# 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, the von Klitzing constant agreed by the International Committee for Weights and Measures (CIPM) in 1988, as well as Δ*ν*_{Cs} 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 *V*_{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 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:

- 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}= 483597.9×10^{9}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 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) |
---|---|---|---|

^{133}Cs hyperfine transition frequency |
Δν(^{133}Cs)_{hfs} = 9192631770 Hz |
Δν(^{133}Cs)_{hfs} = 9192631770 Hz[9] | |

Josephson constant | K_{J-90} = 483597.9 GHz/V[10] |
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[11] |
R_{K} = 25812.8074555(59) Ω |
R_{K} = 6.62607015×10^{−34} J⋅s/(1.602176634×10^{−19} C)^{2} |

- The conventional volt,
*V*_{90}, 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/*V*_{90}.*See Josephson voltage standard.* - The conventional ohm,
*Ω*_{90}, 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*Ω*_{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

Unit | Symbol | Definition | Related to SI | SI value (CODATA 2014) | SI value (2019) |
---|---|---|---|---|---|

conventional volt | V_{90} |
see above |
K_{J-90}/K_{J} V |
1.0000000983(61) V | 1.00000010666... V[12] |

conventional ohm | Ω_{90} |
see above |
R_{K}/R_{K-90} Ω |
1.00000001765(23) Ω | 1.00000001779... Ω[13] |

conventional ampere | A_{90} |
V_{90}/Ω_{90} |
K_{J-90}/K_{J}⋅R_{K-90}/R_{K} A |
1.0000000806(61) A | 1.00000008887... A[14] |

conventional coulomb | C_{90} |
s⋅A_{90} = s⋅V_{90}/Ω_{90} |
K_{J-90}/K_{J}⋅R_{K-90}/R_{K} C |
1.0000000806(61) C | 1.00000008887... C[15] |

conventional watt | W_{90} |
A_{90}V_{90} = V_{90}^{2}/Ω_{90} |
(K_{J-90}/K_{J})^{2}_{ }⋅R_{K-90}/R_{K} W |
1.000000179(12) W | 1.00000019553... W[16] |

conventional farad | F_{90} |
C_{90}/V_{90} = s/Ω_{90} |
R_{K-90}/R_{K} F |
0.99999998235(23) F | 0.99999998220... F[17] |

conventional henry | H_{90} |
s⋅Ω_{90} |
R_{K}/R_{K-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 *K*_{J}, *R*_{K} and Δ*ν*_{Cs} 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.

## Comparison with natural units

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

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 | |||||||

Planck's constant | |||||||

Reduced Planck's constant | |||||||

Elementary charge | |||||||

Josephson constant | |||||||

von Klitzing constant | |||||||

Characteristic impedance of vacuum | |||||||

Electric constant (vacuum permittivity) | |||||||

Magnetic constant (vacuum permeability) | |||||||

Newtonian constant of gravitation | |||||||

Electron mass | |||||||

Hartree energy | |||||||

Rydberg constant | |||||||

Caesium hyperfine transition frequency |

## 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 1 October 2017.

- "Resolution 1 of the 13th CGPM (1967) – SI unit of time (second)". Retrieved 18 February 2019.
- "Resolution 1 of the 17th CGPM (1983) – Definition of the metre". Retrieved 18 February 2019.
- "CIPM, 1988: Recommendation 1 – Representation of the volt by means of the Josephson effect". Retrieved 18 February 2019.
- "CIPM, 1988: Recommendation 2 – Representation of the ohm by means of the quantum Hall effect". Retrieved 18 February 2019.
- "Resolution 2 of the 19th CGPM (1991) – The Josephson and quantum-Hall effects". Retrieved 18 February 2019.
- "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.
- "26th CGPM Resolutions" (PDF).
*BIPM*. Retrieved 18 February 2019. - 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. - "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. - "2018 CODATA Value: conventional value of Josephson constant".
*The NIST Reference on Constants, Units, and Uncertainty*. NIST. 20 May 2019. Retrieved 20 May 2019. - "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. - "2018 CODATA Value: conventional value of volt-90".
*The NIST Reference on Constants, Units, and Uncertainty*. NIST. 20 May 2019. Retrieved 1 June 2019. - "2018 CODATA Value: conventional value of ohm-90".
*The NIST Reference on Constants, Units, and Uncertainty*. NIST. 20 May 2019. Retrieved 1 June 2019. - "2018 CODATA Value: conventional value of ampere-90".
*The NIST Reference on Constants, Units, and Uncertainty*. NIST. 20 May 2019. Retrieved 1 June 2019. - "2018 CODATA Value: conventional value of coulomb-90".
*The NIST Reference on Constants, Units, and Uncertainty*. NIST. 20 May 2019. Retrieved 1 June 2019. - "2018 CODATA Value: conventional value of watt-90".
*The NIST Reference on Constants, Units, and Uncertainty*. NIST. 20 May 2019. Retrieved 1 June 2019. - "2018 CODATA Value: conventional value of farad-90".
*The NIST Reference on Constants, Units, and Uncertainty*. NIST. 20 May 2019. Retrieved 1 June 2019. - "2018 CODATA Value: conventional value of henry-90".
*The NIST Reference on Constants, Units, and Uncertainty*. NIST. 20 May 2019. Retrieved 1 June 2019.