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The ohm (symbol: Ω, the uppercase Greek letter omega) is the unit of electrical resistance in the 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.
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 . 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, a double vowel in the prefixed units "kiloohm" and "megaohm" is commonly simplified, producing "kilohm" and "megohm".
In alternating current circuits, electrical impedance is also measured in ohms.
where is the power, is the resistance, is the voltage across the resistor, and 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 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 , ohm for , volt for and ampere for , which are related as in ) this formula remains valid numerically when these units are used (and thought of as being cancelled or omitted).
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 Poggendorff's Annalen der Physik und Chemie. 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, Latimer Clark (1822–1898) and Sir Charles Bright (1832–1888) presented a paper at the British Association for the Advancement of Science 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 Maxwell 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 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. 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. 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. 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.
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.R. Dzuiba and others, Stability of Double-Walled Maganin Resistors in NIST Special Publication Proceedings of SPIE, The Institute, 1988 pp. 63–64
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 in terms of these constants.
Historically, some document editing software applications have used the Symbol typeface to render the character Ω.E.g. recommended in HTML 4.01: 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, 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 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 , distinct from Greek omega among letterlike symbols, but it is only included for backward 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 code ALT 234 may produce the Ω symbol. In Mac OS, does the same.
Historical units of resistance
Absolute foot/second × 107 using imperial units 0.3048 considered obsolete even in 1884 Thomson's unit using imperial units 0.3202 , considered obsolete even in 1884 Jacobi copper unit A specified copper wire long weighing 0.6367 Used in 1850s Weber's absolute unit × 107 Based on the meter and the second 0.9191 Siemens mercury unit 1860. A column of pure mercury 0.9537 100 cm and 1 mm2 cross section at 0 °C British Association (B.A.) "ohm" 1863 1.000 Standard coils deposited at Kew Observatory in 1863 Historical Studies in International Corporate Business. Teich p34 Digney, Breguet, Swiss 9.266–10.420 Iron wire 1 km long and 4 mm2 cross section Matthiessen 13.59 of pure annealed copper wire at 15.5 °C Varley 25.61 One mile of special -inch-diameter copper wire German mile 57.44 A German mile () of iron wire diameter Abohm 10−9 Electromagnetic absolute unit in centimeter–gram–second units Statohm 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.
Symbol
The symbol Ω was suggested, because of the similar sound of ohm and omega, by William Henry Preece in 1867. In documents printed before Second World War the unit symbol often consisted of the raised lowercase omega (ω), such that 56 Ω was written as 56ω.
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