Conventional electrical unit

Last updated

A conventional electrical unit (or conventional unit where there is no risk of ambiguity) is a unit of measurement in the field of electricity which is based on the so-called "conventional values" of the Josephson constant, the von Klitzing constant agreed by the International Committee for Weights and Measures (CIPM) in 1988, as well as ΔνCs used to define the second. These units are very similar in scale to their corresponding SI units, but are not identical because of the different values used for the constants. They are distinguished from the corresponding SI units by setting the symbol in italic typeface and adding a subscript "90" – e.g., the conventional volt has the symbol V90 – as they came into international use on 1 January 1990.

Contents

This system was developed to increase the precision of measurements: The Josephson and von Klitzing constants can be realized with great precision, repeatability and ease, and are exactly defined in terms of the universal constants e and h. The conventional electrical units represent a significant step towards using "natural" fundamental physics for practical measurement purposes. They achieved acceptance as an international standard in parallel to the SI system of units and are commonly used outside of the physics community in both engineering and industry. Addition of the constant c would be needed to define units for all dimensions used in physics, as in the SI.

The SI system made the transition to equivalent definitions 29 years later but with values of the constants defined to match the old SI units more precisely. Consequently, the conventional electrical units differ slightly from the corresponding SI units, now with exactly defined ratios.

Historical development

Several significant steps have been taken in the last half century to increase the precision and utility of measurement units:

Definition

Conventional electrical units are based on defined values of the caesium-133 hyperfine transition frequency, Josephson constant and the von Klitzing constant, the first two which allow a very precise practical measurement of time and electromotive force, and the last which allows a very precise practical measurement of electrical resistance. [8]

ConstantConventional exact value
(CIPM, 1988; until 2018)
Empirical value (in SI units)
(CODATA, 2014 [8] )
Exact value
(SI units, 2019)
133Cs hyperfine transition frequencyΔν(133Cs)hfs = 9192631770 HzΔν(133Cs)hfs = 9192631770 Hz [9]
Josephson constantKJ-90 = 483597.9 GHz/V [10] KJ = 483597.8525(30) GHz/VKJ = 2 × 1.602176634×10−19 C/6.62607015×10−34 Js
von Klitzing constantRK-90 = 25812.807 Ω [11] RK = 25812.8074555(59) ΩRK = 6.62607015×10−34 Js/(1.602176634×10−19 C)2

Conversion to SI units

UnitSymbolDefinitionRelated to SISI value (CODATA 2014)SI value (2019)
conventional volt V90see aboveKJ-90/KJ V1.0000000983(61) V1.00000010666... V [12]
conventional ohm Ω90see aboveRK/RK-90 Ω1.00000001765(23) Ω1.00000001779... Ω [13]
conventional ampere A90V90/Ω90KJ-90/KJRK-90/RK A1.0000000806(61) A1.00000008887... A [14]
conventional coulomb C90 sA90 = sV90/Ω90KJ-90/KJRK-90/RK C1.0000000806(61) C1.00000008887... C [15]
conventional watt W90A90V90 = V902/Ω90(KJ-90/KJ)2
 
RK-90/RK W
1.000000179(12) W1.00000019553... W [16]
conventional farad F90C90/V90 = s/Ω90RK-90/RK F0.99999998235(23) F0.99999998220... F [17]
conventional henry H90 sΩ90RK/RK-90 H1.00000001765(23) H1.00000001779... H [18]

The 2019 revision of the SI defines all these units in a way that fixes the numeric values of KJ, RK and ΔνCs exactly, albeit with values of the first two that differ slightly from the conventional values. Consequently, these conventional units all have known exact values in terms of the redefined SI units. Because of this, there is no accuracy benefit from maintaining the conventional values.

See also

Related Research Articles

A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.

<span class="mw-page-title-main">International System of Units</span> Modern form of the metric system

The International System of Units, internationally known by the abbreviation SI, is the modern form of the metric system and the world's most widely used system of measurement. Coordinated by the International Bureau of Weights and Measures it is the only system of measurement with official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.

