International System of Electrical and Magnetic Units

Earlier systems

The link between electromagnetic units and the more familiar units of length, mass and time was first demonstrated by Gauss in 1832 with his measurement of the Earth's magnetic field, and the principle was extended to electrical measurements by Neumann in 1845. A complete system of metric electrical and magnetic units was proposed by Weber in 1851.

The development of the electric telegraph (an invention of Gauss and Weber) demonstrated the need for accurate electrical measurements. At the behest of Thomson, the British Association for the Advancement of Science (B.A.) set up a committee in 1862 to examine the options for standardizing electrical and magnetic units. After much discussion, the committee decided to adapt Weber's proposals to the CGS system of units: however the resulting "absolute" units were both difficult to realize and (often) impractically small. To overcome these handicaps, the B.A. also proposed a set of "practical" or "reproduceable" units, which were not directly linked to the CGS system but which were, as near as experimental accuracy allowed, equal to multiples of the corresponding CGS units.

1893 system

The B.A. system of practical units gained considerable international support, and was adopted – with one important modification – by the First International Conference of Electricians (Paris, 1881). The British Association had constructed an artefact representation of the ohm (a standard length of resistance wire which had a resistance of 10⁹ CGS units of electric resistance, that is one ohm) whereas the international conference preferred a method of realization that could be repeated in different laboratories in different countries. The chosen method was based on the resistivity of mercury, by measuring the resistance of a column of mercury of specified dimensions (106 cm × 1 mm²): however, the chosen length of column was almost 3 millimetres too short, leading to a difference of 0.28% between the new practical units and the CGS units which were supposedly their basis.

The anomaly was resolved at another international conference, in Chicago in 1893, by a correction in the definition of the ohm. The units agreed at this conference were termed "international" units, to distinguish them from their predecessors.

The 1893 system had three base units: the international ampere, the international ohm and the international volt.

The international units did not have the same formal legal status as the metre and the kilogram through the Metre Convention (1875), although several countries adopted the definition within their national laws (e.g., the United States, through Public Law 105 of July 12, 1894).

Overdefinition and the 1908 modification

The 1893 system of units was overdefined, as can be seen from an examination of Ohm's law:

V = IR

By Ohm's law, knowing any two of the physical quantities V, I or R (potential difference, current or resistance) will define the third, and yet the 1893 system defines the units for all three quantities. With improvements in measurement techniques, it was soon recognised that

1 V_int ≠ 1 A_int × 1 Ω_int.

The solution came at an international conference in London in 1908. The essential point was to reduce the number of base units from three to two by redefining the international volt as a derived unit. There were several other modifications of less practical importance:

the international ampere and the international ohm were formally defined in terms of the corresponding CGS electromagnetic units, with the 1893 definitions retained as preferred realizations;

the preferred realization of the international volt was in terms of the electromotive force of a Weston cell at 20 °C (1.0184 V_int), as this type of cell has a lower temperature coefficient than the Clark cell;

several other derived units for use in electrical and magnetic measurements were formally defined:

International Coulomb

the electric charge transferred by a current of one international ampere in one second;

International Farad

the capacitance of a capacitor charged to a potential of one international volt by one international coulomb of electricity;

Joule

10⁷ units of work in the CGS system, represented sufficiently well for practical use by the energy expended in one second by an international ampere in an international ohm;

Watt

10⁷ units of power in the CGS system, represented sufficiently well for practical use by the work done at the rate of one joule per second;

Henry

the inductance in a circuit when an electromotive force induced in this circuit is one international volt, while the inducing current varies at the rate of one ampere per second.

SI units

With advances in the theory of electromagnetism and in quantity calculus, it became apparent that a coherent absolute system of units could only include one electromagnetic base unit. The first such system was proposed by Giorgi in 1901: it used the ohm as the additional base unit in the MKS system, and so is often referred to as the MKSΩ system or the Giorgi system.

An additional problem with the CGS system of electrical units, pointed out as early as 1882 by Heaviside, was that they were not "rationalized", that is they failed to properly take account of permittivity and permeability as properties of a medium. Giorgi was also a great proponent of rationalization of the electrical units.

The choice of electrical unit for the base unit in a rationalized system depends only on practical considerations, particularly the ability to realize the unit accurately and reproducibly. The ampere rapidly gained support over the ohm, as many national standards laboratories were already realizing the ampere in absolute terms using ampere balances. The International Electrotechnical Commission (IEC) adopted the Giorgi system with the ampere replacing the ohm in 1935, and this choice of base units is often called the MKSA system.

The International Committee for Weights and Measures (CIPM) approved a new set of definitions for electrical units, based on the rationalized MKSA system, in 1946, and these were internationally adopted under the Metre Convention by the 9th General Conference on Weights and Measures in 1948. Under this system, which would become the International System of Units (SI), the ohm is a derived unit.

The SI definitions of the electrical units are formally equivalent to the 1908 international definitions, and so there should not have been any change in the size of the units. Nevertheless, the international ohm and the international volt were not usually realized in absolute terms but by reference to a standard resistance and a standard electromotive force respectively. The realizations recommended in 1908 are not exactly equivalent to the absolute definitions: recommended conversion factors are

1 Ω_int ≈ 1.000 49 Ω 1 V_int ≈ 1.000 34 V

although slightly different factors may apply for individual standards in national measurement laboratories. As the international ampere was usually realized by means of an ampere balance rather than electrolytically, 1 A_int = 1 A. The conversion factor for the "electrolytic" ampere (A_elec) can be calculated from modern values of the atomic weight of silver and the Faraday constant:

1 A_elec = 1.000 022(2) A