# Coulomb

(Redirected from Coulomb (unit))
Coulomb
Unit systemSI derived unit
Unit ofElectric charge
SymbolC
Named afterCharles-Augustin de Coulomb
Conversions
1 C in ...... is equal to ...
SI base units   As
CGS units   2997924580 statC
Atomic units   6.24150934(14)e×1018[1]

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:

${\displaystyle 1~{\text{C}}=1~{\text{A}}\times 1~{\text{s}}}$

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

${\displaystyle 1~{\text{C}}=1~{\text{F}}\times 1~{\text{V}}}$

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, will take effect on 20 May 2019.[2] The new definition defines the elementary charge (the charge of the proton) as exactly 1.602176634×10−19 coulombs.

## Name and notation

This SI unit is named after Charles-Augustin de Coulomb. As with every International System of Units (SI) unit named for a person, the first letter of its symbol is upper case (C). However, when an SI unit is spelled out in English, it is treated as a common noun and should always begin with a lower case letter (coulomb)—except in a situation where any word in that position would be capitalized, such as at the beginning of a sentence or in material using title case.[3]

## Definition

The SI system defines the coulomb in terms of the ampere and second: 1 C = 1 A × 1 s.[4] The second is defined in terms of a frequency naturally emitted by caesium atoms.[5] The ampere is defined using Ampère's force law;[6] the definition relies in part on the mass of the international prototype kilogram, a metal cylinder housed in France.[7] In practice, the Kibble balance is used to measure amperes with the highest possible accuracy.[7]

Since the charge of one electron is known to be about 1.6021766208(98)×10−19 C,[8] 1 C can also be considered the charge of roughly 6.241509×1018 electrons or +1 C the charge of that many positrons or protons, where the number is the reciprocal of 1.602177×10−19.

By 1873, the British Association for the Advancement of Science had defined the volt, ohm, and farad, but not the coulomb.[9] 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.[10] 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 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.[11]

The proposed redefinition of the ampere and other SI base units would fix the numerical value of the elementary charge to exactly 1.602176634×10−19 when expressed in coulombs, and therefore it would fix the value of the coulomb when expressed as a multiple of the fundamental charge (the numerical values of those quantities are the multiplicative inverses of each other).

## SI prefixes

Submultiples Multiples Value SI symbol Name Value 10−1 C dC decicoulomb 101 C daC decacoulomb 10−2 C cC centicoulomb 102 C hC hectocoulomb 10−3 C mC millicoulomb 103 C kC kilocoulomb 10−6 C µC microcoulomb 106 C MC megacoulomb 10−9 C nC nanocoulomb 109 C GC gigacoulomb 10−12 C pC picocoulomb 1012 C TC teracoulomb 10−15 C fC femtocoulomb 1015 C PC petacoulomb 10−18 C aC attocoulomb 1018 C EC exacoulomb 10−21 C zC zeptocoulomb 1021 C ZC zettacoulomb 10−24 C yC yoctocoulomb 1024 C YC yottacoulomb Common multiples are in bold face.

## Conversions

• One coulomb is the magnitude (absolute value) of electrical charge in 6.24150934(14)×1018 protons or electrons.[1]
• The inverse of this number gives the elementary charge of 1.6021766208(98)×10−19 C.[8]
• The magnitude of the electrical charge of one mole of elementary charges (approximately 6.022×1023, the Avogadro number) is known as a faraday unit of charge (closely related to the Faraday constant). One faraday equals 96485.3399 coulombs. In terms of the Avogadro constant (NA), one coulomb is equal to approximately 1.036×10−5 mol × NA elementary charges.
• One ampere hour equals 3600 C, hence 1 mA⋅h = 3.6 C.
• One statcoulomb (statC), the obsolete CGS electrostatic unit of charge (esu), is approximately 3.3356×1010 C or about one-third of a nanocoulomb.

## Relation to elementary charge

The elementary charge, the charge of a proton (equivalently, the negative of the charge of an electron), is approximately 1.6021766208(98)×10−19 C[8]. In SI, the elementary charge in coulombs is an approximate value: no experiment can be infinitely accurate. However, in other unit systems, the elementary charge has an exact value by definition, and other charges are ultimately measured relative to the elementary charge.[12] For example, in conventional electrical units, the values of the Josephson constant KJ and von Klitzing constant RK are exact defined values (written KJ-90 and RK-90), and it follows that the elementary charge e = 2/(KJRK) is also an exact defined value in this unit system.[12] Specifically, e90 = (2×10−9)/(25812.807 × 483597.9) C exactly.[12] SI itself may someday change its definitions in a similar way.[12] For example, one possible proposed redefinition is "the ampere...is [defined] such that the value of the elementary charge e (charge on a proton) is exactly 1.602176487×10−19 coulombs",[13] (in which the numeric value is the 2006 CODATA recommended value, since superseded). This proposal is not yet accepted as part of the SI.

## In everyday terms

• The charges in static electricity from rubbing materials together are typically a few microcoulombs.[14]
• The amount of charge that travels through a lightning bolt is typically around 15 C, although large bolts can be up to 350 C.[15]
• The amount of charge that travels through a typical alkaline AA battery from being fully charged to discharged is about 5 kC = 5000 C ≈ 1400 mA⋅h.[16]

## Notes and references

1. ^ a b 6.24150934(14)×1018 is the reciprocal of the 2010 CODATA recommended value 1.602176565(35)×10−19 for the elementary charge in coulomb.
2. ^ Draft Resolution A "On the revision of the International System of units (SI)" to be submitted to the CGPM at its 26th meeting in November of 2018. (PDF)
3. ^ "SI Brochure, Appendix 1," (PDF). BIPM. p. 144.
4. ^ "SI brochure, section 2.2.2". BIPM.
5. ^
6. ^
7. ^ a b "Watt Balance". BIPM.
8. ^ a b c "CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015-09-22. 2014 CODATA recommended values
9. ^ W. Thomson, et al. (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."
10. ^ (Anon.) (September 24, 1881) "The Electrical Congress," The Electrician, 7 .
11. ^ Donald Fenna, A Dictionary of Weights, Measures, and Units, OUP (2002), 51f.
12. ^ a b c d Mills, I. M.; Mohr, P. J.; Quinn, T. J.; Taylor, B. N.; Williams, E. R. (2005). "Redefinition of the kilogram: a decision whose time has come". Metrologia. 42 (2): 71. Bibcode:2005Metro..42...71M. doi:10.1088/0026-1394/42/2/001.
13. ^ Report of the CCU to the 23rd CGPM
14. ^ Martin Karl W. Pohl. "Physics: Principles with Applications" (PDF). DESY. Archived from the original (PDF) on 2011-07-18.
15. ^ Hasbrouck, Richard. Mitigating Lightning Hazards, Science & Technology Review May 1996. Retrieved on 2009-04-26.
16. ^ How to do everything with digital photography – David Huss, p. 23, at Google Books, "The capacity range of an AA battery is typically from 1100–2200 mAh."