View source for Siemens (unit)

{{Short description|SI unit of electric conductance}}
{{For|the deprecated "mercury unit"|Siemens mercury unit}}
{{Redirect-distinguish-text|Siemen|the company [[Siemens]]}}
{{Infobox Unit
| name = siemens
| image = 
| caption = 
| standard = [[SI]]
| quantity = [[Electrical resistance and conductance|electric conductance]]
| symbol = S
| namedafter = [[Werner von Siemens|Ernst Werner von Siemens]]
| units1 = [[SI&nbsp;base&nbsp;unit]]s
| inunits1 = [[kilogram|kg]]{{sup|&minus;1}}&sdot;[[metre|m]]{{sup|&minus;2}}&sdot;[[second|s]]{{sup|3}}&sdot;[[ampere|A]]{{sup|2}}
| units2 = inverse ohm
| inunits2 = 1 Ω{{sup|&minus;1}}
| units3 = mho
| inunits3 = 1 ℧
}}
The '''siemens''' (symbol: '''S''') is the unit of [[electric conductance]], [[susceptance|electric susceptance]], and [[admittance|electric admittance]] in the [[International System of Units]] (SI). Conductance, susceptance, and admittance are the reciprocals of [[Electrical resistance|resistance]], [[Electrical reactance|reactance]], and [[Electrical impedance|impedance]] respectively; hence one siemens is equal to the reciprocal of one [[Ohm (unit)|ohm]] ({{math|Ω{{sup|&minus;1}}}}) and is also referred to as the ''[[#Mho|mho]]''. The siemens was adopted by the [[International Electrotechnical Commission|IEC]] in 1935,<ref>{{cite conference |url=http://www.bipm.org/utils/common/pdf/CGPM/CGPM14.pdf#page=53 |title=Minutes |conference=14th General Conference on Weights and Measures |year=1971 |page=53}}</ref> and the 14th [[General Conference on Weights and Measures]] approved the addition of the siemens as a derived unit in 1971.<ref name="CGPM14">{{cite conference |url=http://www.bipm.org/utils/common/pdf/CGPM/CGPM14.pdf#page=78 |title=Minutes |conference=14th General Conference on Weights and Measures |year=1971 |page=78}}</ref>

The unit is named after [[Werner von Siemens|Ernst Werner von Siemens]]. In English, the same word ''siemens'' is used both for the singular and plural.<ref>{{cite report |chapter-url=https://www.nist.gov/pml/nist-guide-si-chapter-9-rules-and-style-conventions-spelling-unit-names |title=NIST Guide to the SI |chapter=Chapter 9: Rules and Style Conventions for Spelling Unit Names |publisher=National Institute of Standards and Technology |year=2008 |access-date=2017-12-22 |archive-date=2019-05-06 |archive-url=https://web.archive.org/web/20190506222742/https://www.nist.gov/pml/nist-guide-si-chapter-9-rules-and-style-conventions-spelling-unit-names |url-status=dead }}</ref> Like other SI units named after people, the symbol (S) is capitalized but the name of the unit is not. For the siemens this distinguishes it from the [[second]], symbol (lower case) s.

The related property, [[Electrical resistivity and conductivity|electrical conductivity]], is measured in units of siemens per metre (S/m).

== Definition ==
For an element conducting [[direct current]], [[electrical resistance and conductance|electrical resistance {{mvar|R}} and electrical conductance {{mvar|G}}]] are defined as

:<math>G = \frac{1}{R} = \frac{I}{V} 
 </math>

where {{mvar|I}} is the [[electric current]] through the object and {{mvar|V}} is the [[voltage]] (electrical potential difference) across the object.

The unit '''siemens''' for the conductance&nbsp;''G'' is defined by
:<math>\mathrm{[S]} = [\Omega^{-1}] = [\mathrm{A}/\mathrm{V}]</math> <!-- 2019-09-21 added brackets to show we're focusing on units and removed the stacked division to fit units in brackets -->
where {{math|Ω}} is the [[Ohm (unit)|ohm]], {{math|A}} is the [[ampere]], and {{math|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&nbsp;Ω)<sup>&minus;1</sup>, which is equal to a conductance of 200&nbsp;mS.

== Mho<!-- This section is linked from [[Mho]] --> ==
{{Other uses|MHO (disambiguation)}}

A historical equivalent for the ''siemens'' is the '''''mho''''' ({{IPAc-en|'|m|oʊ}}). The name is derived from the word ''[[ohm]]'' spelled backwards as the reciprocal of one ohm, at the suggestion of [[Sir William Thomson]] (Lord Kelvin) in 1883.<ref>{{cite book |last=Thomson |first=William |title=The Practical Applications of Electricity |date=1884 |publisher=Institution of Civil Engineers |pages=149–174 at p 171 (Lecture given 3 May 1883) |chapter=Electrical Units of Measurement |chapter-url=https://archive.org/details/practicalapplic00bramgoog/page/n182/mode/2up?q=mho}} Available online. Thomson helpfully added that the proper pronunciation of "mho" could be obtained by taking a phonograph and turning it backwards.</ref> Its symbol is an upside-down capital [[Greek alphabet|Greek]] letter [[omega]].

[[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.<ref>{{cite report |title=NIST Guide to the SI |chapter=Chapter 5: Units Outside the SI |year=2008 |chapter-url=https://www.nist.gov/pml/nist-guide-si-chapter-5-units-outside-si |publisher=National Institute of Standards and Technology |access-date=2017-12-22}}</ref>{{clarify|reason=does this edict extend to the associated symbol of the upside-down ohm sign?|date=November 2024}}

The SI term ''siemens'' is used universally in science and often in electrical applications, while ''mho'' is still used in some electronic contexts.<ref>Al Dahaan, S., Al-Ansari, N., & Knutsson, S. (2016). Influence of groundwater hypothetical salts on electrical conductivity total dissolved solids. Engineering, 8(11), 823-830.</ref><ref>SINGH, S., GAUTAM, P. K., KUMAR, P., BISWAS, A., & SARKAR, T. (2021). Delineating the characteristics of saline water intrusion in the coastal aquifers of Tamil Nadu, India by analysing the Dar-Zarrouk parameters. Contributions to Geophysics & Geodesy, 51(2).</ref>

The upside-down 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.<ref>{{cite book |first=Eugene R. |last=Weiner |title=Applications of Environmental Aquatic Chemistry: A practical guide |page=109 |publisher=CRC Press |year=2013 |isbn=978-1439853320}}</ref> So, for example, a [[pentode]]’s [[transconductance]] of {{val|2.2|u=mS}} might alternatively be written as {{val|2.2|u=m℧}} or {{val|2200|u=μ℧}} (most common in the 1930s) or {{val|2.2|u=mA|up=V}}.

The ''ohm'' had officially replaced the [[siemens mercury unit|old "''siemens'' unit"]], a unit of ''resistance'', at an international conference in 1881.<ref>{{cite web |url=http://www.tech-faq.com/siemens.html |title=Siemens (unit of electrical conductance) |website=www.tech-faq.com|date=6 April 2019 }}</ref>

== Notes and references ==
{{reflist|25em}}

== External links ==
* {{cite web |url=http://www.bipm.org/en/si/si_brochure/ |type=brochure |title=The International System of Units |publisher=[[BIPM]]}}
* {{cite web |url=http://www.sizes.com/units/siemens.htm |title=Different units named after Siemens |website=sizes.com}}

{{SI units}}

{{DEFAULTSORT:Siemens (Unit)}}
[[Category:SI derived units]]
[[Category:Units of electrical conductance]]
[[Category:Werner von Siemens]]