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Ohm  

General information  
Unit system 
SI derived unit 
Unit of 
Electrical resistance 
Symbol  Ω 
Named after 
Georg Ohm 
Derivation  Ω = V/A 
Conversions  
1 Ω in …  … is equal to … 
SI base units 
kg ⋅ m ^{2}⋅ s ^{−3}⋅ A ^{−2} 
The ohm (symbol:
Ω
) is the
SI derived unit
of
electrical resistance
, named after German physicist
Georg Ohm
. 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. As of 2020, the definition of the ohm is expressed in terms of the
quantum Hall effect
.
Definition[
edit
]
The ohm is defined as an electrical resistance between two points of a conductor when a constant potential difference of one
volt
, applied to these points, produces in the conductor a current of one
ampere
, the conductor not being the seat of any
electromotive force
.^{}
[1]
 Ω=VA=1S=WA2=V2W=sF=Hs=J⋅sC2=kg⋅m2s⋅C2=Js⋅A2=kg⋅m2s3⋅A2{displaystyle Omega ={dfrac {text{V}}{text{A}}}={dfrac {1}{text{S}}}={dfrac {text{W}}{{text{A}}^{2}}}={dfrac {{text{V}}^{2}}{text{W}}}={dfrac {text{s}}{text{F}}}={dfrac {text{H}}{text{s}}}={dfrac {{text{J}}{cdot }{text{s}}}{{text{C}}^{2}}}={dfrac {{text{kg}}{cdot }{text{m}}^{2}}{{text{s}}{cdot }{text{C}}^{2}}}={dfrac {text{J}}{{text{s}}{cdot }{text{A}}^{2}}}={dfrac {{text{kg}}{cdot }{text{m}}^{2}}{{text{s}}^{3}{cdot }{text{A}}^{2}}}}
in which the following units appear:
volt
(V),
ampere
(A),
siemens
(S),
watt
(W),
second
(s),
farad
(F),
henry
(H),
joule
(J),
coulomb
(C),
kilogram
(kg),
and metre
(m).
Following the
2019 redefinition of the SI base units
, in which the ampere and the kilogram were redefined in terms of
fundamental constants
, the ohm is affected by a very small scaling in measurement.
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
resistors
. In other cases resistance varies, such as in the case of the
thermistor
, which exhibits a strong dependence of its resistance with temperature.
A vowel of the prefixed units kiloohm and megaohm is commonly omitted, producing kilohm and megohm.^{}
[2]
^{}
[3]
^{}
[4]
^{}
[5]
In alternating current circuits,
electrical impedance
is also measured in ohms.
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Conversions[
edit
]
The
siemens
(symbol: S) is the
SI derived unit
of
electric conductance
and
admittance
, also known as the
mho
(ohm spelled backwards, symbol is ℧); it is the
reciprocal
of resistance in ohms (Ω).
Power as a function of resistance[
edit
]
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 law
:
 P=V⋅I=V2R=I2⋅R{displaystyle P=Vcdot I={frac {V^{2}}{R}}=I^{2}cdot R}
where:
 P is the power
 R is the resistance
 V is the
voltage
across the resistor
 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. Nonlinear 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
integration
of “instantaneous” power over that interval.
Since the ohm belongs to a
coherent system of units
, when each of these quantities has its corresponding SI unit (
watt
for P, ohm for R,
volt
for V and
ampere
for I, which are related as in
§ Definition
, this formula remains valid numerically when these units are used (and thought of as being cancelled or omitted).
History[
edit
]
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.^{}
[6]
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 socalled “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 absoluteunits 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 centimetergramsecond, 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
Poggendorffs
Annalen der Physik und Chemie
.^{}
[7]
He proposed a column of pure mercury, of one square millimeter cross section, one metre 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,
Latimer Clark
(1822–1898) and
Sir Charles Bright
(1832–1888) presented a paper at the
British Association for the Advancement of Science
meeting ^{}
[8]
suggesting that standards for electrical units be established and suggesting names for these units derived from eminent philosophers, ‘Ohma’, ‘Farad’ and ‘Volt’. The
BAAS
in 1861 appointed a committee including
Maxwell
and
Thomson
to report upon standards of electrical resistance.^{}
[9]
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.^{}
[10]
In the third report of the committee, 1864, the resistance unit is referred to as “B.A. unit, or Ohmad”.^{}
[11]
By 1867 the unit is referred to as simply ohm.^{}
[12]
The B.A. ohm was intended to be 10^{9} 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
Congrès internationale des électriciens
(international conference of electricians) defined a practical unit of ohm for the resistance, based on
CGS
units, using a mercury column 1 sq. mm. in crosssection, approximately 104.9 cm in length at 0 °C,^{}
[13]
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^{[}
citation needed
] 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. 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.^{}
[14]
The unit was based upon the ohm equal to 10^{9} 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 crosssectional 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.^{}
[14]
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[
edit
]
Unit^{ [15] }  Definition  Value in B.A. ohms  Remarks 

