# Coulomb

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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 in magnitude (absolute value) to the charge of approximately 6.241Template:E electrons, but has the opposite sign.

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

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

## Contents

## Name and notation

Template:SI unit lowercase^{[1]}

## Definition

In the SI system, the coulomb is defined in terms of the ampere and second: 1 C = 1 A × 1 s.^{[2]} The second is defined in terms of a frequency which is naturally emitted by caesium atoms.^{[3]} The ampere is defined using Ampère's force law;^{[4]} the definition relies in part on the mass of the international prototype kilogram, a metal cylinder housed in France.^{[5]} In practice, the watt balance is used to measure amperes with the highest possible accuracy.^{[5]}

Since the charge of one electron is known to be about −Template:Physconst −1 C can also be considered to be the charge of roughly Template:Gaps (or +1 C the charge of that many positrons or protons), where the number is the reciprocal of Template:Gaps.

## SI prefixes

Template:SI multiples See also SI prefix.

## Conversions

- The magnitude of the electrical charge of one mole of elementary charges (approximately 6.022Template:E, or Avogadro's number) is known as a faraday unit of charge (closely related to the Faraday constant). One faraday equals Template:Gaps. In terms of Avogadro's number (
*N*_{A}), one coulomb is equal to approximately 1.036 ×*N*_{A}Template:E elementary charges. - One ampere-hour = 3600 C, 1 mA⋅h = 3.6 C.
- The elementary charge is Template:Physconst
- One statcoulomb (statC), the obsolete CGS electrostatic unit of charge (esu), is approximately 3.3356Template:E C or about one-third of a nanocoulomb.
- One coulomb is the magnitude (absolute value) of electrical charge in Template:Gaps protons or electrons.
^{[6]}

## Relation to elementary charge

The elementary charge, the charge of a proton (equivalently, the negative of the charge of an electron), is approximately Template:Physconst. 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 *K*_{J} and von Klitzing constant *R*_{K} are exact defined values (written *K*_{J-90} and *R*_{K-90}), and it follows that the elementary charge *e* =2/(*K*_{J}*R*_{K}) is also an exact defined value in this unit system.^{[7]} Specifically, *e*_{90} = (2Template:E)/(Template:Gaps × Template:Gaps) 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 Template:Gaps coulombs",^{[8]} (in which the numeric value is the 2006 CODATA recommended value, since superseded). 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 Template:Val, placed one meter apart, would experience a repulsive force of Template:Val, a force roughly equal to the weight of Template:Gaps 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 Template:Val. 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.

## See also

- Abcoulomb, a cgs unit of charge
- Ampère's circuital law
- Coulomb's law
- Electrostatics
- Elementary charge
- Faraday (unit), an obsolete unit
- Quantity of electricity

## Notes and references

- ↑ Template:Cite web
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- ↑ Template:Cite web
- ↑
^{5.0}^{5.1}Template:Cite web - ↑ Template:Gaps is the reciprocal of the 2010 CODATA recommended value Template:Gaps for the elementary charge in coulomb.
- ↑
^{7.0}^{7.1}^{7.2}^{7.3}Template:Cite doi - ↑ Report of the CCU to the 23rd CGPM
- ↑ Template:Cite web
- ↑ Template:Cite web
- ↑ Hasbrouck, Richard. Mitigating Lightning Hazards, Science & Technology Review May 1996. Retrieved on 2009-04-26.
- ↑ Template:Google books, "The capacity range of an AA battery is typically from 1100–2200 mAh."