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{{Short description|Unit of measurement in the field of electricity}}
{{refimprove|date=November 2018}}
{{Use dmy dates|date=July 2013}}
A '''conventional electrical unit''' (or '''conventional unit''' where there is no risk of ambiguity) is a [[unit of measurement]] in the field of [[electricity]] which is based on the so-called "conventional values" of the [[Josephson constant]], the [[von Klitzing constant]] agreed by the [[International Committee for Weights and Measures]] (CIPM) in 1988, as well as [[Hyperfine structure|Δ''ν''<sub>Cs</sub>]] used to define the [[second]]. These units are very similar in scale to their corresponding [[SI unit]]s, but are not identical because of the different values used for the constants. They are distinguished from the corresponding SI units by setting the symbol in italic typeface and adding a subscript "90" – e.g., the conventional volt has the symbol ''V''{{sub|90}} – as they came into international use on 1 January 1990.

This system was developed to increase the precision of measurements: The Josephson and von Klitzing constants can be realized with great precision, repeatability and ease, and are exactly defined in terms of the [[physical constant|universal constant]]s [[Elementary charge|''e'']] and [[Planck constant|''h'']]. The conventional electrical units represent a significant step towards using "natural" fundamental physics for practical measurement purposes.  They achieved acceptance as an international standard in parallel to the [[SI]] system of units and are commonly used outside of the physics community in both engineering and industry.  Addition of the constant [[Speed of light|''c'']] would be needed to define units for all dimensions used in physics, as in the SI.

The SI system made the transition to equivalent definitions 29 years later but with values of the constants defined to match the old SI units more precisely. Consequently, the conventional electrical units differ slightly from the corresponding SI units, [[2019 redefinition of the SI base units|now]] with exactly defined ratios.

== Historical development ==
Several significant steps have been taken in the last half century to increase the precision and utility of measurement units:
* In 1967, the thirteenth [[General Conference on Weights and Measures]] (CGPM) defined the [[second]] of atomic time in the International System of Units as the duration of {{val|9192631770}} periods of the radiation corresponding to the transition between the two [[hyperfine structure|hyperfine]] levels of the ground state of the cesium-133 atom.<ref>{{cite web |title=Resolution 1 of the 13th CGPM (1967) – SI unit of time (second) |url=https://www.bipm.org/en/CGPM/db/13/1/ |access-date=2019-02-18 |archive-date=11 April 2021 |archive-url=https://web.archive.org/web/20210411132806/https://www.bipm.org/en/CGPM/db/13/1/ |url-status=dead }}</ref>
* In 1983, the seventeenth CGPM redefined the [[metre]] in terms of the second and the speed of light, thus fixing the speed of light at exactly {{val|299792458|u=m/s}}.<ref>{{cite web |title=Resolution 1 of the 17th CGPM (1983) – Definition of the metre |url=https://www.bipm.org/en/CGPM/db/17/1/ |access-date=2019-02-18 |archive-date=29 March 2019 |archive-url=https://web.archive.org/web/20190329222730/https://www.bipm.org/en/CGPM/db/17/1/ |url-status=dead }}</ref>
* In 1988, the CIPM recommended adoption of conventional values for the Josephson constant as exactly {{nowrap|1=''K''{{sub|J-90}} = {{val|483597.9|e=9|u=Hz/V}}}}<ref>{{cite web |url=https://www.bipm.org/en/CIPM/db/1988/1/ |title=CIPM, 1988: Recommendation 1 – Representation of the volt by means of the Josephson effect |access-date=2019-02-18 |archive-date=21 January 2021 |archive-url=https://web.archive.org/web/20210121214055/https://www.bipm.org/en/CIPM/db/1988/1/ |url-status=dead }}</ref> and for the von Klitzing constant as exactly {{nowrap|1=''R''{{sub|K-90}} = {{val|25812.807|u=Ω}}}}<ref>{{cite web |url=https://www.bipm.org/en/CIPM/db/1988/2/ |title=CIPM, 1988: Recommendation 2 – Representation of the ohm by means of the quantum Hall effect |access-date=2019-02-18 |archive-date=21 January 2021 |archive-url=https://web.archive.org/web/20210121221140/https://www.bipm.org/en/CIPM/db/1988/2/ |url-status=dead }}</ref> as of 1 January 1990.
* In 1991, the eighteenth CGPM noted the conventional values for the Josephson constant and the von Klitzing constant.<ref>{{cite web |title=Resolution 2 of the 19th CGPM (1991) – The Josephson and quantum-Hall effects |url=https://www.bipm.org/en/CGPM/db/19/2/ |access-date=2019-02-18 |archive-date=26 January 2021 |archive-url=https://web.archive.org/web/20210126100105/https://www.bipm.org/en/CGPM/db/19/2/ |url-status=dead }}</ref>
* In 2000, the CIPM approved the use of the [[quantum Hall effect]], with the value of ''R''{{sub|K-90}} to be used to establish a reference standard of resistance.<ref>{{cite web |title=CIPM, 2000 – use of the von Klitzing constant to express the value of a reference standard of resistance as a function of the quantum Hall effect |url=https://www.bipm.org/en/committees/cipm/cipm-2000.html |access-date=2019-02-18 |archive-date=21 January 2021 |archive-url=https://web.archive.org/web/20210121212712/https://www.bipm.org/en/committees/cipm/cipm-2000.html |url-status=dead }}</ref>
* In 2018, the twenty-sixth CGPM resolved to abrogate the conventional values of the Josephson and von Klitzing constants with the [[2019 redefinition of SI base units]].<ref>{{cite web |url=https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf |title=26th CGPM Resolutions |website=BIPM |access-date=2019-02-18}}</ref>

