# Coulomb

{{#invoke:Hatnote|hatnote}} Template:Infobox Unit 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:

${\displaystyle 1\ \mathrm {C} =1\ \mathrm {A} \cdot 1\ \mathrm {s} }$

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

${\displaystyle 1\ \mathrm {C} =1\ \mathrm {F} \cdot 1\ \mathrm {V} }$

## 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.

## 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 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 = (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.

## Notes and references

1. Template:Cite web
2. Template:Cite web
3. Template:Cite web
4. Template:Cite web
5. Template:Cite web
6. Template:Gaps is the reciprocal of the 2010 CODATA recommended value Template:Gaps for the elementary charge in coulomb.
7. Template:Cite doi
8. Report of the CCU to the 23rd CGPM
9. Template:Cite web
10. Template:Cite web
11. Hasbrouck, Richard. Mitigating Lightning Hazards, Science & Technology Review May 1996. Retrieved on 2009-04-26.
12. Template:Google books, "The capacity range of an AA battery is typically from 1100–2200 mAh."