Coulomb

The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI).^[1][2] It is defined to be equal to the electric charge delivered by a 1 ampere current in 1 second, with the elementary charge e as a defining constant in the SI.^[2][1]

Definition

The SI defines the coulomb as "the quantity of electricity carried in 1 second by a current of 1 ampere" by fixing the value of the elementary charge, .^[3] Inverting the relationship, the coulomb can be expressed in terms of the elementary charge:

1 ~ \mathrm{C} = \frac{e}{1.602\,176\,634 \times 10^{-19}} 
\approx 6.241509\times 10^{18} ~ e .

The approximation can be extended to any number of digits. It is not an integer multiple of the elementary charge.

The coulomb was previously defined in terms of the ampere based on the force between two wires, as 1 A × 1 s.^[4] The 2019 redefinition of the ampere and other SI base units fixed the numerical value of the elementary charge when expressed in coulombs and therefore fixed the value of the coulomb when expressed as a multiple of the fundamental charge.

SI prefixes

Like other SI units, the coulomb can be modified by adding a prefix that multiplies it by a power of 10.

Conversions

• The magnitude of the electrical charge of one mole of elementary charges (approximately , the Avogadro number) is known as a faraday unit of charge (closely related to the Faraday constant). One faraday equals In terms of the Avogadro constant (N_A), one coulomb is equal to approximately 1.036×10^-5 mol × N_A elementary charges.
• Every farad of capacitance can hold one coulomb per volt across the capacitor.
• One ampere hour equals 3,600 C, hence 1 mA⋅h = 3.6 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.

In everyday terms

• The charges in static electricity from rubbing materials together are typically a few microcoulombs.^[5]
• The amount of charge that travels through a lightning bolt is typically around 15 C, although for large bolts this can be up to 350 C.^[6]
• The amount of charge that travels through a typical alkaline AA battery from being fully charged to discharged is about 5 kC = 5,000 C ≈ 1,400 mA⋅h.^[7]
• A typical smartphone battery can hold 10,800 C ≈ 3,000 mA⋅h.

Name and history

^[8]

By 1878, the British Association for the Advancement of Science had defined the volt, ohm, and farad, but not the coulomb.^[9] In 1881, the International Electrical Congress, now the International Electrotechnical Commission (IEC), approved the volt as the unit for electromotive force, the ampere as the unit for electric current, and the coulomb as the unit of electric charge.^[10] At that time, the volt was defined as the potential difference [i.e., what is nowadays called the "voltage (difference)"] across a conductor when a current of one ampere dissipates one watt of power. The coulomb (later "absolute coulomb" or "abcoulomb" for disambiguation) was part of the EMU system of units. The "international coulomb" based on laboratory specifications for its measurement was introduced by the IEC in 1908. The entire set of "reproducible units" was abandoned in 1948 and the "international coulomb" became the modern coulomb.^[11]

See also

• Abcoulomb, a cgs unit of charge
• Ampère's circuital law
• Coulomb's law
• Electrostatics
• Elementary charge
• Faraday constant, the number of coulombs per mole of elementary charges

Notes and references

1. ^ International Bureau of Weights and Measures (Dec 2022), The International System of Units (SI), Vol. 2, no. 1, 9th ed., ISBN 978-92-822-2272-0, archived 18 October 2021 at the Wayback Machine
2. ^ BIPM (20 May 2019). "Mise en pratique for the definition of the ampere in the SI". BIPM. Retrieved 2022-02-18.
3. ^
4. ^ "The NIST Reference on Units, Constants, and Uncertainty". NIST. 12 April 2010.
5. ^ Martin Karl W. Pohl. "Physics: Principles with Applications". DESY. Archived 2011-07-18 at the Wayback Machine.
6. ^ Hasbrouck, Richard. Mitigating Lightning Hazards Archived 2013-10-05 at the Wayback Machine, Science & Technology Review May 1996. Retrieved on 2009-04-26.
7. ^ How to do everything with digital photography – David Huss, "The capacity range of an AA battery is typically from 1100–2200 mAh."
8. ^ "SI Brochure, Appendix 1". BIPM. p. 144. Archived 2006-06-18 at the Wayback Machine.
9. ^ W. Thomson, et al. (1873) "First report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units," Report of the 43rd Meeting of the British Association for the Advancement of Science (Bradford, September 1873), pp. 222–225. From p. 223: "The 'ohm', as represented by the original standard coil, is approximately 10⁹ C.G.S. units of resistance; the 'volt' is approximately 10⁸ C.G.S. units of electromotive force; and the 'farad' is approximately 1/10⁹ of the C.G.S. unit of capacity."
10. ^ (Anon.) (September 24, 1881) "The Electrical Congress", The Electrician, 7.
11. ^ Donald Fenna, A Dictionary of Weights, Measures, and Units, OUP (2002), 51f.