# ohm

Physical unit
Unit name ohm
Unit symbol ${\ displaystyle \ mathrm {\ Omega}}$ Physical quantity (s) Electrical resistance
Reactive resistance Apparent
resistance , impedance
Formula symbol ${\ displaystyle R; \, X; \, Z}$ dimension ${\ displaystyle {\ mathsf {M \; L ^ {2} \; T ^ {- 3} \; I ^ {- 2}}}}$ system International system of units
In SI units ${\ displaystyle \ mathrm {1 \, \ Omega = 1 \; {\ frac {V} {A}} = 1 \; {\ frac {kg \, m ^ {2}} {A ^ {2} \, s ^ {3}}}}}$ Named after Georg Simon Ohm

The ohm is the SI unit of electrical resistance with the unit symbol (large Greek omega ). It is named after the German physicist Georg Simon Ohm . The reciprocal of the electrical resistance, i.e. the electrical conductance , has the unit Siemens . ${\ displaystyle \ Omega}$ ## definition

In the SI system of units, the ohm is defined as the resistance that exists between two points on an electrical conductor when a constant potential difference ( electrical voltage ) of 1  volt in the conductor generates a current of 1  ampere :

${\ displaystyle \ mathrm {1 \, \ Omega = 1 \, {\ frac {V} {A}}}}$ ## history

In 1861 the two English electrical engineers Josiah Latimer Clark and Charles Tilston Bright suggested naming the unit of electrical resistance with volt (after the Italian physicist Alessandro Volta ) and the unit of electrical voltage with Ohma .

At the first international electricity congress on September 21, 1881 the name ohm was used as a "practical unit" of electrical resistance for 1 000 000 000  cm / s fixed; In the variant of a cgs system on which this is based (more precisely: electromagnetic cgs units) 1 cm / s is the "fundamental" resistance unit. To achieve the unit one ohm , a more precisely specified mercury prism was introduced at a fixed temperature (0 ° C). Werner Siemens had described this design in 1860 in the Annalen der Physik , with dimensions according to which a value of approximately 0.944 ohms results, which was referred to as 1 Siemens or a Siemens unit (SE). Siemens manufactured and sold silver wire as a secondary standard .

At the Fourth International Electricity Congress, held in Chicago in 1893, this implementation regulation was modified and, for the German Reich, was incorporated into the "Law on Electrical Units of Measure" of June 1, 1898 . In the formulation of the International Conference for Electrical Units and Standards in London in 1908, it contains the following stipulations: 14.4521 g of mercury , mercury column 106.300 cm long with the same cross-section throughout, constant current, temperature of the melting ice. The Ohm realized in this way was called "International Ohm". Improved measurement options and voltage sources with more constant but slightly different voltage values ​​( normal elements ) resulted in unacceptable deviations between practical and international ohms in the course of the following period. Furthermore, there was a discrepancy in the units of mechanical or electrical energy and power that was greater than the deviations from practical and international ohms.

Basically, the definitions of the "international" electrical units, originally intended only as implementation regulations - there were also amps and volts - had become independent and had appeared as a separate system of units alongside the Gaussian cgs units with the practical electrical units. That is why the 9th CGPM reintroduced the absolute ohm in 1948 , now as the only ohm, so to speak. Precision determinations at that time showed: 1 international ohm is equal to 1,000 49  ohms. In this form, the Ohm was adopted into the MKSA system and this was later integrated into the Système international d'unités .

## Realization through the quantum Hall effect

In the case of strong magnetic fields and low temperatures around a few Kelvin, it can be seen that the Hall voltage divided by the current cannot assume any values ​​if the magnetic field strength is varied. Instead, there is always an integer fraction of the Von Klitzing constant . The value of the constant is in this case and the fractions are , , ...; with slightly different test conditions, values ​​as assumed can also be used. ${\ displaystyle U _ {\ mathrm {H}}}$ ${\ displaystyle I}$ ${\ displaystyle R _ {\ mathrm {K}} = {\ tfrac {h} {e ^ {2}}}}$ ${\ displaystyle R_ {K} = 25 \, 812 {,} 807 \ ldots \ Omega}$ ${\ displaystyle R _ {\ mathrm {K}}}$ ${\ displaystyle {\ tfrac {R _ {\ mathrm {K}}} {2}}}$ ${\ displaystyle {\ tfrac {R _ {\ mathrm {K}}} {3}}}$ ${\ displaystyle {\ tfrac {2R _ {\ mathrm {K}}} {3}}}$ The accuracy with which this quantum Hall effect can be reproduced is so good that in 1990 the best known value of R K , referred to as R K-90 , was established by international agreements as the standard for realizing electrical resistance. With the redefinition of the SI in 2019, the constants e and h were assigned fixed values, and the ohm is now defined by these constants . Since then, the representation of the ohm has been freely selectable; the 1990 agreement became obsolete.

## Representation in computer systems and coding

The ohm symbol is coded as follows:

character Unicode Surname HTML
position designation hexadecimal decimal named
Ω U + 03A9 Greek capital letter omega Greek capital letter Omega & # x03A9; & # 937; Ω

According to the Unicode standard, the physical unit ohm should be represented by the Greek capital letter Omega. Although Unicode also contains a character called OHM SIGN (Ohm sign, U + 2126: Ω), this was only included for compatibility with older character coding standards and should not be used in newly created texts .

Wikisource: Law relating to electrical units. From June 1, 1898 (German Empire)  - Sources and full texts

## Individual evidence

1. a b “L'ohm est la résistance électrique qui existe entre deux points d'un conducteur lorsqu'une différence de potenciel constante de 1 volt, appliquée entre ces deux points, produit, dans ce conducteur, un courant de 1 ampère, ce conducteur n'étant le siège d'aucune force électromotrice. " Decision of the CIPM of 1946 (ratified in 1948 by the 9th CGPM): Comité International des Poids et Mesures - Procès verbaux des séances . 2 e series . XX série, 1947, p. 132 ( bipm.org [PDF]). The wording is on page 138 of the PDF document.
2. a b “The ohm is the electric resistance between two points of 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 . ” Source: SI brochure, 9th edition. (2019) Appendix 1, page 160 bipm.org (PDF)
3. HG Jerrard et al .: A Dictionary of Scientific Units: Including dimensionless numbers and scales , Springer-Science + Business Media, Southampton, 1986, p. 152.
4. Gustav Zickner: On the introduction of the absolute ohm , doi: 10.7795 / 310.19500101Z
5. News from the Quantum Hall Effect . Media information no.168, Technische Universität Berlin, July 23, 1996.
6. ^ CIPM, 1988: Recommendation 2 - Representation of the ohm by means of the quantum Hall effect. In: bipm.org. CIPM , accessed on March 2, 2020 .
7. Resolution 1 of the 26th CGPM (2018) - Appendix 1. In: bipm.org. Bureau International des Poids et Mesures , accessed March 2, 2020 .
8. HTML 5.2 - W3C Recommendation, chap. 8.5 Named character references, December 14, 2017
9. Unicode Consortium: The Unicode Standard, Version 5.0. (PDF) 2007, p. 493 , accessed on September 8, 2014 (English).