Ohm — Mediated Wiki

{{use dmy dates|date=October 2020|cs1-dates=y}} {{short description|SI derived unit of electrical resistance}} {{about|the SI derived unit}} {{infobox Unit | name = ohm | image = [[File:Leeds and Northrup one ohm standard resistance.jpg|240px]] | caption = A laboratory one-ohm standard resistor, {{circa|1917}} | standard = [[SI]] | quantity = [[electrical resistance]] | symbol= Ω | namedafter = [[Georg Ohm]] | units1 = [[SI base unit]]s | inunits1 = [[kilogram|kg]]⋅[[metre|m]]2⋅[[second|s]]−3⋅[[ampere|A]]−2 }}

The '''ohm''' (symbol: '''Ω''', the uppercase Greek letter [[omega]]) is the unit of [[electrical resistance]] in the [[International System of Units|International System of Units (SI)]]. It is named after German physicist [[Georg Ohm]] (1789–1854). Various empirically derived standard units for electrical resistance were developed in connection with early [[telegraphy]] practice, and the [[British Association for the Advancement of Science]] proposed a unit derived from existing units of mass, length and time, and of a convenient scale for practical work as early as 1861.

Following the [[2019 revision of the SI]], in which the [[ampere]] and the [[kilogram]] were redefined in terms of fundamental constants, the ohm is now also defined as an exact value in terms of these constants.

== Definition == The ohm is defined as an electrical resistance between two points of a conductor when a constant [[Electric potential|potential difference]] of one [[volt]] (V), applied to these points, produces in the conductor a current of one [[ampere]] (A), the conductor not being the seat of any [[electromotive force]].<ref name="BIPM_SI9"/> : <math> \Omega = \frac{\mathrm{V}}{\mathrm{A}} = \frac{1}{\mathrm{S}} = \frac{\mathrm{W}}{\mathrm{A^{2}}} = \frac{\mathrm{V}^{2}}{\mathrm{W}} = \frac{\mathrm{s}}{\mathrm{F}} = \frac{\mathrm{H}}{\mathrm{s}} = \frac{\mathrm{Wb}}{\mathrm{C}} = \frac{\mathrm{J{\cdot}s}}{\mathrm{C^{2}}} = \frac{\mathrm{J}}{\mathrm{s{\cdot}A^{2}}} = \frac{\mathrm{kg{\cdot}m^{2}}}{\mathrm{s{\cdot}C^{2}}} = \frac{\mathrm{kg{\cdot}m^{2}}}{\mathrm{s^{3}{\cdot}A^{2}}} </math>

In many cases the resistance of a conductor is approximately constant within a certain range of voltages, temperatures, and other parameters. These are called [[linear]] [[resistor]]s. In other cases resistance varies, such as in the case of the [[thermistor]], which exhibits a strong dependence of its resistance with temperature.

In the US, consecutive vowels in the prefixed units "kiloohm" and "megaohm" are commonly reduced to one, producing "kilohm" and "megohm".<ref name="SI10-2002"/><ref name="Thompson-Taylor_2008"/><ref name="NIST_2016"/><ref name="Aubrecht-French-Iona_2012"/>[[File:Electronic multi meter.jpg|thumb|One of the functions of many types of [[multimeter]]s is the measurement of resistance in ohms.]]

In alternating current circuits, [[electrical impedance]] is also measured in ohms.

=== Relation to conductance === The [[siemens (unit)|siemens]] (S) is the [[SI derived unit]] of [[electric conductance]] and [[admittance]], historically known as the "mho" (''ohm'' spelled backwards, symbol is ℧); it is one [[Multiplicative inverse|reciprocal]] ohm: {{nowrap|1 S {{=}} 1 Ω−1.}}

== Power as a function of resistance == The power dissipated by a [[resistor]] may be calculated from its resistance, and the voltage or current involved. The formula is a combination of [[Ohm's law]] and [[Joule's first law|Joule's law]]: <math display=block>P=V I =\frac{V^2}{R} = I^2 R,</math>

where {{mvar|P}} is the power, {{mvar|R}} is the resistance, {{mvar|V}} is the [[voltage]] across the resistor, and {{mvar|I}} is the current through the resistor.

