Capacitor
A capacitor is an electrical/electronic device that can store energy in the electric field between a pair of conductors (called "plates"). The process of storing energy in the capacitor is known as "charging", and involves electric charges of equal magnitude, but opposite polarity, building up on each plate.
Capacitors are often used in electric and electronic circuits as energy-storage devices. They can also be used to differentiate between high-frequency and low-frequency signals. This property makes them useful in electronic filters.
Capacitors are occasionally referred to as condensers. This is considered an antiquated term in English, but most other languages use an equivalent, like "Kondensator" in German, "condensador" in Spanish, or "Kondensa" in Japanese.
History
In October 1745, Ewald Georg von Kleist of Pomerania in Germany invented the first recorded capacitor: a glass jar with water inside as one plate was held on the hand as the other plate. A wire in the mouth of the bottle received charge from an electric machine, and released it as a spark.[1]
In the same year, Dutch physicist Pieter van Musschenbroek independently invented a very similar capacitor. It was named the Leyden jar, after the University of Leyden where van Musschenbroek worked. Daniel Gralath was the first to combine several jars in parallel into a "battery" to increase the charge storage capacity.
Benjamin Franklin investigated the Leyden jar, and proved that the charge was stored on the glass, not in the water as others had assumed. The earliest unit of capacitance was the 'jar', equivalent to about 1 nanofarad.
Early capacitors were also known as condensers, a term that is still occasionally used today. It was coined by Alessandro Volta in 1782 (derived from the Italian condensatore), with reference to the device's ability to store a higher density of electric charge than a normal isolated conductor. Most non-English European languages still use a word derived from "condensatore".
Physics
A capacitor consists of two conductive electrodes, or plates, separated by a dielectric.
Capacitance
The capacitor's capacitance (C) is a measure of the amount of charge (Q) stored on each plate for a given potential difference or voltage (V) which appears between the plates:
- <math>C = {Q \over V}</math>
In SI units, a capacitor has a capacitance of one farad when one coulomb of charge is stored due to one volt applied potential difference across the plates. Since the farad is a very large unit, values of capacitors are usually expressed in microfarads (µF), nanofarads (nF), or picofarads (pF).
The capacitance is proportional to the surface area of the conducting plate and inversely proportional to the distance between the plates. It is also proportional to the permittivity of the dielectric (that is, non-conducting) substance that separates the plates.
The capacitance of a parallel-plate capacitor is given by:
- <math>C \approx \frac{\varepsilon A}{d}; A \gg d^2</math>[2]
where ε is the permittivity of the dielectric (see Dielectric constant), A is the area of the plates and d is the spacing between them.
In the diagram, the rotated molecules create an opposing electric field that partially cancels the field created by the plates, a process called dielectric polarization.
Stored energy
As opposite charges accumulate on the plates of a capacitor due to the separation of charge, a voltage develops across the capacitor due to the electric field of these charges. Ever-increasing work must be done against this ever-increasing electric field as more charge is separated. The energy (measured in joules, in SI) stored in a capacitor is equal to the amount of work required to establish the voltage across the capacitor, and therefore the electric field. The energy stored is given by:
- <math> E_\mathrm{stored} = {1 \over 2} C V^2 = {1 \over 2} {Q^2 \over C} = {1 \over 2} {V Q} </math>
where V is the voltage across the capacitor.
The maximum energy that can be (safely) stored in a particular capacitor is limited by the maximum electric field that the dielectric can withstand before it breaks down. Therefore, capacitors made with the same dielectric have about the same maximum energy density (joules of energy per cubic meter), if the dielectric volume dominates the total volume.
Hydraulic model
As electrical circuitry can be modeled by fluid flow, a capacitor can be modeled as a chamber with a flexible diaphragm separating the input from the output. As can be determined intuitively as well as mathematically, this provides the correct characteristics:
- The pressure difference (voltage difference) across the unit is proportional to the integral of the flow (current).
- A steady state current cannot pass through it because the pressure will build up across the diaphragm until it equally opposes the source pressure,
- but a transient pulse or alternating current can be transmitted.
- An overpressure results in bursting of the diaphragm, analogous to dielectric breakdown.
