For the unit of capacity used for Rhine wine, see aum.
The unit of electrical resistance in SI; a derived unit. One ohm is the “electrical resistance between two points on a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere, the conductor not being the seat of any electromotive force.” (CIPM, Resolution 2, 1946.)
Ohms are volt⁄ampere, or in terms of SI base units only,
.
The ohm is named for Georg Simon Ohm (1787–1854). Ohm’s name was first used as an electrical unit in 1861, when Charles Bright and Latimer Clark proposed the ohma be a unit of electromotive force.1
Telegraphy created a need for standards of resistance, which were made to correspond to various lengths of telegraph wire.
In 1833, Karl Friedrich Gauss showed that all magnetic units could be defined in terms of the mechanical units (meter, kilogram, seconds). Twenty-one years later Wilhelm Weber showed how to define a complete system of electrical units in terms of mechanical units. It thus became possible to formulate “scientific” definitions of a unit of resistance.
In 1861 at a meeting in Manchester the British Association for the Advancement of Science created a committee to report on “standards of electrical resistance.” By 1864 this committee had created the “B.A. unit” of resistance, an absolute unit based on a meter-gram-second system of units. However, on working out the size of the mgs unit of resistance they found it would be much too small for the needs of the telegraph engineers. So they recommended a practical unit of resistance, the ohm, to be 107 times bigger than the mgs absolute unit of resistance. In one sense the choice of 107 was arbitrary, except that it made, for example, a mile of the usual size of telegraph wire have a resistance of 10 such ohms.
The committee also prepared a standard for the unit, made of wire.
In 1868 the British Assn. set up another committee “for the selection and nomenclature of dynamical and electrical units.” In 1872 that committee recommended a change to the cgs system and changed the name from “B.A. unit of resistance” to “ohm”.2
The First International Conference of Electricians (Paris, 1881), accepted the British Assn's definition of the ohm but also sought “reproducible standards.” Such units were called “practical units” because they could be fairly easily realized in the average laboratory, which the absolute definitions certainly could not be. T. C. Mendenhall describes the result:
After much discussion and not without very considerable opposition, there was proposed at that time a material representation of the ohm which was known to be somewhat in error. The real ohm must always be that defined by the Committee of the British Association for the Advancement of Science, and any material representation which may be adopted should only be considered an approximation to this. It was first agreed that this theoretical ohm should be represented by the resistance offered to an unvarying current of electricity by a column of mercury one square millimeter in cross section and one hundred and six centimeters in length, at a definite temperature. Even at the time of the acceptance of this ohm it was well known that the length of the column was nearly three millimeters too small to correctly represent the ohm of the British Association Committee. This result had been established by investigations by Rowland in this country, and by other experimentalists in Europe. In consequence of the inaccuracy of this first material representation of the ohm it did not meet with much favor, although it was quickly taken up among practical men, and resistance coils in great numbers were wound in accordance with this definition, being generally, but incorrectly, known as the “Legal Ohm.” I do not know that this unit was ever adopted by any government, or even by any municipal corporation.3
At the International Electrical Congress in Chicago in 1893 it was decided to change the name from “reproducible ohm” to “international ohm,” and the definition was restated as the resistance at 0° centigrade of a column of mercury 106.3 cm in length, having a uniform cross section, and with a mass of 14.4521 grams. That particular mass was chosen to make the cross section 1 square millimeter. (Public Bill 105, passed by Congress on July 12, 1894, made the international ohm the legal definition of the ohm in the United States.) The next International Conference (London, 1908) confirmed the previous conference's decisions.
As instrumentation improved the need for units defined “reproducibly” declined. The CIPM finally did away with the international ohm and all the other practical units in 1946 (Resolution 2), replacing it with the new absolute definition given above. This decision was adopted by the Ninth CGPM in 1948.
Improving technology opened entirely new ways of making a resistance standard, and in 1988 the CIPM adopted as a conventional value "25812.807 Ω for the von Klitzing constant, RK, that is to say, for the quotient of the Hall potential difference divided by current corresponding to the plateau i = 1 in the quantum Hall effect" (CIPM Recommendation 2, CI-1988). This value was to be used by all standards laboratories after 1 January 1990. While not a redefinition of the ohm, the new standard permitted enhanced precision in measuring it.
1. Electrician, volume 1, pages 3, 9, 11 (1861).
2. British Association for the Advancement of Science.
Reports of the Committee on Electrical Standards appointed by the British
Association....
London: E. and F.N. Spon, 1873.
3. T. C. Mendenhall.
Legal Units of Electric Measure.
Science, New Series, volume 1, no. 1, pages 9-15 (4 January 1895).
