View source for Coulomb

{{Use British English Oxford spelling|date=October 2019}}
{{Other uses}}
{{Infobox unit
| bgcolour =
| name = Coulomb
| image =
| caption =
| standard = [[SI derived unit]]
| quantity = [[Electric charge]]
| symbol = C
| dimension = T&sdot;I
| namedafter = [[Charles-Augustin de Coulomb]]
| units1 = [[SI base unit]]s
| inunits1 = [[Ampere|A]]&sdot;[[second|s]]
| units2 = [[CGS unit]]s
| inunits2 = {{gaps|2|997|924|580}} [[statcoulomb|statC]]
| units3 = [[Atomic units]]
| inunits3 = {{gaps|6.241|509|074|e=18|[[elementary charge|''e'']]}}<ref name=recip>{{val|6.241509126|(38)|e=18}} is the reciprocal of the 2014 CODATA recommended value {{val|1.6021766208|(98)|e=−19}} for the elementary charge in coulomb.</ref>
}}
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]]:
:<math>1 ~ \text{C} = 1 ~ \text{A} \times 1 ~ \text{s}</math>

Thus, it is also the amount of excess charge on a [[capacitor]] of one [[farad]] charged to a potential difference of one [[volt]]:
:<math>1 ~ \text{C} = 1 ~ \text{F} \times 1 ~ \text{V}</math>

Under the [[2019 redefinition of the SI base units]], which took effect on 20 May 2019,<ref name=BIPM9>
{{cite web
 |title=SI Brochure (2019)
 |work=SI Brochure
 |url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf
 |page=127
 |publisher=[[BIPM]]
 |accessdate=May 23, 2019}}</ref> the [[elementary charge]] (the charge of the [[proton]]) is exactly {{val|1.602176634|e=-19}} coulombs. Thus the coulomb is exactly the charge of 1/({{val|1.602176634|e=-19}}) protons, which is approximately {{val|6.2415090744|e=18}} protons ({{val|1.036|e=-5}} [[Mole (unit)|mol]]). The same number of [[electron]]s has the same magnitude but opposite sign of charge, that is, a charge of −1&nbsp;C.

==Name and notation==
{{SI unit lowercase|Charles-Augustin de Coulomb|coulomb|C}}<ref>{{cite web |url=http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf |publisher=BIPM |title=SI Brochure, Appendix 1 |page=144}}</ref>

==Definition==
The [[SI system]] defines the coulomb in terms of the [[ampere]] and [[second]]: 1&nbsp;C&nbsp;= 1&nbsp;A&nbsp;× 1&nbsp;s.<ref>{{cite web
|url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf
|publisher=[[BIPM]]
|page=130
|title=SI brochure (2019)
|work=SI Brochure
|accessdate=May 23, 2019}}</ref> The [[2019 redefinition of SI base units#Ampere|2019 redefinition of the ampere]] and other SI base units fixed the numerical value of the [[elementary charge]] when expressed in coulombs, and therefore fixed the value of the coulomb when expressed as a multiple of the fundamental charge (the numerical values of those quantities are the [[multiplicative inverse]]s of each other). The ampere is defined by taking the fixed numerical value of the elementary charge e to be {{val|1.602176634|e=-19}} coulomb.<ref name=ampere>{{cite web
|url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf
|publisher=[[BIPM]]
|page=132
|title=SI brochure (2019)
|work=SI Brochure
|accessdate=May 23, 2019}}</ref>

Thus, one coulomb is the charge of {{val|6,241,509,074,460,762,607.776|u=protons}}, where the number is the reciprocal of {{physconst|e|after=.}}

