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.[4]

By 1878, the British Association for the Advancement of Science had defined the volt, ohm, and farad, but not the coulomb.[5] 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.[6] 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.[7]

The SI defines the coulomb in terms of the ampere and second: 1 C = 1 A × 1 s.[8] The ampere is defined by taking the fixed numerical value of the elementary charge e to be 1.602176634×10⁻¹⁹ coulombs,[9] but was previously defined in terms of the forces 2 wires exert on each other. The coulomb was originally defined, using the latter definition of the ampere, as 1 A × 1 s.[10] 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 (the numerical values of those quantities are the multiplicative inverses of each other).

One coulomb is the charge of approximately 6241509074460762607.776 elementary charges, where the number is the reciprocal of 1.602176634×10⁻¹⁹ C.[11] This is also 160.2176634 zC of charge. The exact value of 1 coulomb is

$${\displaystyle {\begin{alignedat}{2}1~\mathrm {C} &={\frac {1}{1.602\,176\,634\times 10^{-19}}}~e\\[0.9ex]&={\frac {1}{1.602\,176\,634}}\times 10^{19}~e\\[0.9ex]&={\frac {10^{28}}{1\,602\,176\,634}}~e\\[0.9ex]&={\frac {5\times 10^{27}}{801\,088\,317}}~e\qquad {\text{ (written in lowest terms) }}\\[0.9ex]&=\left(6\,241\,509\,074\,460\,762\,607+{\tfrac {621\,837\,581}{801\,088\,317}}\right)e\\\end{alignedat}}}$$

elementary charges where ${\displaystyle {\tfrac {621\,837\,581}{801\,088\,317}}={\tfrac {621\,837\,581}{3^{2}\times 19\times 389\times 12\,043}}\approx 0.776\,24\ldots }$ and the numerator ${\displaystyle 621\,837\,581}$ is a prime number.

It is impossible to realize exactly 1 C of charge, since the number of elementary charges is not an integer. It is also impossible to realize charge at the yoctocoulomb scale or lower.

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

• The magnitude of the electrical charge of one mole of elementary charges (approximately 6.022×10²³, the Avogadro number) is known as a faraday unit of charge (closely related to the Faraday constant). One faraday equals 9.648533212...×10⁴ coulombs.[12] In terms of the Avogadro constant (N_A), one coulomb is equal to approximately 1.036×10⁻⁵ mol × N_A elementary charges.
• A capacitor of one farad can hold one coulomb at a drop of one volt.
• One ampere hour equals 3600 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.

• The charges in static electricity from rubbing materials together are typically a few microcoulombs.[13]
• 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.[14]
• The amount of charge that travels through a typical alkaline AA battery from being fully charged to discharged is about 5 kC = 5000 C ≈ 1400 mA⋅h.[15]
• A typical smartphone battery can hold 10,800 C ≈ 3000 mA⋅h.

• 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