A linear resistor has a constant resistance value over all applied voltages or currents; many practical resistors are linear over a useful range of currents. Non-linear resistors have a value that may vary depending on the applied voltage (or current). Where [[alternating current]] is applied to the circuit (or where the resistance value is a function of time), the relation above is true at any instant, but calculation of average power over an interval of time requires [[integral|integration]] of "instantaneous" power over that interval.

Since the ohm belongs to a [[Coherence (units of measurement)|coherent system of units]], when each of these quantities has its corresponding SI unit ([[watt]] for {{mvar|P}}, ohm for {{mvar|R}}, [[volt]] for {{mvar|V}} and [[ampere]] for {{mvar|I}}, which are related as in {{section link||Definition}}) this formula remains valid numerically when these units are used (and thought of as being cancelled or omitted).

== History == The rapid rise of electrotechnology in the last half of the 19th century created a demand for a rational, coherent, consistent, and international system of units for electrical quantities. Telegraphers and other early users of electricity in the 19th century needed a practical standard unit of measurement for resistance. Resistance was often expressed as a multiple of the resistance of a standard length of telegraph wires; different agencies used different bases for a standard, so units were not readily interchangeable. Electrical units so defined were not a coherent system with the units for energy, mass, length, and time, requiring conversion factors to be used in calculations relating energy or power to resistance.<ref name="Hunt_1994"/>

Two different methods of establishing a system of electrical units can be chosen. Various artifacts, such as a length of wire or a standard [[electrochemical]] cell, could be specified as producing defined quantities for resistance, voltage, and so on. Alternatively, the electrical units can be related to the mechanical units by defining, for example, a unit of current that gives a specified force between two wires, or a unit of charge that gives a unit of force between two unit charges. This latter method ensures coherence with the units of energy. Defining a unit for resistance that is coherent with units of energy and time in effect also requires defining units for potential and current. It is desirable that one unit of electrical potential will force one unit of electric current through one unit of electrical resistance, doing one unit of work in one unit of time, otherwise, all electrical calculations will require conversion factors.

Since so-called "absolute" units of charge and current are expressed as combinations of units of mass, length, and time, [[dimensional analysis]] of the relations between potential, current, and resistance show that resistance is expressed in units of length per time – a velocity. Some early definitions of a unit of resistance, for example, defined a unit resistance as one quadrant of the Earth per second.

The absolute-unit system related magnetic and electrostatic quantities to metric base units of mass, time, and length. These units had the great advantage of simplifying the equations used in the solution of electromagnetic problems, and eliminated conversion factors in calculations about electrical quantities. However, the centimeter–gram–second, CGS, units turned out to have impractical sizes for practical measurements.

Various artifact standards were proposed as the definition of the unit of resistance. In 1860 [[Werner Siemens]] (1816–1892) published a suggestion for a reproducible resistance standard in [[Johann Christian Poggendorff|Poggendorff's]] ''[[Annalen der Physik und Chemie]]''.<ref name="Siemens_1860"/> He proposed a column of pure mercury, of one square millimeter cross section, one meter long: [[Siemens mercury unit]]. However, this unit was not coherent with other units. One proposal was to devise a unit based on a mercury column that would be coherent – in effect, adjusting the length to make the resistance one ohm. Not all users of units had the resources to carry out [[metrology]] experiments to the required precision, so working standards notionally based on the physical definition were required.

