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Conventional electrical unit

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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 ΔνCs used to define the second. These units are very similar in scale to their corresponding SI units, 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 V90 – 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 universal constants e and 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 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, now with exactly defined ratios.

Historical development

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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 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.[1]
  • 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 299792458 m/s.[2]
  • In 1988, the CIPM recommended adoption of conventional values for the Josephson constant as exactly KJ-90 = 483597.9×109 Hz/V[3] and for the von Klitzing constant as exactly RK-90 = 25812.807 Ω[4] as of 1 January 1990.
  • In 1991, the eighteenth CGPM noted the conventional values for the Josephson constant and the von Klitzing constant.[5]
  • In 2000, the CIPM approved the use of the quantum Hall effect, with the value of RK-90 to be used to establish a reference standard of resistance.[6]
  • In 2018, the twenty-sixth CGPM resolved to abrogate the conventional values of the Josephson and von Klitzing constants with the 2019 revision of the SI.[7]

Definition

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Conventional electrical units are based on defined values of the caesium-133 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.[8]

Constant Conventional exact value
(CIPM, 1988; until 2018) 		Empirical value (in SI units)
(CODATA, 2014[8]) 		Exact value
(SI units, 2019)
133Cs hyperfine transition frequency Δν(133Cs)hfs = 9192631770 Hz Δν(133Cs)hfs = 9192631770 Hz‍[9]
Josephson constant KJ-90 = 483597.9 GHz/V[10] KJ = 483597.8525(30) GHz/V KJ = ⁠2 × 1.602176634×10−19 C/6.62607015×10−34 J⋅s⁠
von Klitzing constant RK-90 = 25812.807 Ω[11] RK = 25812.8074555(59) Ω RK = ⁠6.62607015×10−34 J⋅s/(1.602176634×10−19 C)2⁠
  • The conventional volt, V90, is the electromotive force (or electric potential difference) measured against a Josephson effect standard using the defined value of the Josephson constant, KJ-90; that is, by the relation KJ = 483597.9 GHz/V90. See Josephson voltage standard.
  • The conventional ohm, Ω90, is the electrical resistance measured against a quantum Hall effect standard using the defined value of the von Klitzing constant, RK-90; that is, by the relation RK = 25812.807 Ω90.
  • 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

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Unit Symbol Definition Related to SI SI value (CODATA 2014) SI value (2019)
conventional volt V90 see above ⁠KJ-90/KJ⁠ V 1.0000000983(61) V 1.00000010666... V‍[12]
conventional ohm Ω90 see above ⁠RK/RK-90⁠ Ω 1.00000001765(23) Ω 1.00000001779... Ω‍[13]
conventional ampere A90 V90/Ω90 ⁠KJ-90/KJ⁠⋅⁠RK-90/RK⁠ A 1.0000000806(61) A 1.00000008887... A‍[14]
conventional coulomb C90 s⋅A90 = s⋅V90/Ω90 ⁠KJ-90/KJ⁠⋅⁠RK-90/RK⁠ C 1.0000000806(61) C 1.00000008887... C‍[15]
conventional watt W90 A90V90 = V902/Ω90 (⁠KJ-90/KJ⁠)2
 ⋅⁠RK-90/RK⁠ W 		1.000000179(12) W 1.00000019553... W‍[16]
conventional farad F90 C90/V90 = s/Ω90 ⁠RK-90/RK⁠ F 0.99999998235(23) F 0.99999998220... F‍[17]
conventional henry H90 s⋅Ω90 ⁠RK/RK-90⁠ H 1.00000001765(23) H 1.00000001779... H‍[18]

The 2019 revision of the SI defines all these units in a way that fixes the numeric values of KJ, RK and ΔνCs 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

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References

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  1. ^ "Resolution 1 of the 13th CGPM (1967) – SI unit of time (second)". Archived from the original on 11 April 2021. Retrieved 18 February 2019.
  2. ^ "Resolution 1 of the 17th CGPM (1983) – Definition of the metre". Archived from the original on 29 March 2019. Retrieved 18 February 2019.
  3. ^ "CIPM, 1988: Recommendation 1 – Representation of the volt by means of the Josephson effect". Archived from the original on 21 January 2021. Retrieved 18 February 2019.
  4. ^ "CIPM, 1988: Recommendation 2 – Representation of the ohm by means of the quantum Hall effect". Archived from the original on 21 January 2021. Retrieved 18 February 2019.
  5. ^ "Resolution 2 of the 19th CGPM (1991) – The Josephson and quantum-Hall effects". Archived from the original on 26 January 2021. Retrieved 18 February 2019.
  6. ^ "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". Archived from the original on 21 January 2021. Retrieved 18 February 2019.
  7. ^ "26th CGPM Resolutions" (PDF). BIPM. Retrieved 18 February 2019.
  8. ^ a b Mohr, Peter J.; Newell, David B.; Taylor, Barry N. (2015). "CODATA recommended values of the fundamental physical constants: 2014". Zenodo. arXiv:1507.07956. doi:10.5281/zenodo.22826.
  9. ^ "2022 CODATA Value: hyperfine transition frequency of Cs-133". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  10. ^ "2022 CODATA Value: conventional value of Josephson constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  11. ^ "2022 CODATA Value: conventional value of von Klitzing constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  12. ^ "2022 CODATA Value: conventional value of volt-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  13. ^ "2022 CODATA Value: conventional value of ohm-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  14. ^ "2022 CODATA Value: conventional value of ampere-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  15. ^ "2022 CODATA Value: conventional value of coulomb-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  16. ^ "2022 CODATA Value: conventional value of watt-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  17. ^ "2022 CODATA Value: conventional value of farad-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  18. ^ "2022 CODATA Value: conventional value of henry-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
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