- The capacitance of units connected in parallel is equivalent to the sum of their individual capacitances.
Aging
Certain types of capacitors exhibit decreased capacitance over time. The behavior is different for different types: ceramic capacitors change most near the beginning of life, whereas electrolytic capacitors change most near the end of life.
Ceramic capacitor aging
In ceramic capacitors, the change in capacitance over time, called aging, is due to physical changes over time of the dielectric material used in their construction. The critical factors in this type of aging are
- The type of dielectric material used in their construction (with many types this effect is negligible),
- The temperature of the storage and operation environment, and
- (to a small extent) the voltage of operation.
The rate of change of capacitance decreases over time, so the main concern is the initial stabilization, not the long-term lifetime. [3]
Ceramic capacitor aging can be reversed by heating the capacitor above the Curie Point.
Electrolytic capacitor aging
Electrolytic capacitors' capacitance can decrease as the capacitor approaches end of life due to electrolyte evaporation.
Electric circuits
DC sources
The dielectric between the plates is an insulator and blocks the flow of electrons. A steady current through a capacitor deposits electrons on one plate and removes the same quantity of electrons from the other plate. This process is commonly called 'charging' the capacitor. The current through the capacitor results in the separation of electric charge within the capacitor, which develops an electric field between the plates of the capacitor, equivalently, developing a voltage difference between the plates. This voltage V is directly proportional to the amount of charge separated Q. Since the current I through the capacitor is the rate at which charge Q is forced through the capacitor (dQ/dt), this can be expressed mathematically as:
- <math>i(t) = C\frac{dV}{dt}</math>
where I is the current flowing in the conventional direction measured in amperes, dV/dt is the time derivative of voltage measured in volts per second, and C is the capacitance in farads.
For circuits with a constant (DC) voltage source and consisting of only resistors and capacitors, the voltage across the capacitor cannot exceed the voltage of the source. Thus, an equilibrium is reached where the voltage across the capacitor is constant and the current through the capacitor is zero. For this reason, it is commonly said that capacitors block DC.
AC sources
The current through a capacitor due to an AC source reverses direction periodically. That is, the alternating current alternately charges the plates: first in one direction and then the other. With the exception of the instant that the current changes direction, the capacitor current is non-zero at all times during a cycle. For this reason, it is commonly said that capacitors "pass" AC. However, at no time do electrons actually cross between the plates, unless the dielectric breaks down. Such a situation would involve physical damage to the capacitor and likely to the circuit involved as well.
Since the voltage across a capacitor is proportional to the integral of the current, as shown above, with sine waves in AC or signal circuits this results in a phase difference of 90 degrees, the current leading the voltage phase angle. It can be shown that the AC voltage across the capacitor is in quadrature with the alternating current through the capacitor. That is, the voltage and current are 'out-of-phase' by a quarter cycle. The amplitude of the voltage depends on the amplitude of the current divided by the product of the frequency of the current with the capacitance, C.
Impedance
The ratio of the phasor voltage across a circuit element to the phasor current through that element is called the impedance <math>Z</math>. For a capacitor, the impedance is given by
<math>Z_C = \frac{V_C}{I_C} = \frac{-j}{2 \pi f C} = -j X_C ,</math>
where <math>X_C = \frac{1}{\omega C}</math> is the capacitive reactance, <math>\omega = 2 \pi f \,</math> is the angular frequency, f is the frequency), C is the capacitance in farads, and j is the imaginary unit.
While this relation (between the frequency domain voltage and current associated with a capacitor) is always true, the ratio of the time domain voltage and current amplitudes is equal to <math>X_C</math> only for sinusoidal (AC) circuits in steady state.
See derivation Deriving capacitor impedance.
Hence, capacitive reactance is the negative imaginary component of impedance. The negative sign indicates that the current leads the voltage by 90° for a sinusoidal signal, as opposed to the inductor, where the current lags the voltage by 90°.
The impedance is analogous to the resistance of a resistor. The impedance of a capacitor is inversely proportional to the frequency -- that is, for very high-frequency alternating currents the reactance approaches zero -- so that a capacitor is nearly a short circuit to a very high frequency AC source. Conversely, for very low frequency alternating currents, the reactance increases without bound so that a capacitor is nearly an open circuit to a very low frequency AC source. This frequency dependent behaviour accounts for most uses of the capacitor (see "Applications", below).
