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The ohm (symbol:
Ω
Ω
) is the
SI derived unit SI derived units are units of measurement derived from the seven SI base unit, base units specified by the International System of Units (SI). They are either dimensionless quantity, dimensionless or can be expressed as a product of one or more o ...
of
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epi ...
, named after German physicist
Georg Ohm Georg Simon Ohm (, ; 16 March 1789 – 6 July 1854) was a German physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of inte ...
. 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 The British Science Association (BSA) is a charity Charity may refer to: Giving * Charitable organization or charity, a non-profit organization whose primary objectives are philanthropy and social well-being * Charity (practice), the practice ...
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 The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor that is transverse to an electric ...

quantum Hall effect
.


Definition

The ohm is defined as an electrical resistance between two points of a conductor when a constant potential difference of one
volt The volt is the derived unit for electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work (physics), work energy needed to move a ...

volt
, applied to these points, produces in the conductor a current of one
ampere The ampere (, ; symbol: A), often shortened to "amp",SI supports only the use of symbols and deprecates the use of abbreviations for units. is the base unit of electric current An electric current is a stream of charged particles, such as ele ...

ampere
, the conductor not being the seat of any
electromotive force In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is c ...
. :\Omega = \dfrac = \dfrac = \dfrac = \dfrac = \dfrac = \dfrac = \dfrac = \dfrac = \dfrac=\dfrac in which the following units appear:
volt The volt is the derived unit for electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work (physics), work energy needed to move a ...

volt
(V),
ampere The ampere (, ; symbol: A), often shortened to "amp",SI supports only the use of symbols and deprecates the use of abbreviations for units. is the base unit of electric current An electric current is a stream of charged particles, such as ele ...

ampere
(A),
siemens Siemens AG ( ) is a German multinational Multinational may refer to: * Multinational corporation, a corporate organization operating in multiple countries * Multinational force, a military body from multiple countries * Multinational state, ...
(S),
watt The watt (symbol: W) is a unit of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equa ...

watt
(W),
second The second (symbol: s, also abbreviated: sec) is the of in the (SI) (french: Système International d’unités), commonly understood and historically defined as of a – this factor derived from the division of the day first into 24 s, th ...
(s),
farad The farad (symbol: F) is the SI derived unit SI derived units are units of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, w ...
(F),
henry Henry may refer to: People *Henry (given name) Henry is a masculine given name derived from Old French Old French (, , ; French language, Modern French: ) was the language spoken in Northern France from the 8th century to the 14th century ...
(H),
joule The joule ( ; symbol: J) is a SI derived unit, derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work (physics), work done on) an object when a force of one Newton (unit), newton acts on th ...

joule
(J),
coulomb The coulomb (symbol: C) is the International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' ( ...

coulomb
(C),
kilogram The kilogram (also kilogramme) is the base unit of mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), measure of the body's ''inertia'', the resistance to acceleration (change ...
(kg), and metre (m). Following the
2019 redefinition of the SI base units upright=1.35, The SI system after 1983, but before the 2019 redefinition: Dependence of base unit definitions on other base units (for example, the metre is defined as the distance travelled by light in a specific fraction of a second The ...
, 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 Linearity is the property of a mathematical relationship (''function Function or functionality may refer to: Computing * Function key A function key is a key on a computer A computer is a machine that can be programmed to carry out se ...

linear
resistor A resistor is a that implements as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to , active elements, and terminate s, among other uses. High-power resistors that can dissipat ...

resistor
s. In other cases resistance varies, such as in the case of the
thermistor A thermistor is a type of resistor whose resistance is strongly dependent on temperature Temperature is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source ...

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. In alternating current circuits,
electrical impedance In electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an ident ...
is also measured in ohms.


Conversions

The
siemens Siemens AG ( ) is a German multinational Multinational may refer to: * Multinational corporation, a corporate organization operating in multiple countries * Multinational force, a military body from multiple countries * Multinational state, ...
(symbol: S) is the
SI derived unit SI derived units are units of measurement derived from the seven SI base unit, base units specified by the International System of Units (SI). They are either dimensionless quantity, dimensionless or can be expressed as a product of one or more o ...
of
electric conductance Electricity is the set of physical Physical may refer to: *Physical examination, a regular overall check-up with a doctor *Physical (album), ''Physical'' (album), a 1981 album by Olivia Newton-John **Physical (Olivia Newton-John song), "Physic ...

electric conductance
and
admittance In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance, analogous to how conductance & resistance are defined. The SI unit of admittance i ...
, also known as the mho (ohm spelled backwards, symbol is ℧); it is the
reciprocal Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another poly ...

reciprocal
of resistance in ohms (Ω).


Power as a function of resistance

The power dissipated by a
resistor A resistor is a that implements as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to , active elements, and terminate s, among other uses. High-power resistors that can dissipat ...

resistor
may be calculated from its resistance, and the voltage or current involved. The formula is a combination of
Ohm's law Ohm's law states that the electric current, current through a Electrical conductor, conductor between two points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of proporti ...

