# ohm

For the meaning of any metric prefix, go here.

For the German unit of liquid capacity sometimes called the Ohm, see Ahm.

The unit of electrical resistance in SI; a derived unit. Symbol, Ω (the Greek letter omega, suggested by its pronunciation, ohm-ega). 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 voltampere, 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

For the various ways in which values in ohms are shown on the resistors used in electronic devices, go to resistors.

## examples

It would be preferable to have an absolute standard based on fundamental constants of nature and expressed in SI (Systeme International) units. This can be done using a calculable capacitor (Clothier 1965) and a complicated sequence of capacitance and resistance bridges. In this method an as-maintained unit like ΩNBS is expressed in terms of the change in length of the calculable capacitor. The most accurate measurement was done by Cutkosky (1974). He calibrated ΩNBS in SI units to within ±0.03 ppm. The experiment lasted fifteen years and required such feats as measuring a 0.5 picofarad change of the calculable capacitor to 1 part in 10⁹. The ΩNBS is apparently drifting so the experiment is being repeated.

Marvin E. Cage.
Experimental Aspects and Metrological Applications.
The Quantum Hall Effect. 2nd ed. Springer-Verlag, 1990.
Page 50.

The references in the text are W K Clothier, A Calculable Unit of Capacitance, Metrologia vol 1, no 2, (1965) page 36, and Robert D. Cutkosky, New NBS Measurements of the Absolute Farad and Ohm, IEEE Transactions on Instrumentation and Measurement, vol 23, issue 4, pages 305 - 309 (1974), https://doi.org/10.1109/TIM.1974.4314299

## History of the ohm

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 legal ohm

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.

#### sources for the legal ohm

1

Shortly after the Birmingham meeting of the Association the Secretary received a letter from the Board of Trade enclosing a copy of the general bases of a convention proposed by the French Government for the consideration of the Powers, with the object of carrying out the resolutions of the Paris Congress with regard to electrical standards.

The convention stipulates that a legal character is to be given to (1) the legal ohm; (2) the ampere; (3) the volt; (4) the coulomb; (5) the farad.

It charges the Bureau International des Poids et Mesures, established by the Metric Commission, with the construction and conservation of the international prototypes of the standard of electrical resistance, the comparison and verification of national standards and secondary standards.

These questions had, at the request of some of the English delegates to the Congress of 1883, been considered by the Committee at the Birmingham meeting, and the following series of resolutions, which the Secretary was instructed to forward to the British Government, had been agreed to on the motion of Sir William Thomson, seconded by Professor W. G. Adams:-

(1) To adopt for a term of ten years the legal ohm of the Paris Congress as a legalised standard sufficiently near to the absolute ohm for commercial purposes.

(2) That at the end of the ten years' period the legal ohm should be defined to a closer approximation to the absolute ohm.

(3) That the resolutions of the Paris Congress with respect to the ampere, the volt, the coulomb, and the farad be adopted.

(4) That the resistance standards belonging to the Committee of the British Association on electrical standards now deposited at the Cavendish Laboratory at Cambridge be accepted as the English legal standards conformable to the adopted definition of the Paris Congress.

Fourteenth Report- Manchester 1887.
Reports of the Committee on Electrical Standards Appointed by the British Association for the Advancement of Science.
Cambridge: Cambridge Univ. Press, 1913.
Pages 339-340.

2

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.

T. C. Mendenhall.
Legal Units of Electric Measure.
Science, New Series, volume 1, no. 1, pages 9-15 (4 January 1895).

3

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.

### The international ohm

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.

#### sources for the international ohm

1

During the Edinburgh meeting the Committee were honoured with the presence of Dr von Helmholtz, M. Guillaume of Paris, Professor Carhart of the United States, Dr Lindeck and Dr Kahle of the Berlin Reichsanstalt. These gentlemen came by invitation to consider the question of establishing identical electric standards in various countries, and two meetings of the Committee were held, at which discussions took place. Major Cardew, of the Board of Trade, was present, and took part in the discussion. Dr von Helmholtz drew special attention to the need for having a unit of resistance defined in terms of a specified column of mercury, and pointed out that the difficulty arising from the uncertainty of the relation between the centimetre and the gramme might be avoided by defining the mass of mercury column of given length, which has a resistance of one ohm. After discussion the following resolutions were agreed to:-

1. That the resistance of a specified column of mercury be adopted as the practical unit of resistance.

2. That 14.4521 grammes of mercury in the form of a column of uniform cross section 106.3 cm. in length at 0° C. be the specified column.

3. That standards in mercury or solid metal having the same resistance as this column be made and deposited as standards of resistance for industrial purposes.

4. That such standards be periodically compared with each other, and also that their values be redetermined at intervals in terms of a freshly set up mercury column.

It was further agreed that these resolutions should be communicated to the Electrical Standards Committee of the Board of Trade.

Dr von Helmholtz expressed his full concurrence in these decisions, which are, as he informed the Committee, in accord with the recommendations which have already been laid by the Curatorium of the Reichsanstalt, as well as by himself, before the German Government.