Reactance is so called because the capacitor doesn't dissipate power, but merely stores energy. In electrical circuits, as in mechanics, there are two types of load, resistive and reactive. Resistive loads (analogous to an object sliding on a rough surface) dissipate the energy delivered by the circuit as heat, while reactive loads (analogous to a spring or frictionless moving object) store this energy, ultimately delivering the energy back to the circuit.
Also significant is that the impedance is inversely proportional to the capacitance, unlike resistors and inductors for which impedances are linearly proportional to resistance and inductance respectively. This is why the series and shunt impedance formulae (given below) are the inverse of the resistive case. In series, impedances sum. In parallel, conductances sum.
Laplace equivalent (s-domain)
When using the Laplace transform in circuit analysis, the capacitive impedance is represented in the s domain by:
<math>Z(s)=\frac{1}{Cs}</math>
where C is the capacitance, and s (= σ+jω) is the complex frequency.
Displacement current
The physicist James Clerk Maxwell invented the concept of displacement current, dD/dt, to make Ampère's law consistent with conservation of charge in cases where charge is accumulating as in a capacitor. He interpreted this as a real motion of charges, even in vacuum, where he supposed that it corresponded to motion of dipole charges in the aether. Although this interpretation has been abandoned, Maxwell's correction to Ampère's law remains valid.
Networks
Series or parallel arrangements
Capacitors in a parallel configuration each have the same potential difference (voltage). Their total capacitance (Ceq) is given by:
- <math> C_{eq} = C_1 + C_2 + \cdots + C_n \,</math>
The reason for putting capacitors in parallel is to increase the total amount of charge stored. In other words, increasing the capacitance also increases the amount of energy that can be stored. Its expression is:
- <math> E_\mathrm{stored} = {1 \over 2} C V^2 .</math>
The current through capacitors in series stays the same, but the voltage across each capacitor can be different. The sum of the potential differences (voltage) is equal to the total voltage. Their total capacitance is given by:
- <math> \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}</math>
In parallel the effective area of the combined capacitor has increased, increasing the overall capacitance. While in series, the distance between the plates has effectively been increased, reducing the overall capacitance.
In practice capacitors will be placed in series as a means of economically obtaining very high voltage capacitors, for example for smoothing ripples in a high voltage power supply. Three "600 volt maximum" capacitors in series, will increase their overall working voltage to 1800 volts. This is of course offset by the capacitance obtained being only one third of the value of the capacitors used. This can be countered by connecting 3 of these series set-ups in parallel, resulting in a 3x3 matrix of capacitors with the same overall capacitance as an individual capacitor but operable under three times the voltage. In this application, a large resistor would be connected across each capacitor to ensure that the total voltage is divided equally across each capacitor and also to discharge the capacitors for safety when the equipment is not in use.
Another application is for use of polarized capacitors in alternating current circuits; the capacitors are connected in series, in reverse polarity, so that at any given time one of the capacitors is not conducting...
Capacitor/inductor duality
In mathematical terms, the ideal capacitor can be considered as an inverse of the ideal inductor, because the voltage-current equations of the two devices can be transformed into one another by exchanging the voltage and current terms. Just as two or more inductors can be magnetically coupled to make a transformer, two or more charged conductors can be electrostatically coupled to make a capacitor. The mutual capacitance of two conductors is defined as the current that flows in one when the voltage across the other changes by unit voltage in unit time.
Capacitor types
Template:Mergeto Template:Cleanup-section
By dielectric material
- Vacuum : Two metal, usually copper, electrodes are separated by a vacuum. The insulating envelope is usually glass or ceramic. Typically of low capacitance - 10 - 1000 pF and high voltage, up to tens of kilovolts, they are most often used in radio transmitters and other high voltage power devices. Both fixed and variable types are available. Vacuum variable capacitors can have a minimum to maximum capacitance ratio of up to 100, allowing any tuned circuit to cover a full decade of frequency. Vacuum is the most perfect of dielectrics with a zero loss tangent. This allows very high powers to be transmitted without significant loss and consequent heating.
