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:

Coulomb
Unit systemSI derived unit
Unit ofElectric charge
SymbolC 
Named afterCharles-Augustin de Coulomb
Conversions
1 C in ...... is equal to ...
   SI base units   A⋅s
   CGS units   2997924580 statC
   Atomic units   6.241509074e×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:

Under the 2019 redefinition of the SI base units, which took effect on 20 May 2019,[2] the elementary charge (the charge of the proton and of the electron, but also of other fundamental particles) is exactly 1.602176634×10−19 coulombs. Thus the coulomb is the charge of exactly 1/(1.602176634×10−19) elementary charges, which is approximately 6.2415090744×1018 elementary charges (1.036×10−5 mol). The same number of electrons has the same magnitude but opposite sign of charge, that is, a charge of −1 C.

Name and notation

The coulomb is named after Charles-Augustin de Coulomb. As with every SI unit named for a person, its symbol starts with an upper case letter (C), but when written in full it follows the rules for capitalisation of a common noun; i.e., "coulomb" becomes capitalised at the beginning of a sentence and in titles, but is otherwise in lower case.[3]

Definition

The SI system defines the coulomb in terms of the ampere and second: 1 C = 1 A × 1 s.[4] The 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 inverses of each other). The ampere is defined by taking the fixed numerical value of the elementary charge e to be 1.602176634×10−19 coulomb.[5]

Thus, one coulomb is the charge of 6241509074460762607.776 elementary charges, where the number is the reciprocal of 1.602176634×10−19 C.[6]

By 1873, the British Association for the Advancement of Science had defined the volt, ohm, and farad, but not the coulomb.[7] 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.[8] 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.[9]

SI prefixes
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.

Conversions
  • 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 96485.33212... coulombs.[10] 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 3.3356×10−10 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.[11]
  • 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.[12]
  • 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.[13]

See also

Notes and references
  1. 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. "SI Brochure (2019)" (PDF). SI Brochure. BIPM. p. 127. Retrieved May 23, 2019.
  3. "SI Brochure, Appendix 1" (PDF). BIPM. p. 144.
  4. "SI brochure (2019)" (PDF). SI Brochure. BIPM. p. 130. Retrieved May 23, 2019.
  5. "SI brochure (2019)" (PDF). SI Brochure. BIPM. p. 132. Retrieved May 23, 2019.
  6. "2018 CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  7. 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."
  8. (Anon.) (September 24, 1881) "The Electrical Congress," The Electrician, 7 .
  9. Donald Fenna, A Dictionary of Weights, Measures, and Units, OUP (2002), 51f.
  10. "2018 CODATA Value: Faraday constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  11. Martin Karl W. Pohl. "Physics: Principles with Applications" (PDF). DESY. Archived from the original (PDF) on 2011-07-18.
  12. Hasbrouck, Richard. Mitigating Lightning Hazards Archived 2013-10-05 at the Wayback Machine, Science & Technology Review May 1996. Retrieved on 2009-04-26.
  13. 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."
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