Coulomb

For other uses, see Coulomb (disambiguation).

Coulomb
Unit system	SI derived unit
Unit of	Electric charge
Symbol	C
Named after	Charles-Augustin de Coulomb
Conversions
1 C in ...	... is equal to ...
SI base units	1 A s
CGS units	2997924580 statC
Atomic units	6.24150965(16)e×10^18

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

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.

Definition

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

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 6.241509324×10^¹⁸ electrons (or protons), the reciprocal of 1.60217657×10^⁻¹⁹.

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
10−27 C	rC	rontocoulomb	1027 C	RC	ronnacoulomb
10−30 C	qC	quectocoulomb	1030 C	QC	quettacoulomb
Common multiples are in bold face.

See also SI prefix.

Conversions

• The magnitude of the electrical charge of one mole of elementary charges (approximately 6.022×10²³, or Avogadro's number) is known as a faraday unit of charge (closely related to the Faraday constant). One faraday equals 96485.3399 coulombs. In terms of Avogadro's number (N_A), one coulomb is equal to approximately 1.036 × N_A×10⁻⁵ elementary charges.
• One ampere-hour = 3600 C, 1 mA⋅h = 3.6 C.
• The elementary charge is 1.602176487×10^⁻¹⁹ 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.
• One coulomb is the magnitude (absolute value) of electrical charge in 6.24150965(16)×10^¹⁸ protons or electrons.

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. 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. 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_JR_K) is also an exact defined value in this unit system. Specifically, e₉₀ = (2×10⁻⁹)/(25812.807 × 483597.9) C exactly. SI itself may someday change its definitions in a similar way. 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" This proposal is not yet accepted as part of the SI; the SI definitions are unlikely to change until at least 2015.

In everyday terms

• The charges in static electricity from rubbing materials together are typically a few microcoulombs.
• The amount of charge that travels through a lightning bolt is typically around 15 C, although large bolts can be up to 350 C.
• 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.
• 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.

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

External links

• Electrical units history.