- Air : Air dielectric capacitors consist of metal plates separated by an air gap. The metal plates, of which there may be many interleaved, are most often made of aluminium or silver-plated brass. Nearly all air dielectric capacitors are variable and are used in radio tuning circuits.
- Plastic film: Made from high quality polymer film (usually polycarbonate, polystyrene, polypropylene, polyester (Mylar), and for high quality capacitors polysulfone), and metal foil or a layer of metal deposited on surface of the plastic film in a the metalized film type. They have good quality and stability, and are suitable for timer circuits. Their inductance limits use at high frequencies.
- Mica: Similar to glass. Often high voltage. Suitable for high frequencies. Expensive. Excellent tolerance & stability.
- Paper: Used for relatively high voltages. Known for long term failures.
- Glass: Used for high voltages. Expensive. Stable temperature coefficient in a wide range of temperatures.
- Ceramic: Chips of alternating layers of metal and ceramic, or disks of ceramic with metal on both sides of the disk. Characteristics vary widely depending on the type of ceramic dielectric. The dielectrics are broadly categorized as Class 1 or Class 2. Class 2 ceramic capacitors have strong variation of capacitance with temperature, high dissipation factor, high frequency coefficient of dissipation, and their capacitance depends on applied voltage and changes with aging. However they find massive use in common low-precision coupling and filtering applications. Suitable for high frequencies.
- Aluminum electrolytic: Polarized. One electrode made of aluminum foil, etched aluminium to acquire much larger surface area. The dielectric is oxide grown on the etched aluminum plate, and the second electrode is a liquid electrolyte. They can achieve high capacitance but suffer from poor tolerances, high instability, gradual loss of capacitance especially when subjected to heat, and high leakage current. The conductivity of the electrolyte drops at low temperatures, increasing equivalent series resistance. Bad frequency characteristics make them unsuited for high-frequency applications. Special types with low equivalent series resistance are available.
- Tantalum electrolytic: Similar to the aluminum electrolytic capacitor but with better frequency and temperature characteristics. High dielectric absorption and high leakage [4]. Although they share many of the disadvantages of aluminum electrolytics, they perform better on most attributes; for example, they have much better performance at low temperatures.
- OS-CON (or OC-CON) capacitors are a polymerized organic semiconductor solid-electrolyte type that offer longer life at higher cost than standard electrolytics.
- Supercapacitors: Made from carbon aerogel, carbon nanotubes, or highly porous electrode materials. Extremely high capacity. Can be used in some applications instead of rechargeable batteries.
- Varactors or varicap capacitors are specialized, reverse-biased diodes whose capacitance varies with voltage. Used in phase-locked loops, amongst other applications.
- AC capacitors are capacitors specifically designed to work on line (mains) voltage ac power circuits. These are commonly used electric motor circuits. They 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 tend to have rather high DC breakdown voltages;
By construction
- Axial capacitors
- Feedthrough capacitors for RF decoupling usage
- Gimmick capacitors, made from two insulated wires that have been twisted together [2]
- Radial capacitors
- Surface mount (leadless) capacitors
- Trimmer capacitors
- Beehive types
- Compression types
- Tuning capacitor (air spaced)
- Discoidal capacitors
Applications
| Capacitor | Polarized capacitors |
Variable capacitor |
|---|---|---|
| Capacitor symbol | Variable capacitor symbol |
Capacitors have various uses in electronic and electrical systems.
Energy storage
A capacitor can store electric energy when disconnected from its charging circuit, so it can be used like a temporary battery. Capacitors are commonly used in electronic devices to maintain power supply while batteries are being changed. (This prevents loss of information in volatile memory.)
Power conditioning
Reservoir capacitors are used in power supplies where they smooth the output of a full or half wave rectifier. They can also be used in charge pump circuits as the energy storage element in the generation of higher voltages than the input voltage.
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.
Power factor correction
Capacitors are used in power factor correction. Such capacitors often come as three capacitors connected as a three phase load. Usually, the values of these capacitors are given not in farads but rather as a reactive power in volt-amperes reactive (VAr). The purpose is to counteract inductive loading from electric motors and fluorescent lighting in order to make the load appear to be mostly resistive.