Nineteenth Report- Edinburgh 1892.
Reports of the Committee on Electrical Standards Appointed by the British Association for the Advancement of Science.
Cambridge: Cambridge Univ. Press, 1913.
Pages 434 & 435.

2

The resolutions adopted by the Committee at Edinburgh were communicated to the Electrical Standards Committee of the Board of Trade. After consideration the Board of Trade Committee drew up an amended report, in harmony with the Edinburgh resolutions, for presentation to the President (see Appendix I.).

The resolutions were accepted at Edinburgh by Dr von Helmholtz on behalf of Germany, while in France an official committee decided last June to adhere to the propositions of the Board of Trade. Austria and Italy are connected by treaty with Germany for telegraph purposes, and in consequence adopt the same units.

The Committee have learnt with pleasure from Mr W. H. Preece, one of the English delegates to the International Congress of Electricians at Chicago, that the Congress have accepted a series of resolutions defining the fundamental units practically identical with the Edinburgh resolutions.

Thus these resolutions have now been accepted as a basis for legislation throughout the British Empire, the whole of Western Europe, and the United States of America.

In March last M. Mascart wrote to the Secretary asking the opinion of the Committee as to a name for the standard of resistance defined at Edinburgh. A circular letter was issued inviting members of the Committee to express their views on four names which had been suggested, viz.: “International,” “Normal,” “Etalion,” or “Ohm de 1893.” After receiving replies to the circular from twelve members of the Committee, the Secretary wrote to Professor Mascart to the effect that the number of members who expressed a preference for the name “International” was greater than the number declaring in favour of any other name, but that he thought that the Committee would accept whichever of the first three suggestions commended itself to the French Committee appointed to deal with the matter.

Twentieth Report- Nottingham, 1893.
Reports of the Committee on Electrical Standards Appointed by the British Association for the Advancement of Science.
Cambridge: Cambridge Univ. Press, 1913.
Pages 465 & 466.

3

Report of the Action of the International Electrical Congress held in Chicago, August 1893,
in the Matter of Units of Electrical Measure.

Washington, D. C. November 6, 1893.

His Excellency Dr H. von Helmholtz was made Honorary President of the Congress; Dr Elisha Gray, of Chicago, was Chairman of the General Congress; and Professor H. A. Rowland, of Baltimore, was President of the Chamber of Delegates.

Meetings of the Chamber continued during six days, at the end of which its members unanimously agreed in the adoption of the following resolution:-

Resolved, That the several Governments represented by the delegates of this International Congress of Electricians be, and they are hereby, recommended to formally adopt as legal units of electrical measure the following: As a unit of resistance, the international ohm, which is based upon the ohm equal to 10⁹ units of resistance of the C.G.S. system of electro-magnetic units, and is represented by the resistance offered to an unvarying electric current by a column of mercury at the temperature of melting ice 14.4521 grammes in mass, of a constant cross-sectional area and of the length of 106.3 cm.

4

Order in Council regarding Standards for Electrical Measurements.

At the Court at Osborne House, Isle of Wight, August 23, 1894.

Present: The Queen's Most Excellent Majesty in Council.

Whereas by “The Weights and Measures Act 1889” it is among other things enacted that the Board of Trade shall from time to time cause such new denominations of standards for the measurement of electricity as appear to them to be required for use in trade to be made and duly verified.

And whereas it has been made to appear to the Board of Trade that new denominations of standards are required for use in trade based upon the following units of electrical measurement, viz.-

1. The ohm, which has the value 10⁹ in terms of the centimetre and the second of time, and is represented by the resistance offered to an unvarying electric current by a column of mercury at the temperature of melting ice 14.4521 grammes in mass of a constant cross-sectional area and of a length of 106.3 centimetres.

And whereas they have caused the said new denominations of standards to be made and duly verified.

Now, therefore, her Majesty, by virtue of the power vested in her by the said Act, by and with the advice of her Privy Council, is pleased to approve the several denominations of standards set forth in the schedule hereto as new denominations of standards for electrical measurement.

5

Notes on the Present Condition of the Work on Electric Units
at the National Physical Laboratory.

1. The Ohm. (a) Absolute Unit.- The value of a resistance in absolute measure is still subject to considerable uncertainty; the most satisfactory value is obtained from the mean of the results obtained for the ratio of the International Ohm to the absolute ohm.

A provisional design has been prepared for the Lorenz apparatus which the Drapers' Company are kindly presenting to the National Physical Laboratory, and experiments to test the more important features of the design are in progress. It is hoped to realise the ohm in absolute measure to within 1 part in 100,000. The experience gained in the construction of many of the fittings of the ampere balance will greatly facilitate the work.

(b) International Unit.- Further comparisons of some of the mercury standards of the National Physical Laboratory were made in October and November 1906. There appears to have been no change in any of the tubes which affects the resistance of the contained mercury columns by as much as 1 part in 100,000.

F. E. Smith.
Reports of the Committee on Electrical Standards Appointed by the British Association for the Advancement of Science.
Cambridge: Cambridge Univ. Press, 1913.
Page 700-701.

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 first 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.

H. B. Brooks.
Transactions of the American Institute of Electrical Engineers, volume 50, page 1318 (1931).

## examples

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 èlèments 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.