# Siemens (unit)

Short description: SI unit of electric conductance
siemens
Unit systemSI derived unit
Unit ofElectric conductance
SymbolS or Ω−1, ℧
Named afterErnst Werner von Siemens
Conversions
1 S in ...... is equal to ...
SI base units   kg−1m−2s3A2

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 redundantly equal to the reciprocal of one ohm (Ω−1) 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 word siemens is used both for the singular and plural.

The related property, electrical conductivity, is measured in units of siemens per metre (S/m).

## Definition

For an element conducting direct current, electrical resistance R and electrical conductance G are defined as

$\displaystyle{ G = \frac{1}R = \frac{I}{V} }$

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

$\displaystyle{ \mathrm{[S]} = [\Omega^{-1}] = [\mathrm{A}/\mathrm{V}] }$

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

Another name for the siemens is the mho (/ˈm/). As the reciprocal of one ohm, it is the word ohm spelled backwards, at the suggestion of Sir William Thomson (Lord Kelvin) in 1883. Its symbol is an inverted capital Greek letter omega: U+2127 INVERTED OHM SIGN.

NIST's Guide for the Use of the International System of Units (SI) refers to the mho as an "unaccepted special name for an SI unit", and indicates that it should be strictly avoided.

The SI term siemens is used universally in science and often in electrical applications, while mho is still used in some electronic contexts.

The inverted capital omega symbol (℧), while not an official SI abbreviation, is less likely to be confused with a variable than the letter 'S' when writing the symbol by hand. The usual typographical distinctions (such as italic for variables and roman for units) are difficult to maintain. Likewise, it is difficult to distinguish the symbol 'S' (siemens) from the lower-case 's' (seconds), potentially causing confusion. So, for example, a pentode’s transconductance of 2.2 mS might alternatively be written as 2.2 m℧ or 2200 μ℧ (most common in the 1930s) or 2.2 mA/V.

A handwritten 'S' can also be misread as the frequency-space variable 's', commonly used in transfer functions.

The ohm had officially replaced the old "siemens unit", a unit of resistance, at an international conference in 1881.

## Notes and references

1. "Minutes". 14th General Conference on Weights and Measures. 1971. p. 78.
2. ﻿NIST Guide to the SI﻿ (Report). National Institute of Standards and Technology. 2008.
3. Thomson, William (1884). "Electrical Units of Measurement". The Practical Applications of Electricity. Institution of Civil Engineers. pp. 149–174 at p 171 (Lecture given 3 May 1883).  Available online. Thomson helpfully added that the proper pronunciation of "mho" could be obtained by taking a phonograph and turn it backwards.
4. ﻿NIST Guide to the SI﻿ (Report). National Institute of Standards and Technology. 2008.
5. Weiner, Eugene R. (2013). Applications of Environmental Aquatic Chemistry: A practical guide. CRC Press. p. 109. ISBN 1439853320.