Resistance Unit

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The ohm (symbol: Ω) is the unit of electrical resistance in the International System of Units (SI). It is named after German physicist Georg Simon 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.[1]

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 as an exact value in terms of these constants.

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.[2]

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 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 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).

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.[7]

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.

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 mm2 in cross-section, approximately 104.9 cm in length at 0 C,[14] 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.[15] 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.[15] 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.

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.

The symbol Ω was suggested, because of the similar sound of ohm and omega, by William Henry Preece in 1867.[19] 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 typeface to render the character Ω.[20] 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.

Due to the extraordinary reproducibility of the quantum Hall resistance, its perfect long-term stability and world-wide uniformity, the ohm can be realised as a certain fraction of the von-Klitzing constant. Already since 1990, on basis of a recommendation by the CIPM (Comité International des Poids et Mesures), resistance comparisons and calibrations world-wide had to be referred to a fixed numerical value of the von-Klitzing constant, RK-90 = 25812.807 Ω90. The introduction of this conventional reference value for the von Klitzing constant had considerable practical advantages in terms of maintainance and dissemination of the unit ohm. At the same time, however, this also meant that the conventional unit Ω90 was not compliant with the International System of Units (SI) valid at that time. An SI-realization of the ohm was, e.g., possible with a Thompson-Lampard capacitor (calculable capacitance; due to the complexity of the corresponding measurement setup, the achievable accuracies were inferior to the reproducibility of quantum Hall resistors.

At PTB, the resistance unit is realised from the quantum Hall resistance. For this purpose, our working group operates a cryostat with a superconducting solenoid. To guarantee that the Hall resistance takes the precisely quantised value, some internationally accepted criteria have to be fulfilled [Delahaye, Jeckelmann, Metrologia 40, 217-223 (2003)]. Firstly, the longitudinal resistance should be zero because a vanishing longitudinal resistance is a measure for complete quantisation (otherwise a correction has to be applied). Furthermore, all contact resistances of the quantum Hall device have to be sufficiently small. Prior to every calibration, these criteria have to be verified experimentally. Moreover, the resistance values calibrated at PTB and at other national metrology institutes have to be compared from time to time, to guarantee a world-wide uniformity of the resistance unit ohm.

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When spelled out in full, unit names are treated like ordinary English nouns. Thus the names of all units start with a lower-case letter, except at the beginning of a sentence or in capitalized material such as a title. In keeping with this rule, the unit symbols for Ampere is a capitalized \"A\" and Volt is capitalized \"V\" because both unit names are based on the names of scientists. 59ce067264