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	6.241510×1018 e

The coulomb (symbol: C) is the SI derived unit of electric charge, transported by a steady current of one ampere in one second.

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

One coulomb equals the total charge of approximately 6.2×10¹⁸ protons; equivalently, negative one (-1) coulomb is the electric charge of 6.2×10¹⁸ electrons.

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

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

Name and notation

The unit is named after Charles-Augustin de Coulomb. 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: 1C = 1A × 1s. The second is defined in terms of a frequency which is naturally emitted by caesium atoms. The ampere is defined in terms of some physical constants, and 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.

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	not used	1021 C	ZC	zettacoulomb
10−24 C	yC	not used	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 protons (approximately 6.022×10²³, or Avogadro's number) is known as a faraday unit of charge (closely related to the Faraday constant). One faraday is equal to 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, one mAh = 3.6 C
• The elementary charge is 1.602176487×10⁻¹⁹ C
• One statcoulomb (statC), the CGS electrostatic unit of charge (esu), is approximately 3.3356×10⁻¹⁰ C or about 1/3 nC.
• One coulomb is the amount of electrical charge in 6.24150965(16)×10¹⁸ protons, or equivalently, negative one (-1) coulomb is the electrical charge of 6.24150965(16)×10¹⁸ electrons.

Relation to elementary charge and "conventional Coulomb"

The elementary charge, the charge of a proton (equivalently, the negative of the charge of an electron), is approximately 1.602176487(40)×10⁻¹⁹ coulombs. 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, and it follows that the elementary charge $e=2/(K_{J}R_{K})$ is also an exact defined value in this unit system. Specifically, $e=(2\times 10^{-9})/(25812.807\times 483597.9)C_{90}$ exactly. (The symbol C₉₀ is the conventional electrical unit of charge, called "conventional Coulomb"). SI itself may someday change its definitions in a similar way.

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 15C, although large bolts can be up to 350C.
• The amount of charge that travels through a typical alkaline AA battery is about 10 kC = 10⁴ C = 2800 mAh. After that charge has flowed, the battery must be discarded or recharged.
• According to Coulomb's Law, two point charges of +1 C, one meter apart, would experience a repulsive force of 9×10⁹ N, a force roughly equal to the weight of 900,000 metric tons of mass.

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