Definitions

# Siemens (unit)

The siemens (symbol: S) is the SI derived unit of electric conductance. It is equal to inverse ohm. It is named after the German inventor and industrialist Ernst Werner von Siemens, and was previously called the mho. In English, the term siemens is used both for the singular and plural. The 14th General Conference on Weights and Measures approved the addition of the siemens as an SI derived unit in 1971.

## Definition

For a physical object, typically an electronic device, with electrical resistance R, the conductance G is defined as

$G = frac\left\{1\right\}R = frac\left\{I\right\}V,$

where I is the current through the object and V is the voltage (electrical potential difference) across the object.

The unit siemens for the conductance G is defined by

$mbox\left\{S\right\} = Omega^\left\{-1\right\} = dfrac\left\{mbox\left\{A\right\}\right\}\left\{mbox\left\{V\right\}\right\} = dfrac\left\{mbox\left\{C\right\}^2 cdot mbox\left\{s\right\}\right\}\left\{mbox\left\{kg\right\} cdot mbox\left\{m\right\}^2\right\} = dfrac\left\{mbox\left\{A\right\}^\left\{2\right\} cdot mbox\left\{s\right\}^3\right\}\left\{mbox\left\{kg\right\} cdot mbox\left\{m\right\}^2\right\}.$
Note that the last term is in SI base units where A is the symbol for ampere, the unit of electric current; kg is the symbol for kilogram, the unit of mass; m is the symbol for metre, the unit of length; and s is the symbol for the time unit second. C is the symbol for the SI derived unit of electric charge, the coulomb; V is the symbol for the SI derived unit of voltage, the volt; and Ω is the symbol for the SI derived unit of electrical resistance, the ohm.

So for a device with conductance one siemens, then the electric current through it with one volt across it is one ampere, and for each extra volt across it the electric current through it increases by one ampere.

Example: The conductance of a resistor with resistance six ohms is G = 1/(6 Ω) $approx$ 0.167 S.

## Historical/Deprecated

Since 1860 to the middle of 20th century, siemens or siemens mercury unit, was the unit of electrical resistance. It was defined as the resistance of mercury column of 1 meter long and 1 mm squared at 0 degrees Celsius. It was equivalent to 0.953 Ohm approximately. Officially, it ceased usage after 1881, but was widely used in telegraph and telephone services until WWII.

## Mho

The siemens was previously referred to by the term mho, which was derived from spelling ohm backwards and written with an upside-down capital Greek letter Omega: $mho$, Unicode symbol U+2127 (℧). The term siemens, as it is an SI unit, is used universally in science and primarily in electrical applications, while mho is still used primarily in electronic applications. The inverted Omega, while not an official SI abbreviation, has the advantage of being less likely to be confused with a variable than the letter S when doing algebraic calculations by hand, where the usual typographical distinctions (such as italic for variables and Roman for unit names) are difficult to maintain. Furthermore, in some industries (like electronics) it is common to write, contrary to common established and SI-dictated practice, the symbol S instead of s where second is meant, potentially causing confusion.

## References

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