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# Coulomb

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 defined in terms of capacitance and voltage, where one coulomb is defined as 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 (KJ ≡ 4.835 979×1014 Hz/V and RK ≡ 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.[citation needed]

If two point charges of +1 C are held one meter away from each other, the repulsive force they will feel is given by Coulomb's Law as 8.988×109 N [1]. This is roughly equal to the gravitational force of 900,000 metric tons of mass at the surface of the Earth; in everyday terms, it's enough force to accelerate an Airbus A380 airplane up to a final speed of 76,857 km/h in 1 second. In everyday life, most things don't have a large surplus of charge!

## 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. [1]

## SI multiples

SI multiples for coulomb (C)
Submultiples Multiples
Value Symbol Name Value 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
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 (NA), one coulomb is equal to approximately 1.036 × NA ×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.
 This SI unit is named after Charles-Augustin de Coulomb. As with all SI units whose names are derived from the proper name of a person, the first letter of its symbol is uppercase (C). But when an SI unit is spelled out, it should always be written in lowercase (coulomb), unless it begins a sentence or is the name "degree Celsius". — Based on The International System of Units, section 5.2.

• Abcoulomb, a cgs unit of charge
• Statcoulomb, a cgs unit of charge
• Faraday, an obsolete unit
• Coulomb's law
• Current (electricity)