==Definition==
Conventional electrical units are based on defined values of the [[caesium-133]] [[hyperfine structure|hyperfine transition frequency]], [[Josephson constant]] and the [[von Klitzing constant]], the first two which allow a very precise practical measurement of [[time]] and [[electromotive force]], and the last which allows a very precise practical measurement of [[electrical resistance]].<ref name=CODATA2014>{{cite journal
 |last1=Mohr |first1=Peter J.
 |last2=Newell |first2=David B.
 |last3=Taylor |first3=Barry N.
 |year=2015
 |title=CODATA recommended values of the fundamental physical constants: 2014
 |journal=Zenodo
 |arxiv=1507.07956
 |doi=10.5281/zenodo.22826
}}</ref>

{| class="wikitable"
|-
! Constant
! Conventional exact value<br/>(CIPM, 1988; until 2018)
! Empirical value (in SI units)<br/>(CODATA, 2014<ref name=CODATA2014 />)
! Exact value<br>(SI units, 2019)
|-
| <sup>133</sup>Cs hyperfine transition frequency
| {{physconst|DnuCs|symbol=yes|ref=no}}
| 
| {{physconst|DnuCs|symbol=yes}}
|-
| Josephson constant
| ''K''{{sub|J-90}} = {{val|483597.9|u=GHz/V}}{{physconst|KJ90|ref=only}}
| ''K''{{sub|J}} = {{val|483597.8525|(30)|u=GHz/V}}
| ''K''{{sub|J}} = {{sfrac|2 × {{val|1.602176634|e=-19|u=C}}|{{val|6.62607015|e=-34|u=J.s}}}}
|-
| von Klitzing constant
| ''R''{{sub|K-90}} = {{val|25812.807|u=Ω}}{{physconst|RK90|ref=only}}
| ''R''{{sub|K}} = {{val|25812.8074555|(59)|u=Ω}}
| ''R''{{sub|K}} = {{sfrac|{{val|6.62607015|e=-34|u=J.s}}|({{val|1.602176634|e=-19|u=C}}){{sup|2}}}}
|-
|}

*The conventional [[volt]], ''V''{{sub|90}}, is the electromotive force (or electric potential difference) measured against a [[Josephson effect]] standard using the defined value of the Josephson constant, ''K''{{sub|J-90}}; that is, by the relation ''K''{{sub|J}} = {{val|483597.9|u=GHz/''V''{{sub|90}}}}. ''See [[Josephson voltage standard]].''
*The conventional [[ohm]], ''Ω''{{sub|90}}, is the electrical resistance measured against a [[quantum Hall effect]] standard using the defined value of the von Klitzing constant, ''R''{{sub|K-90}}; that is, by the relation ''R''{{sub|K}} = {{val|25812.807|u=''Ω''{{sub|90}}}}.
*Other conventional electrical units are defined by the normal relationships between units paralleling those of SI, as in the conversion table below.

