What is an ohm?

The ohm (symbol: Ω) is the SI derived unit of electrical resistance, named after German physicist Georg Simon Ohm. 

Georg Simon Ohm (16 March 1789 – 6 July 1854) was a German physicist and mathematician. As a high school teacher, Ohm began his research with the new electrochemical cell, invented by Italian scientist Alessandro Volta. Using equipment of his own creation, Ohm found that there is a direct proportionality between the potential difference (voltage) applied across a conductor and the resultant electric current. This relationship is known as Ohm's law.

V (voltage) = I (current in amps) * R (resistance in Ohms)

therefore 
R (resistance in Ohms) =V (voltage) / I (current in amps)

Although several empiraclly-derived standards expressing electrical resistance were developed in connection with early telegraphy practice, the British Association for the Advancement of Science proposed a unit derived from existing units of mass, length and time and of a convenient size for practical work as early as 1861. The definition of the "ohm" unit was revised several times. Today the ohm is a derived unit in the International System of Units, with its value expressed by the quantum Hall effect.

The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere, the conductor not being the seat of any electromotive force. 

In many cases the resistance of a conductor in ohms is approximately constant within a certain range of voltages, temperatures, and other parameters; one speaks of linear resistors. In other cases resistance varies (e.g., thermistors).
Commonly used multiples and sub-multiples in electrical and electronic usage are the milliohm, kilohm, megohm, and gigaohm, though the term 'gigohm', though not official, is in common use for the latter.

In alternating current circuits, electrical impedance is also measured in ohms.
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