In 1861, [[Josiah Latimer Clark|Latimer Clark]] (1822–1898) and [[Charles Tilston Bright|Sir Charles Bright]] (1832–1888) presented a paper at the [[British Association for the Advancement of Science]] meeting <ref>{{cite journal |first1=Latimer|last1=Clark|author1-link=Josiah Latimer Clark |first2=Sir Charles|last2=Bright |author2-link=Charles Tilston Bright |title=Measurement of Electrical Quantities and Resistance|journal=[[The Electrician]]|date=9 November 1861|volume=1|issue=1|pages=3–4|url=https://books.google.com/books?id=7BdbAAAAYAAJ&q=ohma&pg=PA3|access-date=27 February 2014}}</ref> suggesting that standards for electrical units be established and suggesting names for these units derived from eminent philosophers, 'Ohma', 'Farad' and 'Volt'. The [[British Association for the Advancement of Science|BAAS]] in 1861 appointed a committee including [[James Clerk Maxwell|Maxwell]] and [[William Thomson, 1st Baron Kelvin|Thomson]] to report upon standards of electrical resistance.<ref> {{cite conference | title = Report of the Thirty-First Meeting of the British Association for the Advancement of Science; held at Manchester in September 1861 | date = September 1861 | pages=xxxix–xl | url = https://www.biodiversitylibrary.org/item/93052#page/44/mode/2up }}</ref> Their objectives were to devise a unit that was of convenient size, part of a complete system for electrical measurements, coherent with the units for energy, stable, reproducible and based on the French metrical system.<ref> {{cite conference |title=Provisional Report of the Committee appointed by the British Association on Standards of Electrical Resistance |date=September 1862 |conference= Thirty-second Meeting of the British Association for the Advancement of Science |first1 =A. |last1 = Williamson |author1-link = Alexander William Williamson |first2 =C. |last2 = Wheatstone |author2-link = Charles Wheatstone |first3 =W. |last3 = Thomson |author3-link = William Thomson, 1st Baron Kelvin |first4 =W. H. |last4 = Miller |author4-link = William Hallowes Miller |first5 =A. |last5 = Matthiessen |author5-link = Augustus Matthiessen |first6 =Fleeming |last6 = Jenkin |author6-link = Fleeming Jenkin |publisher= John Murray |location= London |pages = 125–163 |url= https://www.biodiversitylibrary.org/page/29361871#page/192/mode/2up |access-date= 27 February 2014 }}</ref> In the third report of the committee, 1864, the resistance unit is referred to as "B.A. unit, or Ohmad".<ref> {{cite conference |title=Report of the Committee on Standards of Electrical Resistance |date=September 1864 |conference= Thirty-fourth Meeting of the British Association for the Advancement of Science |first1 =A. |last1 = Williamson |author1-link = Alexander William Williamson |first2 =C. |last2 = Wheatstone |author2-link = Charles Wheatstone |first3 =W. |last3 = Thomson |author3-link = William Thomson, 1st Baron Kelvin |first4 =W. H. |last4 = Miller |author4-link = William Hallowes Miller |first5 =A. |last5 = Matthiessen |author5-link = Augustus Matthiessen |first6 =Fleeming |last6 = Jenkin |author6-link = Fleeming Jenkin |first7 =Charles |last7 = Bright |author7-link =Charles Tilston Bright |first8 =James Clerk |last8 = Maxwell |author8-link = James Clerk Maxwell |first9 =Carl Wilhelm |last9 = Siemens |author9-link = Carl Wilhelm Siemens |first10 = Balfour |last10 = Stewart |author10-link = Balfour Stewart |first11 = James Prescott |last11 = Joule |author11-link = James Prescott Joule |first12 = C. F. |last12 = Varley|author12-link = C. F. Varley |publisher= John Murray |location= London |page = Foldout facing page 349 |url= https://www.biodiversitylibrary.org/item/93072#page/434/mode/1up |access-date= 27 February 2014 }}</ref> By 1867 the unit is referred to as simply ''ohm''.<ref> {{cite conference |title=Report of the Committee on Standards of Electrical Resistance |date=September 1867 |conference= Thirty-seventh Meeting of the British Association for the Advancement of Science |first1 = A. |last1 = Williamson |author1-link = Alexander William Williamson |first2 = C. |last2 = Wheatstone |author2-link = Charles Wheatstone |first3 = W. |last3 = Thomson |author3-link = William Thomson, 1st Baron Kelvin |first4 = W. H. |last4 = Miller |author4-link = William Hallowes Miller |first5 = A. |last5 = Matthiessen |author5-link = Augustus Matthiessen |first6 = Fleeming |last6 = Jenkin |author6-link = Fleeming Jenkin |first7 = Charles |last7 = Bright |author7-link =Charles Tilston Bright |first8 = James Clerk |last8 = Maxwell |author8-link = James Clerk Maxwell |first9 = Carl Wilhelm |last9 = Siemens |author9-link = Carl Wilhelm Siemens |first10 = Balfour |last10 = Stewart |author10-link = Balfour Stewart |first11 = C. F. |last11 = Varley|author11-link = C. F. Varley |first12 = G. C. |last12 = Foster |first13 = Latimer |last13 = Clark |author13-link = Josiah Latimer Clark |first14 = D. |last14 = Forbes |first15 = Charles |last15 = Hockin |first16 = James Prescott |last16 = Joule |author16-link = James Prescott Joule |publisher= John Murray |location= London |page = 488 |url= https://www.biodiversitylibrary.org/item/93115#page/578/mode/1up |access-date= 27 February 2014 }}</ref>

