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

One coulomb is the amount of electric charge transported in one second by a steady current of one ampere.

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

One coulomb is the amount of charge stored by a capacitance of one farad charged to a potential difference of one volt:

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

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.

Typically, batteries are rated in milliampere-hours. A typical AA battery is rated at 2890 mA·h which converts to 10,404,000 C.

In everyday situations, positive and negative charges are usually balanced out. According to Coulomb's Law, two point charges of +1 C, one meter apart, would experience a repulsive force of 9×10⁹ N, roughly the equivalent of 900,000 metric tons of weight.

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 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 electrons, or Avogadro's number) is known as a faraday (actually –1 faraday, since electrons are negatively charged). One faraday equals 96485.3399 coulombs (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.

• One 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 (unit), 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