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 of conventional values for the Josephson constant as exactly K_J-90 = 483597.9×10⁹ Hz/V^[3] and for the von Klitzing constant as exactly R_K-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 R_K-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 exact value (CIPM, 1988; until 2018)	Empirical value (in SI units) (CODATA, 2014^[8])	Exact value (SI units, 2019)
Josephson constant	K_J-90 = 483597.9 GHz/V	K_J = 483597.8525(30) GHz/V	K_J = 2 × 1.602176634×10⁻¹⁹ C/6.62607015×10⁻³⁴ J⋅s
von Klitzing constant	R_K-90 = 25812.807 Ω	R_K = 25812.8074555(59) Ω	R_K = 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, K_J-90; that is, by the relation K_J = 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, R_K-90; that is, by the relation R_K = 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

Unit	Symbol	Definition	Related to SI	SI value (CODATA 2014)	SI value (2019)
conventional volt	V₉₀	see above	K_J-90/K_J V	(1 + 9.83(61)×10⁻⁸) V	(1 + 10.666510725...×10⁻⁸) V
conventional ohm	Ω₉₀	see above	R_K/R_K-90 Ω	(1 + 1.765(23)×10⁻⁸) Ω	(1 + 1.779366756...×10⁻⁸) Ω
conventional ampere	A₉₀	V₉₀/Ω₉₀	K_J-90/K_J⋅R_K-90/R_K A	(1 + 8.06(61)×10⁻⁸) A	(1 + 8.887143810...×10⁻⁸) A
conventional coulomb	C₉₀	s⋅A₉₀ = s⋅V₉₀/Ω₉₀	K_J-90/K_J⋅R_K-90/R_K C	(1 + 8.06(61)×10⁻⁸) C	(1 + 8.887143810...×10⁻⁸) C
conventional watt	W₉₀	A₉₀V₉₀ = V₉₀²/Ω₉₀	(K_J-90/K_J)² ⋅R_K-90/R_K W	(1 + 17.9(1.2)×10⁻⁸) W	(1 + 19.553655483...×10⁻⁸) W
conventional joule	J₉₀	C₉₀⋅V₉₀ = s⋅V₉₀²/Ω₉₀	(K_J-90/K_J)² ⋅R_K-90/R_K J	(1 + 17.9(1.2)×10⁻⁸) J	(1 + 19.553655483...×10⁻⁸) J
conventional farad	F₉₀	C₉₀/V₉₀ = s/Ω₉₀	R_K-90/R_K F	(1 − 1.765(23)×10⁻⁸) F	(1 − 1.779366724...×10⁻⁸) F
conventional henry	H₉₀	s⋅Ω₉₀	R_K/R_K-90 H	(1 + 1.765(23)×10⁻⁸) H	(1 + 1.779366756...×10⁻⁸) H

The 2019 redefinition of SI base units defines all these units in a way that fixes the numeric values of K_J and R_K 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 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

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