# Siemens (unit)

Siemens | |
---|---|

Unit system | SI derived unit |

Unit of | Electric conductance |

Symbol | S (= Ω^{−1}) |

Named after | Ernst Werner von Siemens |

In SI base units: | kg^{−1}⋅m^{−2}⋅s^{3}⋅A^{2} |

The **siemens** (symbol: S) is the derived unit of electric conductance, electric susceptance and electric admittance in the International System of Units (SI). Conductance, susceptance, and admittance are the reciprocals of resistance, reactance, and impedance respectively; hence one siemens is equal to the reciprocal of one ohm, and is also referred to as the *mho*. The 14th General Conference on Weights and Measures approved the addition of the siemens as a derived unit in 1971.

The unit is named after Ernst Werner von Siemens; in English, the same form *siemens* is used both for the singular and plural.^{[1]}

## Definition[edit]

For a conducting or semiconducting element, electrical resistance *R* and electrical conductance *G* are defined as

where *I* is the electric 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

where Ω is the ohm, A is the ampere, and V is the volt.

For a device with a conductance of one siemens, the electric current through the device will increase by one ampere for every increase of one volt of electric potential difference across the device.

The conductance of a resistor with a resistance of five ohms, for example, is (5 Ω)^{−1}, which is equal to 200 mS.

## Mho[edit]

An alternative name for the *siemens* is the * mho* /moʊ/, the reciprocal of one ohm. It is derived from spelling

*ohm*backwards (a semordnilap) and is written as an upside-down capital Greek letter omega: , Unicode symbol U+2127 (℧). According to Maver

^{[2]}the term

*mho*was suggested by Sir William Thomson (Lord Kelvin). The

*mho*was officially renamed to the

*siemens*, replacing the old meaning of the "

*siemens*unit", at a conference in 1881.

^{[3]}

The term *siemens*, as it is an SI term, is used universally in science and often 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. Likewise, it is difficult to distinguish the symbol *S* from the lower-case *s* where *second* is meant, potentially causing confusion.^{[4]} So, for example, a pentode's transconductance of 2.2 mS might alternatively be written as 2.2 m℧ or 2200 micromhos (most common in the 1930s) or 2.2 mA/V.

## Notes and references[edit]

**^**NIST Guide to SI Units – 9 Rules and Style Conventions for Spelling Unit Names, National Institute of Standards and Technology**^**Maver, William: American Telegraphy and Encyclopedia of the Telegraph: Systems, Apparatus, Operation. 1903.**^**http://www.tech-faq.com/siemens.html**^**Eugene R. Weiner,*Applications of Environmental Aquatic Chemistry: A Practical Guide*, p. 109, CRC Press, 2013 ISBN 1439853320