Absolute foot/second × 10^{7}  using imperial units  0.3048  considered obsolete even in 1884 
Thomson’s unit  using imperial units  0.3202  100 million feet/second, considered obsolete even in 1884 
Jacobi copper unit  A specified copper wire 25 feet long weighing 345 grains  0.6367  Used in 1850s 
Weber’s absolute unit × 10^{7}  Based on the metre and the second  0.9191  
Siemens mercury unit 
1860. A column of pure mercury  0.9537  100 cm and 1 mm^{2} cross section at 0 °C 
British Association (B.A.) “ohm” 
1863  1.000  Standard coils deposited at Kew Observatory in 1863^{ [16] } 
Digney, Breguet, Swiss  9.266–10.420  Iron wire 1 km long and 4 square mm cross section  
Matthiessen  13.59  One mile of 1/16 inch diameter pure annealed copper wire at 15.5 °C  
Varley  25.61  One mile of special 1/16 inch diameter copper wire  
German mile  57.44  A German mile (8,238 yard) of iron wire 1/6th inch diameter  
Abohm 
10^{−9}  Electromagnetic absolute unit in centimeter–gram–second units  
Statohm 
8.987551787 × 10^{11}  Electrostatic absolute unit in centimeter–gram–second units 
Realization of standards[
edit
]
The mercury column method of realizing a physical standard ohm turned out to be difficult to reproduce, owing to the effects of nonconstant 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 longterm 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 accuratelydimensioned 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.^{}
[17]
Following the
2019 redefinition of the SI base units
, in which the
ampere
and the
kilogram
were redefined in terms of
fundamental constants
, the ohm is now also defined in terms of these constants.
Symbol[
edit
]
The symbol Ω was suggested, because of the similar sound of ohm and omega, by
William Henry Preece
in 1867.^{}
[18]
In documents printed before WWII the unit symbol often consisted of the raised lowercase omega (ω), such that 56 Ω was written as 56^{ω}.
Historically, some document editing software applications have used the
Symbol
typeface to render the character Ω.^{}
[19]
Where the font is not supported, a W is displayed instead (“10 W” instead of “10 Ω”, for instance). As W represents the
watt
, the SI unit of
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 260.1
standard recommends substituting the symbol ohm for 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 the British standard
BS 1852
code. It is used in many instances where the value has a decimal place. For example, 5.6 Ω is listed as 5R6. This method avoids overlooking the decimal point, which may not be rendered reliably on components or when duplicating documents.
Unicode
encodes the symbol as U+2126 Ω OHM SIGN, distinct from Greek omega among
letterlike symbols
, but it is only included for backwards compatibility and the Greek uppercase omega character U+03A9 Ω GREEK CAPITAL LETTER OMEGA (HTML Ω
· Ω, Ω
) is preferred.^{}
[20]
In DOS and Windows, the
alt code
ALT 234 may produce the Ω symbol. In Mac OS, ⌥ Opt+Z does the same.
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See also[
edit
]

Electronic color code

History of measurement

International Committee for Weights and Measures

Orders of magnitude (resistance)

Resistivity
Notes and references[
edit
]

^
BIPM SI Brochure: Appendix 1, p. 144

^
SASB/SCC14 – SCC14 – Quantities, Units, and Letter Symbols (20021230).
IEEE/ASTM SI 102002: IEEE/ASTM Standard for Use of the International System of Units (SI): The Modern Metric System
.CS1 maint: multiple names: authors list (
link
)

^
Thompson, Ambler; Taylor, Barry N. (November 2008) [March 2008]. “Chapter 9.3 Spelling unit names with prefixes”.
Guide for the Use of the International System of Units (SI)
(PDF) (2nd corrected printing, 2008 ed.). Gaithersburg, Maryland, USA:
National Institute of Standards and Technology
, U.S. Department of Commerce.
CODEN
NSPUE3
. NIST Special Publication 811.
Archived
(PDF) from the original on 20210131. Retrieved 20210131. p. 31:
Reference
[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)

^
“NIST Guide to the SI”
. Gaithersburg, Maryland, USA:
National Institute of Standards and Technology
(NIST), Physical Measurement Laboratory. 20160825 [20160128]. Chapter 9: Rules and Style Conventions for Spelling Unit Names, 9.3: Spelling unit names with prefixes. Special Publication 811.
Archived
from the original on 20210131. Retrieved 20210131.
[1]

^
Aubrecht II, Gordon J.; French, Anthony P.; Iona, Mario (20120120). “About the International System of Units (SI) Part IV. Writing, Spelling, and Mathematics”.
The Physics Teacher
. 50 (2): 77–79.
Bibcode
:
2012PhTea..50…77A
.
doi
:
10.1119/1.3677278
.

