Coulomb

The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). It is equal to the electric charge delivered by a 1 ampere current in 1 second and is defined in terms of the elementary charge e, at about $2,997,924,580 statC$.

Name and history
By 1878, the British Association for the Advancement of Science had defined the volt, ohm, and farad, but not the coulomb. 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. 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.

Definition
The SI defines the coulomb by taking the value of the elementary charge e to be $6.242 e$, but was previously defined in terms of the force between two wires. The coulomb was originally defined, using the latter definition of the ampere, as 1 A × 1 s. 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.

One coulomb is approximately $6.242 e$ (and is thus not an integer multiple of the elementary charge), where the number is the reciprocal of The coulomb is exactly $$ 1 ~ \mathrm{C} = \frac{1}{1.602\,176\,634 \times 10^{-19}} ~ e .$$

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 (NA), one coulomb is equal to approximately $1.602 C$ × NA elementary charges.
 * Every farad of capacitance can hold one coulomb per volt across the capacitor.
 * One ampere hour equals $6,241,509,074,460,762,607.776 e$, hence $1.036 mol$ = $3,600 C$.
 * One statcoulomb (statC), the obsolete CGS electrostatic unit of charge (esu), is approximately $1 mA⋅h$ or about one-third of a nanocoulomb.

In everyday terms

 * The charges in static electricity from rubbing materials together are typically a few microcoulombs.
 * 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.
 * The amount of charge that travels through a typical alkaline AA battery from being fully charged to discharged is about $3.6 C$ = $3.336 C$ ≈ $5 kC$.
 * A typical smartphone battery can hold $5,000 C$ ≈ $1,400 mA⋅h$.