Farad

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.

Farad
OneFarad5.5Velectrolyticcapacitor
A one farad modern super-capacitor. The scale behind is in inches (top) and centimetres (bottom).
General information
Unit systemSI derived unit
Unit ofCapacitance
SymbolF 
Named afterMichael Faraday
In SI base units:s4A2m−2kg−1

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]

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.

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
  • 1 pF (picofarad, one trillionth (10−12) of a farad)

Equalities

A farad is represented in terms of SI base units as s4A2m−2kg−1

It can further be expressed as:

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

Capacitors Various
Examples of different types of capacitors

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".

Related concepts

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.

See also

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.

External links

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Capacitance

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 (along with resistors and inductors).

The capacitance is a function only of the geometry of the design (e.g. area of the plates and the distance between them) and the permittivity of the dielectric material between the plates of the capacitor. For many dielectric materials, the permittivity and thus the capacitance, is independent of the potential difference between the conductors and the total charge on them.

The SI unit of capacitance is the farad (symbol: F), named after the English physicist Michael Faraday. A 1 farad capacitor, when charged with 1 coulomb of electrical charge, has a potential difference of 1 volt between its plates. The reciprocal of capacitance is called elastance.

Capacitive power supply

A capacitive power supply, also called a capacitive dropper, is a type of power supply that uses the capacitive reactance of a capacitor to reduce the mains voltage to a lower voltage. There are two important limitations: First, the high withstanding voltage required of the capacitor, along with the high-capacitance required for a given output current, mean that this type of supply is only practical for low-power applications. (The capacitance needed increases with the current to be drawn; high capacitance mains-voltage capacitors are expensive and bulky.) The second is that due to the absence of electrical isolation between input and output, anything connected to the power supply must be reliably insulated so that it is not possible for a person to come into electrical contact with it. By the equation of state for capacitance, where , the current is limited to: 1 amp, per farad, per volt-rms, per radian (of phase). Or amps, per farad, per volt-rms, per hertz.

Coulomb

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

Thus, it is also the amount of excess charge on a capacitor of one farad charged to a potential difference of one volt:

The coulomb is equivalent to the charge of approximately 6.242×1018 (1.036×10−5 mol) protons, and −1 C is equivalent to the charge of approximately 6.242×1018 electrons.

A new definition, in terms of the elementary charge, took effect on 20 May 2019. The new definition defines the elementary charge (the charge of the proton) as exactly 1.602176634×10−19 coulombs.

Elastance

Electrical elastance is the inverse of capacitance. The SI unit of elastance is the inverse farad (F−1). The concept is not widely used by electrical and electronic engineers. The value of capacitors is invariably specified in units of capacitance rather than inverse capacitance. However, it is used in theoretical work in network analysis and has some niche applications at microwave frequencies.

The term elastance was coined by Oliver Heaviside through the analogy of a capacitor as a spring. The term is also used for analogous quantities in some other energy domains. It maps to stiffness in the mechanical domain, and is the inverse of compliance in the fluid flow domain, especially in physiology. It is also the name of the generalised quantity in bond-graph analysis and other schemes analysing systems across multiple domains.

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Farad (disambiguation)

The farad (symbol: F) is an SI derived unit of electrical capacitance.

Farad or FARAD may also refer to:

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Jar (unit)

A jar was an early unit of capacitance once used by the British Royal Navy. The term originated as the capacitance of a Leyden jar. Its value is such that one farad is 9×108 jars and one jar is 1111 picofarads.

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Permittivity

In electromagnetism, absolute permittivity, often simply called permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of capacitance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium. Accordingly, a charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium.

The SI unit for permittivity is farad per meter (F/m or F·m−1).

The lowest possible permittivity is that of a vacuum. Vacuum permittivity, sometimes called the electric constant, is represented by ε0 and has a value of approximately 8.85×10−12 F/m.

The permittivity of a dielectric medium is often represented by the ratio of its absolute permittivity to the electric constant. This dimensionless quantity is called the medium’s relative permittivity, sometimes also called "permittivity". Relative permittivity is also commonly referred to as the dielectric constant, a term which has been deprecated in physics and engineering as well as in chemistry.

By definition, a perfect vacuum has a relative permittivity of exactly 1. The difference in permittivity between a vacuum and air can often be considered negligible, as κair = 1.0006.

Relative permittivity is directly related to electric susceptibility (χ), which is a measure of how easily a dielectric polarizes in response to an electric field, given by

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Volt

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