Farad

Farad
A 1 farad capacitor
Unit information
Unit system	SI derived unit
Unit of	Capacitance
Symbol	F
Named after	Michael Faraday
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.

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) = 1000 nF = 1000000 pF
• 1 nF (nanofarad, one billionth (10⁻⁹) of a farad) = 1000 pF
• 1 pF (picofarad, one trillionth (10⁻¹²) of a farad)

Equalities

A farad has the base SI representation of: s⁴ × A² × m⁻² × kg⁻¹

It can further be expressed as:

$\mbox{F} = \,\mathrm{\frac{A \cdot s}{V} = \dfrac{\mbox{J}}{\mbox{V}^2} = \dfrac{\mbox{W} \cdot \mbox{s}}{\mbox{V}^2} = \dfrac{\mbox{C}}{\mbox{V}} = \dfrac{\mbox{C}^2}{\mbox{J}} = \dfrac{\mbox{C}^2}{\mbox{N} \cdot \mbox{m}} = \dfrac{\mbox{s}^2 \cdot \mbox{C}^2}{\mbox{m}^{2} \cdot \mbox{kg}} = \dfrac{\mbox{s}^4 \cdot \mbox{A}^2}{\mbox{m}^{2} \cdot \mbox{kg}} = \dfrac{\mbox{s}}{\Omega}} = \dfrac{\mbox{s}^{2}}{\mbox{H}}$

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

History

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

Explanation

Examples of different types of capacitors

A capacitor 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).^[4] 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.^[5] 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 = 10⁻¹⁵ F), while high-performance test equipment can detect changes in capacitance on the order of tens of attofarads (1 aF = 10⁻¹⁸ F).^[6]

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.^[7][8]

The capacitance of the Earth's ionosphere with respect to the ground is calculated to be about 1 F.^[9]

Informal and deprecated terminology

The picofarad is sometimes colloquially pronounced as "puff" or "pic", as in "a ten-puff capacitor".^[10] Similarly, "mic" (pronounced "mike") is sometimes used informally to signify microfarads. If the Greek letter μ is not available, the notation "uF" is often used as a substitute for "μF" in electronics literature. A "micro-microfarad" (μμF, and confusingly often mmf or MMF), an obsolete unit sometimes found in older texts, is the equivalent of a picofarad. In texts prior to 1960, and on capacitor packages even much more recently, mf or MFD rather than the modern µF frequently represented microfarads. Similarly, mmf represented picofarads.

Related concepts

The reciprocal of capacitance is called electrical elastance, the (non-standard, non-SI) unit of which is the daraf.^[11]

CGS units

The abfarad (abbreviated abF) is an obsolete CGS unit of capacitance equal to 10⁹ farads (1 gigafarad, GF).^[12]

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

• Supercapacitor

Notes

1. The International System of Units (SI) (PDF) (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. Tunbridge, Paul (1992). Lord Kelvin : his influence on electrical measurements and units. London: Peregrinus. pp. 26, 39–40. ISBN 9780863412370. Retrieved 5 May 2015.
4. 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.
5. 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.
6. Gregorian, Roubik (1976). Analog MOS Integrated Circuits for Signal Processing. John Wiley & Sons. p. 78.
7. Pease, Bob (2 September 1993). "What's All This Femtoampere Stuff, Anyhow?". Electronic Design. Retrieved 2013-03-09.
8. Pease, Bob (1 December 2006). "What's All This Best Stuff, Anyhow?". Electronic Design. Retrieved 2013-03-09.
9. 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.
10. "Puff". Wolfram Research. Retrieved 2009-06-09.
11. "Daraf". Webster's Online Dictionary. Retrieved 2009-06-19.
12. Graf, Rudolf F. (1999). Modern Dictionary of Electronics. Newnes. p. 1. ISBN 9780080511986. Retrieved 2016-04-15.

External links

• Farad unit conversion tool