The B.A. ohm was intended to be 109 CGS units but owing to an error in calculations the definition was 1.3% too small. The error was significant for preparation of working standards.

On 21 September 1881 the [[International Electrical Congress]] defined a ''practical'' unit of ohm for the resistance, based on [[CGS]] units, using a mercury column 1 mm2 in cross-section, approximately 104.9 cm in length at 0 °C, similar to the apparatus suggested by Siemens.

A ''legal'' ohm, a reproducible standard, was defined by the international conference of electricians at Paris in 1884 as the resistance of a mercury column of specified weight and 106 cm long; this was a compromise value between the B. A. unit (equivalent to 104.7 cm), the Siemens unit (100 cm by definition), and the CGS unit.<ref>{{cite journal |title=The Electrical Congress Of Paris, 1884 |journal=Nature |date=May 1884 |volume=30 |issue=758 |pages=26–27 |doi=10.1038/030026a0 |bibcode=1884Natur..30...26. |doi-access=free }}</ref> Although called "legal", this standard was not adopted by any national legislation. The "international" ohm was recommended by unanimous resolution at the International Electrical Congress 1893 in Chicago.<ref name=eb11-p742/> The unit was based upon the ohm equal to 109 units of resistance of the C.G.S. system of electromagnetic units. The international ohm is represented by the resistance offered to an unvarying electric current in a mercury column of constant cross-sectional area 106.3 cm long of mass 14.4521 grams and 0 °C. This definition became the basis for the legal definition of the ohm in several countries. In 1908, this definition was adopted by scientific representatives from several countries at the International Conference on Electric Units and Standards in London.<ref name=eb11-p742>{{cite EB1911|wstitle= Units, Physical |volume= 27 | pages = 738–745; see page 742| quote= An Electrical Congress was held in Chicago, U.S.A. in August 1893, to consider......and at the last one held in London in October 1908 were finally adopted|last1= Fleming |first1= John Ambrose |author-link= John Ambrose Fleming }}</ref> The mercury column standard was maintained until the 1948 [[General Conference on Weights and Measures]], at which the ohm was redefined in absolute terms instead of as an artifact standard.

By the end of the 19th century, units were well understood and consistent. Definitions would change with little effect on commercial uses of the units. Advances in metrology allowed definitions to be formulated with a high degree of precision and repeatability.

