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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:

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×10^18[1]

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, 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.

Contents

Name and notationEdit

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]

DefinitionEdit

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 −1.6021766208(98)×10−19 C,[8] −1 C is the charge of approximately 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 prefixesEdit

SI multiples of coulomb (C)
Submultiples Multiples
Value SI symbol Name Value SI symbol Name
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.

See also Metric prefix.

ConversionsEdit

Relation to elementary chargeEdit

The elementary charge, the charge of a proton (equivalently, the negative of the charge of an electron), is 1.6021766208(98)×10−19 C.[8] With the 2019 redefinition of SI base units, as of 20 May 2019 the elementary charge in coulombs has an exact value: 1.602176634×10−19 C.[13]

In everyday termsEdit

  • 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 for large bolts this 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]

See alsoEdit

Notes and referencesEdit

  1. ^ a b 6.241509126(38)×1018 is the reciprocal of the 2014 CODATA recommended value 1.6021766208(98)×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. ^ "SI brochure, section 2.2.1.3". BIPM.
  6. ^ "SI brochure, section 2.2.1.4". BIPM.
  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. ^ "CODATA Value: Faraday constant". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. June 2015. Retrieved 2015-09-25. 2014 CODATA recommended values
  13. ^ The 2019 redefinition is "The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602176634×10−19 when expressed in the unit C [...]."
  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."