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Defining the standard electrical units

Formal definitions of the standard electrical units: ampere, coulomb, charge on an electron, and the volt. Written by Willy McAllister.
Electrical units can be described in a formal manner, and that's what we do here. The standard electrical units are defined in a specific order. The ampere is defined first. It is an SI base unit, the only electrical unit derived from the outcome of an experiment.
Next up after the ampere comes the coulomb and charge on an electron. Then we derive the rest of our favorites, the watt, the volt, and the ohm. These derived electrical units are defined in terms of the ampere and other SI base units (meter, kilogram, second).


The definition of the SI unit of current, the ampere, comes from the study of magnetism. Electric currents in wires give rise to magnetic fields (Biot–Savart Law, 1820). Those magnetic fields in turn give rise to magnetic forces on the wires (Ampere's Force Law, 1825). Two parallel wires carrying current exert a force on each other. The official SI definition of the ampere is:
The ampere is that constant current which—if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum—would produce between these conductors a force equal to 2×107 newtons per meter of length.
The definition of the ampere comes from the outcome of an experiment. To create a standard 1 ampere, you perform some version of the following experiment. Set up two 1-meter-long wires in parallel, and arrange for a way to measure the force on the wires (a strain gauge).
Apply the same current to both wires, flowing in the same direction. Adjust the currents in the wires up or down while measuring the force on the wires. When the force is 2×107 newtons, the current is 1 ampere, by definition. (This is a conceptual experiment. In modern standards laboratories a standard ampere is created by other means.)


The coulomb is the SI unit of charge. The size of a coulomb is derived from the ampere. One coulomb is defined as the amount of charge flowing when the current is 1 ampere.
or equivalently,

Electron charge

In 1897, J.J. Thomson proved the existence of the electron. Twelve years later, starting in 1909, Robert Millikan performed his oil drop experiments to establish the charge of the electron.
The charge on an electron can be expressed in coulombs as e=1.602176565×1019coulomb.
If we invert this expression, we see that the coulomb can be stated in terms of number of electron charges:

Concept check

How many electrons in 1 ampere?
How many coulombs in 1 mole of electrons?
One mole of electrons is 6.02214×1023 electrons — Avogadro's Number.


The watt is the unit of power. Power is the amount of energy transferred or consumed per unit of time; equivalently, power is the rate of doing work. In standard-speak, the watt is the power which in one second gives rise to energy of 1 joule.


The volt is the unit of electric potential difference—electric potential difference is also known as voltage. The size of 1 volt is officially defined as the potential difference between two points of a wire carrying a current of 1 ampere when the power dissipated in the wire is 1 watt.
The volt can also be expressed in terms of energy and charge as,
You can find an intuitive description of voltage in the introductory article on basic electrical quantities. Also, there is a formal derivation of the meaning of voltage in the electrostatics section.


The ohm is the electrical unit of resistance. One ohm is defined as the resistance between two points of a conductor when 1 volt is applied and a current of 1 ampere is flowing.
We've now defined, in order, a basic set of our favorite electrical units.

Systems of Units

Over the last 200 years, there have been three main systems of scientific units:
  • SI
  • MKS
  • cgs
SI is the International System of Units—in French, Système International d'Unités. It is the modern form of the metric system and is the most widely used system of measurement. The system was published in 1960 as the result of discussions that started in 1948. SI is based on the metre-kilogram-second system (MKS). In the United States, the SI is used in science, medicine, government, technology, and engineering.
MKS is based on measuring lengths in meters, mass in kilograms, and time in seconds. MKS is generally used in engineering and beginning physics. It was proposed in 1901. The most familiar units of electricity and magnetism—ohm, farad, coulomb, etc.—are MKS units.
cgs is based on measuring lengths in centimeters, mass in grams, and time in seconds. It was introduced in 1874. The cgs system is commonly used in theoretical physics. The difference between the SI and cgs systems goes much deeper than a simple scaling of the units for length and mass.
There are seven SI base units.

SI base units

ampereAelectric current
candelacdluminous intensity
molemolamount of substance
One SI base unit comes from electricity: the ampere. The ampere has the same lofty status as the meter, kilogram, and second. It is defined as its own thing, not in terms of other units.

SI derived units used in electricity

The remaining electrical units are SI derived units, formed by combinations of the base units. If the ampere is the "first" electrical unit, these derived electrical units follow close behind.
NameSymbolQuantityIn terms of other SI units
voltVvoltage (electric potential difference)W/A
ohmΩresistance, impedanceV/A
siemensSconductanceA/V or 1/Ω
weberWbmagnetic fluxVs
teslaTmagnetic field strengthWb/m2

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