Filtering
Signal coupling
Because capacitors pass AC but block DC signals (when charged up to the applied dc voltage), they are often used to separate the AC and DC components of a signal. This method is known as AC coupling or "capacitive coupling". Here, a large value of capacitance, whose value need not be accurately controlled, but whose reactance is small at the signal frequency, is employed.
Decoupling
A decoupling capacitor is a capacitor used to decouple one part of a circuit from another. 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 as it is used to bypass the power supply or other high impedance component of a circuit.
Noise filters, motor starters, 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 will generate a spark, causing the contact points to oxidize, deteriorate, or sometimes weld together, or destroying a solid-state switch. A snubber capacitor across the newly opened circuit creates a path for this impulse to bypass the contact points, thereby preserving their life; these were commonly found in contact breaker ignition systems, for instance. Similarly, in smaller scale circuits, the spark may not be enough to damage the switch but will still radiate undesirable radio frequency interference (RFI), which a filter capacitor absorbs. Snubber capacitors are usually employed with a low-value resistor in series, to dissipate energy and minimize RFI. Such resistor-capacitor combinations are available in a single package.
In an inverse fashion, to initiate current quickly through an inductive circuit requires a greater voltage than required to maintain it; in uses such as large motors, this can cause undesirable startup characteristics, and a motor starting capacitor is used to increase the coil current to help start the motor.
Capacitors are also used in parallel to interrupt units of a high-voltage circuit breaker in order to equally distribute the voltage between these units. In this case they are called grading capacitors.
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).
Signal processing
The energy stored in a capacitor can be used to represent information, either in binary form, as in DRAMs, or in analogue form, as in analog sampled filters and CCDs. Capacitors can be used in analog circuits as components of integrators or more complex filters and in negative feedback 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 receivers rely on variable capacitors to tune the station frequency. Speakers use passive analog crossovers, and analog equalizers use capacitors to select different audio bands.
In a tuned circuit such as a radio receiver, the frequency selected is a function of the inductance (L) and the capacitance (C) in series, and is given by:
- <math>f = \frac{1}{2 \pi \sqrt{LC}}</math>
This is the frequency at which resonance occurs in an LC circuit.
Other applications
Sensing
Most capacitors are designed to maintain a fixed physical structure. However, various factors can change the structure of the capacitor; the resulting change in capacitance can be used to sense those factors.
Changing the dielectric: the effects of varying the physical and/or electrical characteristics of the dielectric can also be of use. Capacitors with an exposed and porous dielectric can be used to measure humidity in air.
Changing the distance between the plates: Capacitors are used to accurately measure the fuel level in airplanes. Capacitors with a flexible plate can be used to measure strain or pressure. Capacitors are used as the sensor in condenser microphones, where one plate is moved by air pressure, relative to the fixed position of the other plate. Some accelerometers use MEMS capacitors etched on a chip to measure the magnitude and direction of the acceleration vector. They are used to detect changes in acceleration, eg. as tilt sensors or to detect free fall, as sensors triggering airbag deployment, and in many other applications. Some fingerprint sensors use capacitors. Additionally, a user can adjust the pitch of a theremin musical instrument by moving his hand since this changes the effective capacitance between the user's hand and the antenna.
Changing the effective area of the plates: capacitive touch switches [3] [4] [5].
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 applications. These include electromagnetic forming, Marx generators, pulsed lasers (especially TEA lasers), pulse forming networks, radar, fusion research, and particle accelerators.
Large capacitor banks(Reservoir) are used as energy sources for the exploding-bridgewire detonators or slapper detonators in nuclear weapons and other specialty weapons. Experimental work is under way using banks of capacitors as power sources for electromagnetic armour and electromagnetic railguns or coilguns.
See also Explosively pumped flux compression generator.
Hazards and safety
Capacitors may retain a charge long after power is removed from a circuit; this charge can cause shocks (sometimes fatal) or damage to connected equipment. For example, even a seemingly innocuous device such as a disposable camera flash unit powered by a 1.5 volt AA battery contains a capacitor which may be charged to over 300 volts. This is easily capable of delivering an extremely painful shock.