^
Hunt, Bruce J. (1994).
“The Ohm Is Where the Art Is: British Telegraph Engineers and the Development of Electrical Standards”
(PDF). Osiris. 2. 9: 48–63.
doi
:
10.1086/368729
.
S2CID
145557228
. Archived from
the original
on 20140308. Retrieved 20140227.

^
Siemens, Werner
(1860).
“Vorschlag eines reproducirbaren Widerstandsmaaßes”
.
Annalen der Physik und Chemie
(in German). 186 (5): 1–20.
Bibcode
:
1860AnP…186….1S
.
doi
:
10.1002/andp.18601860502
.

^
Clark, Latimer
;
Bright, Sir Charles
(18611109).
“Measurement of Electrical Quantities and Resistance”
.
The Electrician
. 1 (1): 3–4. Retrieved 20140227.

^
Report of the ThirtyFirst Meeting of the British Association for the Advancement of Science; held at Manchester in September 1861
. September 1861. pp. xxxix–xl.

^
Williamson, A.
;
Wheatstone, C.
;
Thomson, W.
;
Miller, W. H.
;
Matthiessen, A.
;
Jenkin, Fleeming
(September 1862).
Provisional Report of the Committee appointed by the British Association on Standards of Electrical Resistance
. Thirtysecond Meeting of the British Association for the Advancement of Science. London: John Murray. pp. 125–163. Retrieved 20140227.

^
Williamson, A.
;
Wheatstone, C.
;
Thomson, W.
;
Miller, W. H.
;
Matthiessen, A.
;
Jenkin, Fleeming
;
Bright, Charles
;
Maxwell, James Clerk
;
Siemens, Carl Wilhelm
;
Stewart, Balfour
;
Joule, James Prescott
;
Varley, C. F.
(September 1864).
Report of the Committee on Standards of Electrical Resistance
. Thirtyfourth Meeting of the British Association for the Advancement of Science. London: John Murray. p. Foldout facing page 349. Retrieved 20140227.

^
Williamson, A.
;
Wheatstone, C.
;
Thomson, W.
;
Miller, W. H.
;
Matthiessen, A.
;
Jenkin, Fleeming
;
Bright, Charles
;
Maxwell, James Clerk
;
Siemens, Carl Wilhelm
;
Stewart, Balfour
;
Varley, C. F.
; Foster, G. C.;
Clark, Latimer
; Forbes, D.; Hockin, Charles;
Joule, James Prescott
(September 1867).
Report of the Committee on Standards of Electrical Resistance
. Thirtyseventh Meeting of the British Association for the Advancement of Science. London: John Murray. p. 488. Retrieved 20140227.

^
“System of measurement units”
. Engineering and Technology History Wiki. Retrieved 20180413.
 ^
^{a}
^{b}
“Units, Physical”.
Encyclopædia Britannica
. 27 (11th ed.). 1911. p. 742.

^
Gordon Wigan (trans. and ed.), Electrician’s Pocket Book, Cassel and Company, London, 1884

^
Historical Studies in International Corporate Business. Teich p34

^
R. Dzuiba and others, Stability of DoubleWalled Maganin Resistors in NIST Special Publication Proceedings of SPIE, The Institute, 1988 pp. 63–64

^
Preece, William Henry (1867),
“The B.A. unit for electrical measurements”
,
Philosophical Magazine
, 33, p. 397, retrieved 20170226

^
E.g. recommended in HTML 4.01:
“HTML 4.01 Specification”
. W3C. 1998. Section 24.1 “Introduction to character entity references”. Retrieved 20181122.

^
Excerpts from
The Unicode Standard, Version 4.0
, accessed 11 October 2006
External links[
edit
]

Scanned books of Georg Simon Ohm at the library of the University of Applied Sciences Nuernberg

Official SI brochure

NIST Special Publication 811

History of the ohm at sizes.com

History of the electrical units.
Categories
:

SI derived units

Units of electrical resistance

Georg Ohm
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