=== Historical units of resistance === {|class=wikitable |- ! align=left | Unit<ref>Gordon Wigan (trans. and ed.), ''Electrician's Pocket Book'', Cassel and Company, London, 1884</ref> ! align=left | Definition ! align=left | Value in B.A. ohms ! align=left | Remarks |- style="vertical-align:top; border-bottom:1px solid #999;" | Absolute foot/second × 107 | using imperial units | 0.3048 | considered obsolete even in 1884 |- style="vertical-align:top; border-bottom:1px solid #999;" | Thomson's unit | using imperial units | 0.3202 | {{convert|100|e6ft/s|km/s|abbr=unit|sigfig=4}}, considered obsolete even in 1884 |- style="vertical-align:top; border-bottom:1px solid #999;" | Jacobi copper unit | A specified copper wire {{cvt|25|ft|sigfig=4}} long weighing {{cvt|345|gr|sigfig=4}} | 0.6367 | Used in 1850s |- style="vertical-align:top; border-bottom:1px solid #999;" | Weber's absolute unit × 107 | Based on the meter and the second | 0.9191 | |- style="vertical-align:top; border-bottom:1px solid #999;" | [[Siemens mercury unit]] | 1860. A column of pure mercury | 0.9537 | 100 cm and 1 mm2 cross section at 0 °C |- style="vertical-align:top; border-bottom:1px solid #999;" | [[British Science Association#Electrical standards|British Association (B.A.) "ohm"]] | 1863 | 1.000 | Standard coils deposited at Kew Observatory in 1863<ref>[https://books.google.com/books?id=OkxGT9mfNGkC&dq=%22Siemens+mercury+unit%22&pg=PA32 Historical Studies in International Corporate Business. Teich p34]</ref> |- style="vertical-align:top; border-bottom:1px solid #999;" | Digney, Breguet, Swiss | | 9.266–10.420 | Iron wire 1 km long and 4 mm2 cross section |- style="vertical-align:top; border-bottom:1px solid #999;" | Matthiessen | | 13.59 | {{cvt|1|mi|sigfig=4}} of {{convert|1/16|inch||adj=mid|-diameter|sigfig=4}} pure annealed copper wire at 15.5 °C |- style="vertical-align:top; border-bottom:1px solid #999;" | Varley | | 25.61 | One mile of special {{frac|1|16}}-inch-diameter copper wire |- style="vertical-align:top; border-bottom:1px solid #999;" | German mile | | 57.44 | A German mile ({{cvt|8,238|yd|disp=or}}) of iron wire {{cvt|1/6|in|sigfig=4}} diameter |- style="vertical-align:top; border-bottom:1px solid #999;" |[[Abohm]] | |10−9 | Electromagnetic absolute unit in centimeter–gram–second units |- style="vertical-align:top; border-bottom:1px solid #999;" |[[Statohm]] | | {{val|8.987551787|e=11}} | Electrostatic absolute unit in centimeter–gram–second units |}

== Realization of standards == The mercury column method of realizing a physical standard ohm turned out to be difficult to reproduce, owing to the effects of non-constant cross section of the glass tubing. Various resistance coils were constructed by the British Association and others, to serve as physical artifact standards for the unit of resistance. The long-term stability and reproducibility of these artifacts was an ongoing field of research, as the effects of temperature, air pressure, humidity, and time on the standards were detected and analyzed.

Artifact standards are still used, but [[metrology]] experiments relating accurately dimensioned inductors and capacitors provided a more fundamental basis for the definition of the ohm. Since 1990 the [[quantum Hall effect]] has been used to define the ohm with high precision and repeatability. The quantum Hall experiments are used to check the stability of working standards that have convenient values for comparison.<ref>R. Dzuiba and others, ''Stability of Double-Walled Maganin Resistors'' in ''NIST Special Publication Proceedings of SPIE'', The Institute, 1988 pp. 63–64</ref>

Following the [[2019 revision of the SI]], in which the [[ampere]] and the [[kilogram]] were redefined in terms of [[Physical constant|fundamental constants]], the ohm is now also defined in terms of these constants.

