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 Δν_{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.
Several significant steps have been taken in the last half century to increase the precision and utility of measurement units:
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} |
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 Δν_{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.