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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 slightly differ from the corresponding SI 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:

Definition

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

Conversion to SI units

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/KJRK-90/RK A 1.0000000806(61) A 1.00000008887... A[14]
conventional coulomb C90 sA90 = sV90/Ω90 KJ-90/KJRK-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 sΩ90 RK/RK-90 H 1.00000001765(23) H 1.00000001779... H[18]

The 2019 redefinition of SI base units 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

References


  1. ^ "Resolution 1 of the 13th CGPM (1967) – SI unit of time (second)". Retrieved 18 February 2019.
  2. ^ "Resolution 1 of the 17th CGPM (1983) – Definition of the metre". Retrieved 18 February 2019.
  3. ^ "CIPM, 1988: Recommendation 1 – Representation of the volt by means of the Josephson effect". Retrieved 18 February 2019.
  4. ^ "CIPM, 1988: Recommendation 2 – Representation of the ohm by means of the quantum Hall effect". Retrieved 18 February 2019.
  5. ^ "Resolution 2 of the 19th CGPM (1991) – The Josephson and quantum-Hall effects". 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". 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. ^ "2018 CODATA Value: hyperfine transition frequency of Cs-133". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 18 August 2019.
  10. ^ "2018 CODATA Value: conventional value of Josephson constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
  11. ^ "2018 CODATA Value: conventional value of von Klitzing constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
  12. ^ "2018 CODATA Value: conventional value of volt-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 1 June 2019.
  13. ^ "2018 CODATA Value: conventional value of ohm-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 1 June 2019.
  14. ^ "2018 CODATA Value: conventional value of ampere-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 1 June 2019.
  15. ^ "2018 CODATA Value: conventional value of coulomb-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 1 June 2019.
  16. ^ "2018 CODATA Value: conventional value of watt-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 1 June 2019.
  17. ^ "2018 CODATA Value: conventional value of farad-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 1 June 2019.
  18. ^ "2018 CODATA Value: conventional value of henry-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 1 June 2019.