== Symbol == The symbol Ω was suggested, because of the similar sound of ohm and omega, by [[William Henry Preece]] in 1867.<ref>{{citation|first1=William Henry|last1=Preece |periodical=[[Philosophical Magazine]]|title=The B.A. unit for electrical measurements |volume=33|year=1867|page=397|url=https://books.google.com/books?id=6Yg7AQAAMAAJ&q=ohm+preece+symbol&pg=PA397|access-date=26 February 2017}}</ref> In documents printed before the Second World War the unit symbol often consisted of the raised lowercase omega (ω), such that 56 Ω was written as 56ω.

Historically, some document editing software applications have used the [[Symbol (typeface)|Symbol typeface]] to render the character Ω.<ref>E.g. recommended in HTML 4.01: {{cite web|url=http://www.w3.org/TR/html401/sgml/entities.html#h-24.1|title=HTML 4.01 Specification|date=1998|website=W3C|at=Section 24.1 "Introduction to character entity references"|access-date=22 November 2018}}</ref> Where the font is not supported, the same document may be displayed with a "W" ("10 W" instead of "10 Ω", for instance). As W represents the [[watt]], the SI unit of [[power (physics)|power]], this can lead to confusion, making the use of the correct Unicode code point preferable.

Where the character set is limited to [[ASCII]], the [[IEEE Std 260.1-2004|IEEE 260.1]] standard recommends using the unit name "ohm" as a symbol instead of Ω.

In the electronics industry it is common to use the character ''R'' instead of the Ω symbol, thus, a 10 Ω resistor may be represented as 10R. This is part of the [[RKM code]]. It is used in many instances where the value has a decimal place. For example, 5.6 Ω is listed as 5R6, or 2200 Ω is listed as 2K2. This method avoids overlooking the decimal point, which may not be rendered reliably on components or when duplicating documents.

[[Unicode]] encodes the symbol as {{unichar|2126|ohm sign}}, distinct from Greek omega among [[letterlike symbols]], but it is only included for backward compatibility and the Greek uppercase omega character {{unichar|03A9|GREEK CAPITAL LETTER OMEGA|html=}} is preferred.<ref>Excerpts from ''[https://www.unicode.org/versions/Unicode4.0.0/ch07.pdf#search=%22character%20U%2B2126%20maps%20OR%20map%20OR%20mapping%22 The Unicode Standard, Version 4.0]'', accessed 11 October 2006</ref> In MS-DOS and Microsoft Windows, the [[alt code]] ALT 234 may produce the Ω symbol. In Mac OS, {{key press|Opt|Z}} does the same.

== See also == * [[Electronic color code]], used for indicating the value of resistors * [[History of measurement]] * [[International Committee for Weights and Measures]] * [[Orders of magnitude (resistance)]] * [[Resistivity]]

