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A one farad modern super-capacitor. The scale behind is in inches (top) and centimetres (bottom).
General information
Unit system SI derived unit
Unit of Capacitance
SymbolF
In SI base units: s 4 A 2 m −2 kg −1

The farad (symbol: F) is the SI derived unit of electrical capacitance, the ability of a body to store an electrical charge. It is named after the English physicist Michael Faraday.

SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.

Capacitance is the ratio of the change in an electric charge in a system to the corresponding change in its electric potential. There are two closely related notions of capacitance: self capacitance and mutual capacitance. Any object that can be electrically charged exhibits self capacitance. A material with a large self capacitance holds more electric charge at a given voltage than one with low capacitance. The notion of mutual capacitance is particularly important for understanding the operations of the capacitor, one of the three elementary linear electronic components.

Michael Faraday FRS was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic induction, diamagnetism and electrolysis.

## Definition

One farad is defined as the capacitance across which, when charged with one coulomb, there is a potential difference of one volt. [1] Equally, one farad can be described as the capacitance which stores a one-coulomb charge across a potential difference of one volt. [2]

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two-types of electric charges; positive and negative. Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects.

The coulomb is the International System of Units (SI) unit of electric charge. It is the charge transported by a constant current of one ampere in one second:

The volt is the derived unit for electric potential, electric potential difference (voltage), and electromotive force. It is named after the Italian physicist Alessandro Volta (1745–1827).

The relationship between capacitance, charge, and potential difference is linear. For example, if the potential difference across a capacitor is halved, the quantity of charge stored by that capacitor will also be halved.

A capacitor is a passive two-terminal electronic component that stores electrical energy in an electric field. The effect of a capacitor is known as capacitance. 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 a condenser or condensator. The original name is still widely used in many languages, but not commonly in English.

For most applications, the farad is an impractically large unit of capacitance. Most electrical and electronic applications are covered by the following SI prefixes:

• 1 mF (millifarad, one thousandth (10−3) of a farad) = 1000 μF = 1000000 nF
• 1 μF (microfarad, one millionth (10−6) of a farad) = 0.000 001 F = 1000 nF = 1000000 pF
• 1 nF (nanofarad, one billionth (10−9) of a farad) = 0.001 μF = 1000 pF

A billion is a number with two distinct definitions:

### Equalities

A farad is represented in terms of SI base units as s 4A 2m −2kg −1

The second is the base unit of time in the International System of Units (SI), commonly understood and historically defined as ​186400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each. Analog clocks and watches often have sixty tick marks on their faces, representing seconds, and a "second hand" to mark the passage of time in seconds. Digital clocks and watches often have a two-digit seconds counter. The second is also part of several other units of measurement like meters per second for velocity, meters per second per second for acceleration, and per second for frequency.

The ampere, often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.

The kilogram or kilogramme is the base unit of mass in the International System of Units (SI). Until 20 May 2019, it remains defined by a platinum alloy cylinder, the International Prototype Kilogram, manufactured in 1889, and carefully stored in Saint-Cloud, a suburb of Paris. After 20 May, it will be defined in terms of fundamental physical constants.

It can further be expressed as:

${\displaystyle {\text{F}}={\dfrac {\text{C}}{\text{V}}}={\dfrac {{\text{A}}{\cdot }{\text{s}}}{\text{V}}}={\dfrac {\text{J}}{{\text{V}}^{2}}}={\dfrac {{\text{W}}{\cdot }{\text{s}}}{{\text{V}}^{2}}}={\dfrac {{\text{N}}{\cdot }{\text{m}}}{{\text{V}}^{2}}}={\dfrac {{\text{C}}^{2}}{\text{J}}}={\dfrac {{\text{C}}^{2}}{{\text{N}}{\cdot }{\text{m}}}}={\dfrac {{\text{s}}^{2}{\cdot }{\text{C}}^{2}}{{\text{m}}^{2}{\cdot }{\text{kg}}}}={\dfrac {{\text{s}}^{4}{\cdot }{\text{A}}^{2}}{{\text{m}}^{2}{\cdot }{\text{kg}}}}={\dfrac {\text{s}}{\Omega }}={\dfrac {1}{\Omega {\cdot }{\text{Hz}}}}={\dfrac {{\text{s}}^{2}}{\text{H}}},}$

where F = farad, A = ampere , V = volt , C = coulomb , J = joule , m = metre , N = newton , s = second , W = watt , kg = kilogram , Ω = ohm , Hz = hertz, H = henry .

## History

The term "farad" was originally coined by Latimer Clark and Charles Bright in 1861, [3] in honor of Michael Faraday, for a unit of quantity of charge, but by 1873, the farad had become a unit of capacitance. [4] In 1881 at the International Congress of Electricians in Paris, the name farad was officially used for the unit of electrical capacitance. [5] [6]

## Explanation

A capacitor generally consists of two conducting surfaces, frequently referred to as plates, separated by an insulating layer usually referred to as a dielectric. The original capacitor was the Leyden jar developed in the 18th century. It is the accumulation of electric charge on the plates that results in capacitance. Modern capacitors are constructed using a range of manufacturing techniques and materials to provide the extraordinarily wide range of capacitance values used in electronics applications from femtofarads to farads, with maximum-voltage ratings ranging from a few volts to several kilovolts.