Ohm's law
and Joule's law: :P=V\cdot I =\frac = I^2\cdot R where: :''P'' is the power :''R'' is the resistance :''V'' is the
voltage Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) 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. Non-linear resistors have a value that may vary depending on the applied voltage (or current). Where
alternating current Alternating current (AC) is an electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through ...
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 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 The watt (symbol: W) is a unit of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equa ...

watt
for ''P'', ohm for ''R'',
volt The volt is the derived unit for electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work (physics), work energy needed to move a ...

volt
for ''V'' and
ampere The ampere (, ; symbol: A), often shortened to "amp",SI supports only the use of symbols and deprecates the use of abbreviations for units. is the base unit of electric current An electric current is a stream of charged particles, such as ele ...

ampere
for ''I'', which are related as in , 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. 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 Electrochemistry is the branch of physical chemistry Physical chemistry is the study of macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying ...
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 In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric current) and units of measure ...
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-units 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 ''
Annalen der Physik und Chemie ''Annalen der Physik'' (English: ''Annals of Physics'') is one of the oldest scientific journals on physics and has been published since 1799. The journal publishes original, Peer review, peer-reviewed papers in the areas of experimental physics, ...
''. He proposed a column of pure mercury, of one square millimeter cross section, one metre long:
Siemens mercury unit The Siemens mercury unit is an obsolete unit of electrical resistance In electronics and electromagnetism, the electrical resistance of an object is a measure of its opposition to the flow of electric current. The Multiplicative inverse, rec ...
. 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 Metrology is the scientific study of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be used to compare with oth ...

metrology
experiments to the required precision, so working standards notionally based on the physical definition were required. In 1861,
Latimer Clark Josiah Latimer Clark FRAS (10 March 1822 – 30 October 1898), was an English electrical engineer, born in Great Marlow, Buckinghamshire. Biography Josiah Latimer Clark was born in Great Marlow, Buckinghamshire, and was younger brother to E ...

Latimer Clark
(1822–1898) and (1832–1888) presented a paper at the
British Association for the Advancement of Science The British Science Association (BSA) is a charity Charity may refer to: Giving * Charitable organization or charity, a non-profit organization whose primary objectives are philanthropy and social well-being * Charity (practice), the practice ...
meeting 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 and Thomson to report upon standards of electrical resistance. 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. In the third report of the committee, 1864, the resistance unit is referred to as "B.A. unit, or Ohmad". By 1867 the unit is referred to as simply ''ohm''. 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 '' Congrès internationale des électriciens'' (international conference of electricians) defined a ''practical'' unit of ohm for the resistance, based on units, using a mercury column 1 sq. mm. 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. Although called "legal", this standard was not adopted by any national legislation. The "international" ohm was recommended by unanimous resolution at the
International Electrical CongressThe International Electrical Congress was a series of international meetings, from 1881 - 1904, in the then new field of applied electricity. The first meeting was initiated by the French government, including official national representatives, lead ...
1893 in Chicago. The unit was based upon the ohm equal to 109 units of resistance of the . 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. The mercury column standard was maintained until the 1948
General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures The International Bureau of Weights and Measures (fr ...
, 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


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 Metrology is the scientific study of measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be used to compare with oth ...

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 The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor that is transverse to an electric ...

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. Following the
2019 redefinition of the SI base units upright=1.35, The SI system after 1983, but before the 2019 redefinition: Dependence of base unit definitions on other base units (for example, the metre is defined as the distance travelled by light in a specific fraction of a second The ...
, in which the
ampere The ampere (, ; symbol: A), often shortened to "amp",SI supports only the use of symbols and deprecates the use of abbreviations for units. is the base unit of electric current An electric current is a stream of charged particles, such as ele ...

ampere
and the
kilogram The kilogram (also kilogramme) is the base unit of mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), measure of the body's ''inertia'', the resistance to acceleration (change ...
were redefined in terms of 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 Sir William Henry Preece (15 February 1834 – 6 November 1913) was a Welsh Welsh may refer to: Related to Wales * Welsh, referring or related to Wales * Welsh language, a Brittonic Celtic language of the Indo-European language family, indigeno ...

William Henry Preece
in 1867. In documents printed before WWII 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 A symbol is a mark, sign, or word In linguistics, a word of a spoken language can be defined as the smallest sequence of phonemes that can be uttered in isolation with semantic, objective or pragmatics, practical meaning (linguistics), m ...
typeface to render the character Ω. 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 watt (symbol: W) is a unit of power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equa ...

watt
, the SI unit of
power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, p ...
, this can lead to confusion, making the use of the correct Unicode code point preferable. Where the character set is limited to
ASCII ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding In computing Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the stu ...
, 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 The RKM code, also referred to as "letter and numeral code for resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ...
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 Unicode, formally the Unicode Standard, is an information technology Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expressed in most of the world's wri ...

Unicode
encodes the symbol as , distinct from Greek omega among
letterlike symbols Letterlike Symbols is a Unicode blockA Unicode block is one of several contiguous ranges of numeric character codes ( code points) of the Unicode Unicode is an information technology Technical standard, standard for the consistent character ...
, but it is only included for backwards compatibility and the Greek uppercase omega character is preferred.Excerpts from
The Unicode Standard, Version 4.0
', accessed 11 October 2006
In MS-DOS and Microsoft Windows, the ALT 234 may produce the Ω symbol. In Mac OS, does the same.


See also

*
Electronic color code ), from top, 2-2-6-1-1; the last two brown bands indicate the multiplier (×10) and the tolerance (1%). An electronic color code is used to indicate the values or ratings of electronic components, usually for resistor A resistor is a passivi ...
*
History of measurement History (from Greek , ''historia'', meaning "inquiry; knowledge acquired by investigation") is the study of the past. Events occurring before the invention of writing systems are considered prehistory Prehistory, also known as pre-literary ...
*
International Committee for Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence Générale des Poids et Mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established in ...
* Orders of magnitude (resistance) *
Resistivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...


Notes and references


External links


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

Official SI brochure





History of the electrical units.
{{SI units SI derived units Units of electrical resistance Georg Ohm