacitance especially when subjected to heat, and high leakage current.
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 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 and leakage.
A feedthrough capacitor 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.
Supercapacitors store large amounts of energy. Alternating current capacitors are specifically designed to work on line mains voltage AC power circuits. They are commonly used in electric motor circuits and are often designed to handle large currents, so they tend to be physically large.
They also are designed with direct current breakdown voltages of at least five times the maximum AC voltage. The dielectric constant for a number of very useful dielectrics changes as a function of the applied electrical field, for example ferroelectric 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:. 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 V an integral relation is found:. 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 such as semiconductor diodes , 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.
Sze This effect is intentionally exploited in diode-like devices known as varicaps. 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 , and is governed by dielectric relaxation processes, such as Debye relaxation. Under transient conditions, the displacement field can be expressed as see electric susceptibility:. See, for example, linear response function. A Fourier transform in time then results 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:. When a parallel-plate capacitor is filled with a dielectric, the measurement of dielectric properties of the medium is based upon the relation:.
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 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. 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.
Protection for synchronous motors is similar to that employed with large induction motors. Temperature may be sensed in both the stator and field windings and used to switch off the electric supply. Considerable heating occurs in the rotor-damper winding during starting, and a timer is frequently installed to prevent repeated starts within a limited time interval. We welcome suggested improvements to any of our articles. You can make it easier for us to review and, hopefully, publish your contribution by keeping a few points in mind.
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Please note that our editors may make some formatting changes or correct spelling or grammatical errors, and may also contact you if any clarifications are needed. Synchronous motors A synchronous motor is one in which the rotor normally rotates at the same speed as the revolving field in the machine. Previous page Linear induction motors.
Page 5 of 6. Next page Permanent-magnet motors. Learn More in these related Britannica articles: Other important energy-conversion devices emerged during the 19th century. During the early s the English physicist and chemist Michael Faraday discovered a means by which to convert mechanical energy into electricity on a large scale.
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Help us improve this article! Contact our editors with your feedback. Introduction Induction motors Construction of induction motors Starting characteristics Protection Wound-rotor induction motors Single-phase induction motors Capacitor induction motor Split-phase motors Shaded-pole motors Servomotors Linear induction motors Induction motors for speed and position control Synchronous motors Permanent-magnet motors Hysteresis motors Reluctance motors Single-phase synchronous motors Direct-current commutator motors Alternating-current commutator motors.
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