Conventional electrical unit

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 and the von Klitzing constant agreed by the International Committee for Weights and Measures (CIPM) in 1988. These units are very similar in scale to their corresponding SI units, but are not identical because of their different definition. 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. The conventional electrical units have achieved acceptance as an international standard and are commonly used outside of the physics community in both engineering and industry.

The conventional electrical units are "quasi-natural" in the sense that they are completely and exactly defined in terms of universal constants. They represent a significant step towards using "natural" fundamental physics for practical measurement purposes. However, the conventional electrical units are unlike other systems of natural units in that some physical constants are not set to unity but rather set to fixed numerical values that are very close to (but not precisely the same as) those in the SI system of units.

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 as of 1 January 1990, of a conventional Josephson constant as exactly KJ-90 = 483597.9×109 Hz/V,[3] and of a conventional von Klitzing constant as exactly RK-90 = 25812.807 Ω.[4]
• 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 redefinition of SI base units.[7]

Definition

Conventional electrical units are based on defined values of the Josephson constant and the von Klitzing constant, which allow practical measurements of electromotive force and electrical resistance respectively. [8]

Constant Conventional (defined) value
(CIPM, 1988)
(Until 2018)
Empirical value (in SI units)
(CODATA, 2014[8])
Josephson constant KJ-90 = 483597.9GHz/V KJ = 483597.8525(30)GHz/V
von Klitzing constant RK-90 = 25812.807Ω RK = 25812.8074555(59)Ω
• 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. 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.
• Other conventional electrical units are defined by the normal physical relationships, as in the conversion table below.

Conversion to SI units

Unit Definition SI equivalent (CODATA 2014)
conventional volt see above V90 = (KJ-90/KJ) V = (1 + 9.83(61)×10−8) V
conventional ohm see above Ω90 = (RK/RK-90) Ω = (1 + 1.765(23)×10−8) Ω
conventional ampere A90 = V90/Ω90 A90 = (1 + 8.06(61)×10−8) A
conventional coulomb C90 = A90s = sV90/Ω90 C90 = (1 + 8.06(61)×10−8) C
conventional watt W90 = A90V90 = V902/Ω90 W90 = (1 + 17.9(1.2)×10−8) W
conventional joule J90 = C90V90 = sV902/Ω90 J90 = (1 + 17.9(1.2)×10−8) J
conventional farad F90 = C90/V90 = s/Ω90 F90 = (1 − 1.765(23)×10−8) F
conventional henry H90 = Ω90s H90 = (1 + 1.765(23)×10−8) H

The 2019 redefinition of SI base units defines all these units in a way that fixes the numeric values of KJ and RK exactly, albeit with values that differ slightly from the conventional values, as well as leaving the definition of the second unchanged. Consequently, these conventional units all have known exact values in terms of the redefined SI units. Because of this, there is be no accuracy benefit from maintaining the conventional values.

Comparison with natural units

Conventional electrical units can be thought of as a scaled version of a system of natural units defined as

${\displaystyle c=e=\hbar =1.}$

This is a more general (or less specific) version of either the particle physics "natural units" or the quantum chromodynamical system of units but without fixing unit mass.

The following table provides a comparison of conventional electrical units with other natural unit systems:

