The coulomb (symbol: C) is the unit of

electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons res ...

in the

International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...

(SI). In the present version of the SI it is equal to the electric charge delivered by a 1

ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...

constant current in 1

second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ea ...

and to

elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundam ...

s, , (about ).

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 The International Electrical Congress was a series of international meetings, from 1881 - 1904, in the then new field of applied electricity. The first meeting was initiated by the French government, including official national representatives, lea ...

, now the

International Electrotechnical Commission The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and ...

(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 .e., what is nowadays called the "voltage (difference)"across a conductor when a current of one ampere dissipates one

watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James ...

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 in terms of the

and

: 1 C = 1 A × 1 s. The ampere is defined by taking the fixed numerical value of the elementary charge ''e'' to be coulombs. The 2019 redefinition of the ampere and other SI base units fixed the numerical value of the

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 inverse In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a fraction ''a''/' ...

s of each other). The ampere was previously defined in terms of two wires of infinite extent. One coulomb is the charge of approximately , where the number is the reciprocal of This is also 160.2176634 zC of charge. The exact value of 1 coulomb is

&= 6\,241\,509\,074\,460\,762\,607 + \tfrac ~ e \\ \end

s where

\tfrac = \tfrac \approx 0.776\,24\ldots

and the numerator

621\,837\,581

is a

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

. 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.

SI prefixes

Like other SI units, the coulomb can be modified by adding a

prefix A prefix is an affix which is placed before the stem of a word. Adding it to the beginning of one word changes it into another word. For example, when the prefix ''un-'' is added to the word ''happy'', it creates the word ''unhappy''. Particul ...

that multiplies it by a

power of 10 A power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The fi ...

Conversions

*The magnitude of the electrical charge of one mole of

s (approximately , the Avogadro number) is known as a faraday unit of charge (closely related to the

Faraday constant In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of ...

). One faraday equals In terms of the

Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining ...

(''N''_A), one coulomb is equal to approximately × ''N''_A elementary charges. *A

capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...

of one

farad The farad (symbol: F) is the unit of electrical capacitance, the ability of a body to store an electrical charge, in the International System of Units (SI). It is named after the English physicist Michael Faraday (1791–1867). In SI base unit ...

can hold one coulomb at a drop of one

volt The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827). Defin ...

. *One ampere hour equals 3600 C, hence = 3.6 C. *One statcoulomb (statC), the obsolete CGS electrostatic unit of charge (esu), is approximately 3.3356 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. *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 5 kC = 5000 C ≈ 1400 mA⋅h., "The capacity range of an AA battery is typically from 1100–2200 mAh." * A typical smartphone battery can hold 10,800 C ≈ 3000 mA⋅h.

Notes and references