== Notes and references == {{Reflist|refs= <ref name="BIPM_SI9">[https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf BIPM SI Brochure: Appendix 1, p.46 (pdf)]</ref> <ref name="Hunt_1994">{{cite journal |author-last=Hunt |author-first=Bruce J. |title=The Ohm Is Where the Art Is: British Telegraph Engineers and the Development of Electrical Standards |journal=Osiris |date=1994 |volume=9 |series=2 |pages=48–63 |url=https://liberalarts.utexas.edu/hps/publications/index.php |access-date=2014-02-27 |doi=10.1086/368729|s2cid=145557228|url-status=dead |archive-url=https://web.archive.org/web/20140308030456/https://webspace.utexas.edu/huntbj/1994-Ohm-Osiris.pdf |archive-date=2014-03-08|url-access=subscription }}</ref> <ref name="NIST_2016">{{cite web |title=NIST Guide to the SI |id=Special Publication 811 |date=2016-08-25 |orig-date=2016-01-28 |publisher=[[National Institute of Standards and Technology]] (NIST), Physical Measurement Laboratory |at=Chapter 9: Rules and Style Conventions for Spelling Unit Names, 9.3: Spelling unit names with prefixes |publication-place=Gaithersburg, Maryland, USA |url=https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-9-rules-and-style-conventions-spelling-unit-names |access-date=2021-01-31 |url-status=live |archive-url=https://web.archive.org/web/20210131024623/https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-9-rules-and-style-conventions-spelling-unit-names |archive-date=2021-01-31}} [http://physics.nist.gov/Pubs/SP811/sec09.html]</ref> <ref name="Thompson-Taylor_2008">{{cite book |title=Guide for the Use of the International System of Units (SI) |chapter=Chapter 9.3 Spelling unit names with prefixes |author-first1=Ambler |author-last1=Thompson |author-first2=Barry N. |author-last2=Taylor |date=November 2008 |orig-date=March 2008 |edition=2nd corrected printing, 2008 |id={{CODEN|NSPUE3}}. NIST Special Publication 811 |publisher=[[National Institute of Standards and Technology]], U.S. Department of Commerce |location=Gaithersburg, Maryland, USA |url=https://physics.nist.gov/cuu/pdf/sp811.pdf |access-date=2021-01-31 |url-status=live |archive-url=https://web.archive.org/web/20210131024615/https://physics.nist.gov/cuu/pdf/sp811.pdf |archive-date=2021-01-31 |quote-page=31 |quote=Reference [[#SI10-2002|[6]]] points out that there are three cases in which the final vowel of an SI prefix is commonly omitted: megohm (not megaohm), kilohm (not kiloohm), and hectare (not hectoare). In all other cases in which the unit name begins with a vowel, both the final vowel of the prefix and the vowel of the unit name are retained and both are pronounced.}} (85 pages)</ref> <ref name="SI10-2002">{{cite tech report |title=IEEE/ASTM SI 10-2002: IEEE/ASTM Standard for Use of the International System of Units (SI): The Modern Metric System. |publisher=IEEE SA|date=2002-12-30 |url=https://standards.ieee.org/ieee/SI_10/3286/}}</ref> <ref name="Aubrecht-French-Iona_2012">{{cite journal |author-first1=Gordon J. |author-last1=Aubrecht II |author-first2=Anthony P. |author-last2=French |author-first3=Mario |author-last3=Iona |date=2012-01-20 |title=About the International System of Units (SI) Part IV. Writing, Spelling, and Mathematics |journal=[[The Physics Teacher]] |volume=50 |issue=2 |doi=10.1119/1.3677278 |bibcode=2012PhTea..50...77A |pages=77–79}}</ref> <ref name="Siemens_1860">{{cite journal |author-first=Werner |author-last=Siemens |author-link=Werner Siemens |periodical=[[Annalen der Physik und Chemie]] |title=Vorschlag eines reproducirbaren Widerstandsmaaßes |volume=186 |issue=5 |date=1860 |pages=1–20 |language=de |doi=10.1002/andp.18601860502 |bibcode=1860AnP...186....1S |url=https://zenodo.org/record/1423670}}</ref> }}

== External links == * [http://www.fh-nuernberg.de/institutionen/bibliothek/bibsuche/texte_online_aufrufen/historische_buecher_der_gso_fh/werke_von_georg_simon_ohm/ Scanned books of Georg Simon Ohm at the library of the University of Applied Sciences Nuernberg] * [http://www.bipm.fr/en/si/si_brochure/ Official SI brochure] * [http://physics.nist.gov/Pubs/SP811/contents.html NIST Special Publication 811] * [http://www.sizes.com/units/ohm.htm History of the ohm at sizes.com] * [http://seaus.free.fr/spip.php?article964 History of the electrical units.] {{SI units}}

[[Category:SI derived units]] [[Category:Units of electrical resistance]] [[Category:Georg Ohm]]