# Coulomb

 Coulomb Unit system SI derived unit Unit of Electric charge Symbol C Named after Charles-Augustin de Coulomb Unit conversions 1 C in... is equal to... SI base units 1 A s CGS units 2997924580 statC Atomic units 6.24150965(16)e×10181

The coulomb (named after Charles-Augustin de Coulomb, unit symbol: C) is a fundamental unit of electrical charge, and is also the SI derived unit of electric charge (symbol: Q or q). It is equal to the charge of approximately 6.241×1018 electrons.

Its SI definition is the charge transported by a constant current of one ampere in one second:

$1\ \mathrm{C} = 1\ \mathrm{A} \times 1\ \mathrm{s}$

One coulomb is also the amount of excess charge on a capacitor of one farad charged to a potential difference of one volt:

$1\ \mathrm{C} = 1\ \mathrm{F} \times 1\ \mathrm{V}$

## Name and notation

This SI unit is named after Charles-Augustin de Coulomb. As with every International System of Units (SI) unit whose name is derived from the proper name of a person, the first letter of its symbol is upper case (C). However, when an SI unit is spelled out in English, it 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 capitalized material such as a title. Note that "degree Celsius" conforms to this rule because the "d" is lowercase. —Based on The International System of Units, section 5.2.2

## Definition

In the SI system, the coulomb is defined in terms of the ampere and second: 1 C = 1 A × 1 s.3 The second is defined in terms of a frequency which is naturally emitted by caesium atoms.4 The ampere is defined using Ampère's force law;5 the definition relies in part on the mass of the international prototype kilogram, a metal cylinder housed in France.6 In practice, the watt balance is used to measure amperes with the highest possible accuracy.6

Since the charge of one electron is known to be about 1.60217657×10−19 coulombs, a coulomb can also be considered to be the charge of roughly 6.241509324×1018 electrons (or protons), the reciprocal of 1.60217657×10−19.

## SI prefixes

Submultiples Multiples Value 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.

## Relation to elementary charge

The elementary charge, the charge of a proton (equivalently, the negative of the charge of an electron), is approximately 1.602176487(40)×10−19 C.1 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.7 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.7 Specifically, e90 = (2×10−9)/(25812.807 × 483597.9) C exactly.7 SI itself may someday change its definitions in a similar way.7 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"8 This proposal is not yet accepted as part of the SI; the SI definitions are unlikely to change until at least 2015.9

## In everyday terms

• The charges in static electricity from rubbing materials together are typically a few microcoulombs.10
• The amount of charge that travels through a lightning bolt is typically around 15 C, although large bolts can be up to 350 C.11
• The amount of charge that travels through a typical alkaline AA battery from being fully charged to discharged is about 5 kC = 5000 C ≈ 1.4 A⋅h. 12
• According to Coulomb's law, two negative point charges of 1 C, placed one meter apart, would experience a repulsive force of 9×109 N, a force roughly equal to the weight of 920000 metric tons of mass on the surface of the Earth.
• The hydraulic analogy uses everyday terms to illustrate movement of charge and the transfer of energy. The analogy equates charge to a volume of water, and voltage to pressure. One coulomb equals (the negative of) the charge of 6.24×1018 electrons. The amount of energy transferred by the flow of 1 coulomb can vary; for example, 300 times fewer electrons flow through a lightning bolt than through an AA battery, but the total energy transferred by the flow of the lightning's electrons is 300 million times greater.

## Notes and references

1. ^ a b c d Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006". Rev. Mod. Phys. 80 (2): 633–730. arXiv:0801.0028. Bibcode:2008RvMP...80..633M. doi:10.1103/RevModPhys.80.633. Direct link to value. The inverse value (the number of elementary charges in 1 C) is given by 1/1.602176487(40)×10−19 = 6.24150965(16)×1018.
2. ^ "SI Brochure, Appendix 1,". BIPM. p. 144.
3. ^ "SI brochure, section 2.2.2". BIPM.
4. ^
5. ^
6. ^ a b "Watt Balance". BIPM.
7. ^ 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.
8. ^ Report of the CCU to the 23rd CGPM
9. ^ Anon (November 2010). "BIPM Bulletin". BIPM. Retrieved 2011-01-28.
10. ^ Martin Karl W. Pohl. "Physics: Principles with Applications". DESY.
11. ^ Hasbrouck, Richard. Mitigating Lightning Hazards, Science & Technology Review May 1996. Retrieved on 2009-04-26.
12. ^ 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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