Quantity Other Systems Conventional electrical units
Name Symbol Planck Stoney Schrödinger Atomic Electronic
Speed of light in vacuum ${\displaystyle c}$ ${\displaystyle 1}$ ${\displaystyle 1}$ ${\displaystyle {\frac {1}{\alpha }}}$ ${\displaystyle {\frac {1}{\alpha }}}$ ${\displaystyle 1}$ ${\displaystyle 299792458}$
Planck's constant ${\displaystyle h}$ ${\displaystyle 2\pi }$ ${\displaystyle {\frac {2\pi }{\alpha }}}$ ${\displaystyle 2\pi }$ ${\displaystyle 2\pi }$ ${\displaystyle {\frac {2\pi }{\alpha }}}$ ${\displaystyle {\frac {4\times 10^{-18}}{(25812.807)(483597.9)^{2}}}}$
Reduced Planck's constant ${\displaystyle \hbar ={\frac {h}{2\pi }}}$ ${\displaystyle 1}$ ${\displaystyle {\frac {1}{\alpha }}}$ ${\displaystyle 1}$ ${\displaystyle 1}$ ${\displaystyle {\frac {1}{\alpha }}}$ ${\displaystyle {\frac {2\times 10^{-18}}{\pi (25812.807)(483597.9)^{2}}}}$
Elementary charge ${\displaystyle e}$ ${\displaystyle {\sqrt {\alpha }}}$ ${\displaystyle 1}$ ${\displaystyle 1}$ ${\displaystyle 1}$ ${\displaystyle 1}$ ${\displaystyle {\frac {2\times 10^{-9}}{(25812.807)(483597.9)}}}$
Josephson constant ${\displaystyle K_{\text{J}}={\frac {2e}{h}}}$ ${\displaystyle {\frac {\sqrt {\alpha }}{\pi }}}$ ${\displaystyle {\frac {\alpha }{\pi }}}$ ${\displaystyle {\frac {1}{\pi }}}$ ${\displaystyle {\frac {1}{\pi }}}$ ${\displaystyle {\frac {\alpha }{\pi }}}$ ${\displaystyle 483597.9\times 10^{9}}$
von Klitzing constant ${\displaystyle R_{\text{K}}={\frac {h}{e^{2}}}}$ ${\displaystyle {\frac {2\pi }{\alpha }}}$ ${\displaystyle {\frac {2\pi }{\alpha }}}$ ${\displaystyle 2\pi }$ ${\displaystyle 2\pi }$ ${\displaystyle {\frac {2\pi }{\alpha }}}$ ${\displaystyle 25812.807}$
Characteristic impedance of vacuum ${\displaystyle Z_{0}=2\alpha R_{\text{K}}}$ ${\displaystyle 4\pi }$ ${\displaystyle 4\pi }$ ${\displaystyle 4\pi \alpha }$ ${\displaystyle 4\pi \alpha }$ ${\displaystyle 4\pi }$ ${\displaystyle 2\alpha (25812.807)}$
Electric constant (vacuum permittivity) ${\displaystyle \varepsilon _{0}={\frac {1}{Z_{0}c}}}$ ${\displaystyle {\frac {1}{4\pi }}}$ ${\displaystyle {\frac {1}{4\pi }}\,}$ ${\displaystyle {\frac {1}{4\pi }}\,}$ ${\displaystyle {\frac {1}{4\pi }}\,}$ ${\displaystyle {\frac {1}{4\pi }}\,}$ ${\displaystyle {\frac {1}{2\alpha (25812.807)(299792458)}}\ }$
Magnetic constant (vacuum permeability) ${\displaystyle \mu _{0}={\frac {Z_{0}}{c}}}$ ${\displaystyle 4\pi }$ ${\displaystyle 4\pi }$ ${\displaystyle 4\pi \alpha ^{2}}$ ${\displaystyle 4\pi \alpha ^{2}}$ ${\displaystyle 4\pi }$ ${\displaystyle {\frac {2\alpha (25812.807)}{299792458}}}$
Newtonian constant of gravitation ${\displaystyle G}$ ${\displaystyle 1}$ ${\displaystyle 1}$ ${\displaystyle 1}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$
Electron mass ${\displaystyle m_{\text{e}}}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle 1}$ ${\displaystyle 1}$ ${\displaystyle -}$
Hartree energy ${\displaystyle E_{\text{h}}=\alpha ^{2}m_{\text{e}}c^{2}}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle 1}$ ${\displaystyle \alpha ^{2}}$ ${\displaystyle -}$
Rydberg constant ${\displaystyle R_{\infty }={\frac {E_{\text{h}}}{2hc}}}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle {\frac {\alpha }{4\pi }}}$ ${\displaystyle {\frac {\alpha ^{3}}{4\pi }}}$ ${\displaystyle -}$
Cesium ground state hyperfine transition frequency ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle 9\ 192\ 631\ 770}$

References

• Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006" (PDF). Reviews of Modern Physics. 80 (2): 633–730. arXiv:0801.0028. Bibcode:2008RvMP...80..633M. doi:10.1103/RevModPhys.80.633. Archived from the original (PDF) on 2017-10-01.

1. ^ "Resolution 1 of the 13th CGPM (1967) – SI unit of time (second)". Retrieved 2019-02-18.
2. ^ "Resolution 1 of the 17th CGPM (1983) – Definition of the metre". Retrieved 2019-02-18.
3. ^ "CIPM, 1988: Recommendation 1 – Representation of the volt by means of the Josephson effect". Retrieved 2019-02-18.
4. ^
5. ^ "Resolution 2 of the 19th CGPM (1991) – The Josephson and quantum-Hall effects". Retrieved 2019-02-18.
6. ^
7. ^ "26th CGPM Resolutions" (PDF). BIPM. Retrieved 2019-02-18.
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.