==Conversion to SI units==
{| class="wikitable"
|-
! Unit
! Symbol
! Definition
! Related to SI
! SI value (CODATA 2014)
! SI value (2019)
|-
| conventional [[volt]]
| ''V''{{sub|90}}
| ''see above''
| {{sfrac|''K''{{sub|J-90}}|''K''{{sub|J}}}}&nbsp;V
| {{val|1.0000000983|(61)|u=V}}
| {{physconst|V90}}
|-
| conventional [[ohm]]
| ''Ω''{{sub|90}} 
| ''see above''
| {{sfrac|''R''{{sub|K}}|''R''{{sub|K-90}}}}&nbsp;Ω
| {{val|1.00000001765|(23)|u=Ω}}
| {{physconst|ohm90}}
|-
| conventional [[ampere]]
| ''A''{{sub|90}} 
| ''V''{{sub|90}}/''Ω''{{sub|90}}
| {{sfrac|''K''{{sub|J-90}}|''K''{{sub|J}}}}⋅{{sfrac|''R''{{sub|K-90}}|''R''{{sub|K}}}}&nbsp;A
| {{val|1.0000000806|(61)|u=A}}
| {{physconst|A90}}
|-
| conventional [[coulomb]]
| ''C''{{sub|90}}
| [[second|s]]⋅''A''{{sub|90}} = [[second|s]]⋅''V''{{sub|90}}/''Ω''{{sub|90}}
| {{sfrac|''K''{{sub|J-90}}|''K''{{sub|J}}}}⋅{{sfrac|''R''{{sub|K-90}}|''R''{{sub|K}}}}&nbsp;C
| {{val|1.0000000806|(61)|u=C}}
| {{physconst|C90}}
|-
| conventional [[watt]]
| ''W''{{sub|90}}
| ''A''{{sub|90}}''V''{{sub|90}} = ''V''{{sub|90}}<sup>2</sup>/''Ω''{{sub|90}}
| {{resize|150%|(}}{{sfrac|''K''{{sub|J-90}}|''K''{{sub|J}}}}{{resize|150%|)}}{{su|b=&nbsp;|p=2|lh=1.5em}}⋅{{sfrac|''R''{{sub|K-90}}|''R''{{sub|K}}}}&nbsp;W
| {{val|1.000000179|(12)|u=W}}
| {{physconst|W90}}
|-
| conventional [[farad]]
| ''F''{{sub|90}}
| ''C''{{sub|90}}/''V''{{sub|90}} = [[second|s]]/''Ω''{{sub|90}}
| {{sfrac|''R''{{sub|K-90}}|''R''{{sub|K}}}}&nbsp;F
| {{val|0.99999998235|(23)|u=F}}
| {{physconst|F90}}
|-
| conventional [[henry (unit)|henry]]
| ''H''{{sub|90}}
| [[second|s]]⋅''Ω''{{sub|90}}
| {{sfrac|''R''{{sub|K}}|''R''{{sub|K-90}}}}&nbsp;H
| {{val|1.00000001765|(23)|u=H}}
| {{physconst|H90}}
|-
|}

The 2019 redefinition of SI base units defines all these units in a way that fixes the numeric values of ''K''{{sub|J}}, ''R''{{sub|K}} and Δ''ν''<sub>Cs</sub> exactly, albeit with values of the first two that differ slightly from the conventional values. Consequently, these conventional units all have known exact values in terms of the redefined SI units.  Because of this, there is no accuracy benefit from maintaining the conventional values.

==See also==
*[[Centimetre–gram–second system of units]]
*[[ITS-90]]

==References==
*{{CODATA2006}}

{{Reflist}}

==External links==
* [http://histoires-de-sciences.over-blog.fr/2013/11/electrical-units-history.html History of the electrical units.]

{{systems of measurement}}

{{DEFAULTSORT:Conventional Electrical Unit}}
[[Category:Electromagnetism]]
[[Category:Metrology]]
[[Category:Systems of units]]