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Practical realizations of the definitions of some important units
Practical realization of units for electrical quantities
SI Brochure: Appendix 2

    The realization to high accuracy of the ampere (a base unit of the SI), the ohm and the volt (derived units of the SI) directly in terms of their definitions is difficult and time consuming. The best such realizations of the ampere are now obtained through combinations of realizations of the watt, the ohm and the volt. The watt realized electrically is compared by balance experiments with the watt realized mechanically. These experiments employ a coil in a magnetic flux and are devised in such a way that it is not necessary to know either the dimensions of the coil or the magnitude of the flux density. The ohm is realized using a Thompson-Lampard capacitor whose capacitance value can be changed by an amount that depends only on the magnitude of a linear displacement of a guard electrode. The volt is realized by means of a balance in which an electrostatic force is measured in terms of a mechanical force. The ampere may thus be deduced from combinations of any two of these units. The relative uncertainty in the value of the ampere obtained in this way is estimated to be a few parts in 107. The ampere, ohm and volt may also be determined from measurements of various combinations of physical constants. Laboratory reference standards for the volt and the ohm based upon the Josephson and quantum-Hall effects are, however, significantly more reproducible and stable than a few parts in 107. In order to take advantage of these highly stable methods of maintaining laboratory reference standards of the electrical units while at the same time taking care not to change their SI definitions, the 18th CGPM in 1987 adopted Resolution 6 which calls for representations of the volt and the ohm to be based on conventional values for the Josephson constant KJ and the von Klitzing constant RK.

    18th CGPM, 1987, Resolution 6:
    forthcoming adjustment to the representations of the volt and of the ohm

    In 1988 the CIPM adopted Recommendations 1 (CI-1988) and 2 (CI-1988) which set exact values for the Josephson and von Klitzing constants, and called for laboratories to base their standards on these values from 1 January 1990.

    CIPM, 1988, Recommendation 1:
    representation of the volt by means of the Josephson effect
    CIPM, 1988, Recommendation 2:
    representation of the ohm by means of the quantum Hall effect

    At its meeting in 1988 the CCE carefully considered the way in which the recommended conventional values KJ-90 and RK-90 should be used and made additional statements to clarify the implications of the Recommendations. These statements may be summarized as follows:

    1. Recommendations 1 (CI-1988) and 2 (CI-1988) do not constitute a redefinition of SI units. The conventional values KJ-90 and RK-90 cannot be used as bases for defining the volt and the ohm (meaning the present units of electromotive force and electrical resistance in the SI). To do so would change the status of mu0 from that of a constant having an exactly defined value (and would therefore abrogate the definition of the ampere) and would also produce electrical units which would be incompatible with the definition of the kilogram and units derived from it.

    2. Concerning the use of subscripts on symbols for quantities or units, the CCE considers that symbols for electromotive force (electric potential, electric potential difference) and electric resistance, and for the volt and the ohm, should not be modified by adding subscripts to denote particular laboratories or dates.

    These statements were subsequently endorsed by the CIPM.

    Based on a review of the relevant RK data as it existed at the time, the CCEM decided in September 2000 that the assigned relative standard uncertainty of a perfectly realized ohm representation based on the quantum Hall effect and RK-90 should be reduced by a factor of two, to 1 part in 107. This decision was subsequently approved by the CIPM in October 2000.

    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

    [last updated: 20 February 2007]

Appendix 2 of the SI Brochure

The mises en pratique are prepared by the relevant Consultative Committees and are then published in electronic form here on the BIPM website, where they may be revised more frequently than if they were printed in the SI Brochure.

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