Coulomb

For other uses, see Coulomb (disambiguation).

The coulomb (symbol: C) is the SI unit of electric charge. It is named after Charles-Augustin de Coulomb.

Definition

1 coulomb is the amount of electric charge transported by a current of 1 ampere in 1 second.

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

It can also be expressed in terms of capacitance and voltage, where one coulomb is equal to one farad of capacitance times one volt of electric potential difference:

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

Explanation

In principle, the coulomb could be defined in terms of the charge of an electron or elementary charge. Since the values of the Josephson (CIPM (1988) Recommendation 1, PV 56; 19) and von Klitzing (CIPM (1988), Recommendation 2, PV 56; 20) constants have been given conventional values (K_J ≡ 4.835 979×10¹⁴ Hz/V and R_K ≡ 2.581 280 7×10⁴ Ω), it is possible to combine these values to form an alternative (not yet official) definition of the coulomb. A coulomb is then equal to exactly 6.241 509 629 152 65×10¹⁸ elementary charges. Combined with the present definition of the ampere, this proposed definition would make the kilogram a derived unit.

From Coulomb's Law one can calculate that two point charges of +1 C, one meter apart, would experience a repulsive force of 8.988×10⁹ N. This is roughly equal to the weight of 900,000 metric tons at the surface of the Earth.

Historical note

The ampere was historically a derived unit—being defined as 1 coulomb per second. Therefore the coulomb, rather than the ampere, was the SI base electrical unit.

In 1960 the SI system made the ampere the base unit.

SI multiples

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.

Conversions

• The electrical charge of one mole of electrons (approximately 6.022×10²³, or Avogadro's number) is known as a faraday (actually –1 faraday, since electrons are negatively charged). One faraday equals 96.485 341 5 kC (the Faraday constant). 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

• 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.

• 1 coulomb is the amount of electrical charge in 6.241506×10¹⁸ electrons or other elementary charged particles.

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.

See also

• Abcoulomb, a cgs unit of charge
• Statcoulomb, a cgs unit of charge
• Faraday, an obsolete unit
• Coulomb's law
• Current (electricity)
• Faraday constant
• Quantity of electricity
• SI
• Ampere
• Ampère's circuital law
• Farad

References

1.Kowalski, Ludwik, "A Short History of the SI Units in Electricity", pp. 97-99 vol 24, The Physics Teacher, Feb 1986