Values of capacitors are usually specified in farads (F), microfarads (μF), nanofarads (nF) and picofarads (pF). [7] The millifarad is rarely used in practice (a capacitance of 4.7 mF (0.0047 F), for example, is instead written as 4700 µF), while the nanofarad is uncommon in North America. [8] The size of commercially available capacitors ranges from around 0.1 pF to 5000F (5 kF) supercapacitors. Parasitic capacitance in high-performance integrated circuits can be measured in femtofarads (1 fF = 0.001 pF = 1015 F), while high-performance test equipment can detect changes in capacitance on the order of tens of attofarads (1 aF = 10−18 F). [9]

A value of 0.1 pF is about the smallest available in capacitors for general use in electronic design, since smaller ones would be dominated by the parasitic capacitances of other components, wiring or printed circuit boards. Capacitance values of 1 pF or lower can be achieved by twisting two short lengths of insulated wire together. [10] [11]

The capacitance of the Earth's ionosphere with respect to the ground is calculated to be about 1 F. [12]

### Informal and deprecated terminology

The picofarad (pF) is sometimes colloquially pronounced as "puff" or "pic", as in "a ten-puff capacitor". [13] Similarly, "mic" (pronounced "mike") is sometimes used informally to signify microfarads.

Nonstandard abbreviations were and are often used. Farad has been abbreviated "f", "fd", and "Fd". For the prefix "micro-", when the Greek small letter "μ" or the legacy micro sign "μ" is not available (as on typewriters) or inconvenient to enter, it is often substituted with the similar-appearing "u" or "U", with little risk of confusion. It was also substituted with the similar-sounding "M" or "m", which can be confusing because M officially stands for 1000000 (or 1000), and m preferably stands for 1/1000. In texts prior to 1960, and on capacitor packages until more recently, "microfarad(s)" was abbreviated "mf" or "MFD" rather than the modern "µF". A 1940 Radio Shack catalog listed every capacitor's rating in "Mfd.", from 0.000005 Mfd. (5 pF) to 50 Mfd. (50 µF). [14]

"Micromicrofarad" or "micro-microfarad" is an obsolete unit found in some older texts and labels, contains a nonstandard metric double prefix. It is exactly equivalent to a picofarad (pF). It is abbreviated μμF, uuF, or (confusingly) "mmf", "MMF", or "MMFD".

The reciprocal of capacitance is called electrical elastance, the (non-standard, non-SI) unit of which is the daraf. [15]

## CGS units

The abfarad (abbreviated abF) is an obsolete CGS unit of capacitance equal to 109 farads (1 gigafarad, GF). [16]

The statfarad (abbreviated statF) is a rarely used CGS unit equivalent to the capacitance of a capacitor with a charge of 1 statcoulomb across a potential difference of 1 statvolt. It is 1/(10−5c2) farad, approximately 1.1126 picofarads.

## Notes

1. The International System of Units (SI) (8th ed.). Bureau International des Poids et Mesures (International Committee for Weights and Measures). 2006. p. 144.
2. Peter M B Walker, ed. (1995). Dictionary of Science and Technology. Larousse. ISBN   0752300105.
3. As names for units of various electrical quantities, Bright and Clark suggested "ohma" for voltage, "farad" for charge, "galvat" for current, and "volt" for resistance. See:
4. Sir W. Thomson, etc. (1873) "First report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units," Report of the 43rd Meeting of the British Association for the Advancement of Science (Bradford, September 1873), pp. 222-225. From p. 223: "The "ohm," as represented by the original standard coil, is approximately 109 C.G.S. units of resistance: the "volt" is approximately 108 C.G.S. units of electromotive force: and the "farad" is approximately 1/109 of the C.G.S. unit of capacity."
5. (Anon.) (September 24, 1881) "The Electrical Congress," The Electrician, 7: 297. From p. 297: "7. The name farad will be given to the capacity defined by the condition that a coulomb in a farad gives a volt."
6. Tunbridge, Paul (1992). Lord Kelvin: his influence on electrical measurements and units. London: Peregrinus. pp. 26, 39–40. ISBN   9780863412370 . Retrieved 5 May 2015.
7. Braga, Newton C. (2002). Robotics, Mechatronics, and Artificial Intelligence. Newnes. p. 21. ISBN   0-7506-7389-3 . Retrieved 2008-09-17. Common measurement units are the microfarad (μF), representing 0.000,001 F; the nanofarad (nF), representing 0.000,000,001 F; and the picofarad (pF), representing 0.000,000,000,001 F.
8. Platt, Charles (2009). Make: Electronics: Learning Through Discovery. O'Reilly Media. p. 61. ISBN   9781449388799 . Retrieved 2014-07-22. Nanofarads are also used, more often in Europe than in the United States.
9. Gregorian, Roubik (1976). Analog MOS Integrated Circuits for Signal Processing. John Wiley & Sons. p. 78.
10. Pease, Bob (2 September 1993). "What's All This Femtoampere Stuff, Anyhow?". Electronic Design. Retrieved 2013-03-09.
11. Pease, Bob (1 December 2006). "What's All This Best Stuff, Anyhow?". Electronic Design. Retrieved 2013-03-09.
12. Williams, L. L. (January 1999). "Electrical Properties of the Fair-Weather Atmosphere and the Possibility of Observable Discharge on Moving Objects" (PDF). Retrieved 2012-08-13.
13. "Puff". Wolfram Research. Retrieved 2009-06-09.
14. "1940 Radio Shack Catalog - Page 54 - Condensers". radioshackcatalogs.com. Archived from the original on 11 July 2017. Retrieved 11 July 2017.
15. "Daraf". Webster's Online Dictionary. Archived from the original on 2011-10-04. Retrieved 2009-06-19.
16. Graf, Rudolf F. (1999). Modern Dictionary of Electronics. Newnes. p. 1. ISBN   9780080511986 . Retrieved 2016-04-15.