Care must be taken to ensure that any large or high-voltage capacitor is properly discharged before servicing the containing equipment. For board-level capacitors, this is done by placing a bleeder resistor across the terminals, whose resistance is large enough that the leakage current will not affect the circuit, but small enough to discharge the capacitor shortly after power is removed. High-voltage capacitors should be stored with the terminals shorted, since temporarily discharged capacitors can develop potentially dangerous voltages when the terminals are left open-circuited.
Large oil-filled old capacitors must be disposed of properly as some contain polychlorinated biphenyls (PCBs). It is known that waste PCBs can leak into groundwater under landfills. If consumed by drinking contaminated water, PCBs are carcinogenic, even in very tiny amounts. If the capacitor is physically large it is more likely to be dangerous and may require precautions in addition to those described above. New electrical components are no longer produced with PCBs. ("PCB" in electronics usually means printed circuit board, but the above usage is an exception.) Capacitors containing PCB were labelled as containing "Askarel" and several other trade names.
High-voltage
Above and beyond usual hazards associated with working with high voltage, high energy circuits, there are a number of dangers that are specific to high voltage capacitors. High voltage 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 called an arc fault, within oil-filled units that vaporizes dielectric fluid, resulting in case bulging, rupture, or even an explosion that disperses flammable oil, starts fires, and damages nearby equipment, called flash - melt down, Rigid cased cylindrical glass or plastic cases are more prone to explosive rupture than rectangular cases due to an inability to easily expand under pressure. Capacitors used in RF or sustained high current applications can overheat, especially in the center of the capacitor rolls. The trapped heat may cause rapid interior heating and destruction, even though the outer case remains relatively cool. Capacitors used within high energy capacitor banks can violently explode when a fault in one capacitor causes sudden dumping of energy stored in the rest of the bank into the failing unit. And, high voltage vacuum capacitors can generate soft X-rays even during normal operation. Proper containment, fusing, and preventative maintenance can help to minimize these hazards.
High voltage capacitors can benefit from a pre-charge to limit in-rush currents at power-up of HVDC circuits. This will extend the life of the component and may mitigate high voltage hazards.
See also
- Capacitance
- Capacitor plague: capacitor failures on computer motherboards
- Circuit design
- Decoupling capacitor
- Electronic component
- Electric displacement field
- Electronics
- Electronic oscillator
- Filter capacitor
- Light emitting capacitor
- Reservoir capacitor
- Supercapacitor
- Vacuum variable capacitor
- Variable capacitor
- Capacitance meter
Notes
- ↑ Edwin J. Houston (1905). Electricity in Every-day Life. P. F. Collier & Son.
- ↑ Numerical Analysis of Potential and Capacitance
- ↑ Ceramic Capacitor Aging Made Simple
- ↑ [1] Ask The Applications Engineer - 21, Steve Guinta, Analog Devices
References
- Zorpette, Glen (2005). "Super Charged: A Tiny South Korean Company is Out to Make Capacitors Powerful enough to Propel the Next Generation of Hybrid-Electric Cars". IEEE Spectrum (North American Edition ed.). 42 (1). ISSN 0018-9235.
- The ARRL Handbook for Radio Amateurs (68th ed ed.). Newington CT USA: The Amateur Radio Relay League. 1991.
- Huelsman, Lawrence P. (1972). Basic Circuit Theory with Digital Computations. Series in computer applications in electrical engineering. Englewood Cliffs: Prentice-Hall. ISBN 0-13-057430-9.
- Philosophical Transactions of the Royal Society LXXII, Appendix 8, 1782 (Volta coins the word condenser)
- A. K. Maini "Electronic Projects for Beginners", "Pustak Mahal", 2nd Edition: March, 1998 (INDIA)
- Spark Museum (von Kleist and Musschenbroek)
- Biography of von Kleist
External links
 |
Wikimedia Commons has media related to Capacitors. |
- The Capacitor Tutorial
- Capacitance and Inductance - a chapter from an online textbook
- Howstuffworks.com: How Capacitors Work
- CapSite 2007: Introduction to Capacitors
- AC circuits
- Capacitor Tutorial - Includes how to read capacitor temperature codes
- Capacitors in Circuits by Ernest Lee, The Wolfram Demonstrations Project.
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