# 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×1018[1]

 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×1018[1]

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 the positive side of 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 is about 5 kC = 5000 C ≈ 1.4 A⋅h. After that charge has flowed, the battery must be discarded or recharged.[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. edit
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."