By 1873, the [[British Association for the Advancement of Science]] had defined the volt, ohm, and farad, but not the coulomb.<ref>W. Thomson, et al. (1873) [https://www.biodiversitylibrary.org/page/29853513#page/324/mode/1up "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 10<sup>9</sup> C.G.S. units of resistance ; the "volt" is approximately 10<sup>8</sup> C.G.S. units of electromotive force ; and the "farad" is approximately 1/10<sup>9</sup> of the C.G.S. unit of capacity."</ref>  In 1881, the [[International Electrical Congress]], now the [[International Electrotechnical Commission]] (IEC), approved the volt as the unit for electromotive force, the ampere as the unit for electric current, and the coulomb as the unit of electric charge.<ref>(Anon.) (September 24, 1881) [https://babel.hathitrust.org/cgi/pt?id=nyp.33433090837489;view=1up;seq=309 "The Electrical Congress,"] ''The Electrician'', '''7''' .</ref>  
At that time, the volt was defined as the potential difference [i.e., what is nowadays called the "voltage (difference)"] across a conductor when a current of one [[ampere]] dissipates one [[watt]] of power.
The coulomb (later "absolute coulomb" or "abcoulomb" for disambiguation) was part of the [[Centimetre–gram–second_system_of_units#Relations_between_ESU_and_EMU_units|EMU]] system of units. The "international coulomb" based on laboratory specifications for its measurement was introduced by the IEC in 1908. The entire set of "reproducible units" was abandoned in 1948 and the "international coulomb" became the modern Coulomb.<ref>Donald Fenna, ''A Dictionary of Weights, Measures, and Units'', OUP (2002), 51f.</ref>

==SI prefixes==
{{SI multiples
| unit=coulomb
| symbol=C
| note=Common multiples are in bold face.
| mc=|m=|n=|p=
}}
See also [[Metric prefix#List of SI prefixes|Metric prefix]].

==Conversions==
*The magnitude of the electrical charge of one [[mole (unit)|mole]] of [[elementary charge]]s (approximately {{physconst|NA|round=3|unit=no|ref=no}}, the Avogadro number) is known as a [[Faraday constant|faraday unit of charge]] (closely related to the [[Faraday constant]]). One faraday equals {{physconst|F|unit=no|after=&nbsp;coulombs.}} In terms of the [[Avogadro constant]] (''N''<sub>A</sub>), one coulomb is equal to approximately {{val|1.036|e=-5|u=mol}}&nbsp;×&nbsp;''N''<sub>A</sub> elementary charges.
*One [[ampere hour]] equals 3600&nbsp;C, hence {{val|1|u=mA&sdot;h}} = 3.6&nbsp;C.
*One [[statcoulomb]] (statC), the obsolete [[CGS]] electrostatic unit of charge (esu), is approximately 3.3356{{e|-10}}&nbsp;C or about one-third of a nanocoulomb.

==In everyday terms==
*The charges in [[static electricity]] from rubbing materials together are typically a few microcoulombs.<ref>{{cite web |url=http://www-zeuthen.desy.de/~pohlmadq/teach/112/ch16.pdf |publisher=[[DESY]] |title=Physics: Principles with Applications |author=Martin Karl W. Pohl | archiveurl=https://web.archive.org/web/20110718230251/http://www-zeuthen.desy.de/~pohlmadq/teach/112/ch16.pdf | archivedate=2011-07-18}}</ref>
*The amount of charge that travels through a [[lightning|lightning bolt]] is typically around 15&nbsp;C, although for large bolts this can be up to 350&nbsp;C.<ref>Hasbrouck, Richard. [https://www.llnl.gov/str/pdfs/05_96.1.pdf Mitigating Lightning Hazards] {{Webarchive|url=https://web.archive.org/web/20131005005230/https://www.llnl.gov/str/pdfs/05_96.1.pdf |date=2013-10-05 }}, Science & Technology Review May 1996. Retrieved on 2009-04-26.</ref>
*The amount of charge that travels through a typical [[alkaline battery|alkaline]] [[AA battery]] from being fully charged to discharged is about 5&nbsp;kC&nbsp;= 5000&nbsp;C&nbsp;≈ 1400&nbsp;[[ampere hour|mA&sdot;h]].<ref>{{Google books|eftR-e1nVAgC|How to do everything with digital photography – David Huss|page=23}}, "The capacity range of an AA battery is typically from 1100–2200 mAh."</ref>

==See also==
*[[Abcoulomb]], a cgs unit of charge
*[[Ampère's circuital law]]
*[[Coulomb's law]]
*[[Electrostatics]]
*[[Elementary charge]]
*[[Faraday constant]], the number of coulombs per mole

==Notes and references==
{{Reflist|30em}}

{{SI units}}

[[Category:SI derived units]]
[[Category:UCUM base units]]
[[Category:Units of electrical charge]]