H. B. Brooks.
Transactions of the American Institute of Electrical Engineers, volume 50, page
1318 (1931).
1
The measures now universally adopted are those of British Association.
1. The unit of resistance is called the ohm. One million ohms = 1 megohm, and one millionth part of an ohm = 1 microhm.
Before the use of the “British Association units,” or ohms, resistances were generally measured in Siemen's units or Varley's units; 1.0456 Siemen's units are equal to one ohm. To convert Siemen's units into ohms, multiply them by .9564. One Varley's unit is equal to about twenty-five ohms.
The ohm is a resistance equal to 107, or ten million absolute electromagnetic units, and the megohm is equal to 1013 absolute units. The ohm is often called the B.A. unit.
Latimer Clark.
An Elementary Treatise on Electrical Measurement for the Use of Telegraph
Inspectors and Operators.
London: E. & F.N. Spon, 1868.
Page 43.
Note that Clark was using the meter-gram-second system of units, hence the 7 of “107”.
2
The values of the absolute units in the C.G.S. system are not convenient for measuring the magnitudes which ordinarily occur. Thus the absolute unit of resistance is that represented by the twenty-thousandth part of a millimetre of pure copper wire a millimetre in diameter. It has therefore been necessary to choose units better suited for practical uses, and at the International Congress of Electricians at Paris in 1884 an International Commission was formed for the purpose of deciding on such units and determining their value. In 1884 the Commission agreed to recommend the following, which are in the main those introduced by the British Association.
The practical unit of resistance is equal to 109 absolute electromagnetic C.G.S. units of resistance, and is called the Ohm. It has been decided to represent it by a column of pure mercury with a cross section of a square millimetre; its exact length has been determined experimentally by the Commission, and has been taken at 1.06 metre. This is known as the legal or Congress ohm.
E. Atkinson.
Elementary Treatise on Physics Experimental and Applied for the use of
colleges and schools. Translated and edited from Ganot's
Éléments de Physique.
Twelfth edition.
London: Longmans, Green, and Co., 1886.
Page 939.
3
The original ohm, or British Association unit, has a resistance equal to that of a column of mercury 1 millim. square, and approximately 104.87 centims in length at 0° C. Its resistance in true ohms is about .98565, and the British Association Committee has recommended that the ratio .9866 should be adopted. The legal ohm (106 centims) was provisionally adopted at the Paris Congress, 1884. The Siemen's unit is 100 centims, or 1 metre of mercury. The true ohm is intended to represent the real value of 109 C.G.S. units. If the value of the ohm be varied, the values of the volt and watt must necessarily vary in the same ratio, but the value of the ampere (1/10 C.G.S.) unit) [sic] will not be affected. Lord Rayleigh made the true ohm = 106.29 centims, and the British Association Committee has recommended that 106.3 centims should be finally adopted. This makes the specific resistance of mercury (that of 1 cube centimetre at 0° C.) in true ohms = 9.4073 × 105.
Latimer Clark.
A Dictionary of Metric and Other Useful Measures.
London: E & F.N. Spon, 1891.
Page 69, footnote.
4
417. PRACTICAL ELECTRIC UNITS.-The units employed by electricians and forming the B. A. system, were selected so that they should be of a convenient magnitude, and yet be decimal multiples of the absolute units of the metre or centimetre-gramme-second absolute system, and also approximate in value to units already in use. But the means of measurement being at first imperfect, the actual values of the units of resistance and current were not correctly ascertained. Then a congress at Paris endeavoured to fix new values before accurate knowledge was obtained, and with that curious tendency of the French mind towards apparent definiteness, they fixed upon a value for the ohm, even then known to be incorrect, merely because it avoided a fraction in the nominal length of a tube of mercury which no one ever made, or probably ever will make in reality. The result is that at this moment no human being knows what a "volt" is, though electricians talk about it solemnly enough, and we hear of true volts, legal volts, the B A volt and Rayleigh's volt: while theorists will work them out to several places of decimals, it is the simple fact that the values of the units are so uncertain that they may involve an error of quite 2 per cent in the calculations. It is a great pity the practical units are not defined upon the C.G.S system simply, and any errors of the standard merely covered by calculation until sufficiently accurate knowledge is attained.
John T. Sprague.
Electricity: Its Theory, Sources, and Applications. 3rd edition, revised and
extended.
London: E & F. N. Spon, 1892.
Page 212-213.
| home | | | units index | | | search | | | your comments  | | | about | | | help | | |
Copyright © 2000 Sizes, Inc. All rights reserved.
Last revised: 14 February 2005.