<span class="mw-page-title-main">SI base unit</span> One of the seven units of measurement that define the metric system

The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all other SI units can be derived. The units and their physical quantities are the second for time, the metre for length or distance, the kilogram for mass, the ampere for electric current, the kelvin for thermodynamic temperature, the mole for amount of substance, and the candela for luminous intensity. The SI base units are a fundamental part of modern metrology, and thus part of the foundation of modern science and technology.

<span class="mw-page-title-main">Volt</span> SI derived unit of voltage

The volt is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI).

<span class="mw-page-title-main">Avogadro constant</span> Fundamental metric system constant defined as the number of particles per mole

The Avogadro constant, commonly denoted NA or L, is an SI defining constant with an exact value of 6.02214076×1023 mol−1 (reciprocal moles). It is defined as the number of constituent particles (usually molecules, atoms, ions, or ion pairs) per mole (SI unit) and used as a normalization factor in the amount of substance in a sample. In the SI dimensional analysis of measurement units, the dimension of the Avogadro constant is the reciprocal of amount of substance, denoted N−1. The Avogadro number, sometimes denoted N0, is the numeric value of the Avogadro constant (i.e., without a unit), namely the dimensionless number 6.02214076×1023; the value chosen based on the number of atoms in 12 grams of carbon-12 in alignment with the historical definition of a mole. The constant is named after the Italian physicist and chemist Amedeo Avogadro (1776–1856).

The dalton or unified atomic mass unit is a unit of mass defined as 1/12 of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest. It is a non-SI unit accepted for use with SI. The atomic mass constant, denoted mu, is defined identically, giving mu = 1/12m(12C) = 1 Da.

<span class="mw-page-title-main">Coulomb</span> SI derived unit of electric charge

The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). It is equal to the electric charge delivered by a 1 ampere current in 1 second and is defined in terms of the elementary charge e, at about 6.241509×1018 e.

<span class="mw-page-title-main">Metrology</span> Science of measurement and its application

Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in France when a length standard taken from a natural source was proposed. This led to the creation of the decimal-based metric system in 1795, establishing a set of standards for other types of measurements. Several other countries adopted the metric system between 1795 and 1875; to ensure conformity between the countries, the Bureau International des Poids et Mesures (BIPM) was established by the Metre Convention. This has evolved into the International System of Units (SI) as a result of a resolution at the 11th General Conference on Weights and Measures (CGPM) in 1960.

The elementary charge, usually denoted by e, is a fundamental physical constant, defined as the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 e.

The magnetic flux, represented by the symbol Φ, threading some contour or loop is defined as the magnetic field B multiplied by the loop area S, i.e. Φ = BS. Both B and S can be arbitrary, meaning that the flux Φ can be as well but increments of flux can be quantized. The wave function can be multivalued as it happens in the Aharonov–Bohm effect or quantized as in superconductors. The unit of quantization is therefore called magnetic flux quantum.

<span class="mw-page-title-main">Klaus von Klitzing</span> German physicist (born 1943)

Klaus von Klitzing is a German physicist, known for discovery of the integer quantum Hall effect, for which he was awarded the 1985 Nobel Prize in Physics.

<span class="mw-page-title-main">Kibble balance</span> Electromechanical weight measuring instrument

A Kibble balance is an electromechanical measuring instrument that measures the weight of a test object very precisely by the electric current and voltage needed to produce a compensating force. It is a metrological instrument that can realize the definition of the kilogram unit of mass based on fundamental constants.

The conductance quantum, denoted by the symbol G0, is the quantized unit of electrical conductance. It is defined by the elementary charge e and Planck constant h as:

The vacuum magnetic permeability is the magnetic permeability in a classical vacuum. It is a physical constant, conventionally written as μ0. It quantifies the strength of the magnetic field induced by an electric current. Expressed in terms of SI base units, it has the unit kg⋅m⋅s−2·A−2. It can be also expressed in terms of SI derived units, N·A−2.

A g-factor is a dimensionless quantity that characterizes the magnetic moment and angular momentum of an atom, a particle or the nucleus. It is the ratio of the magnetic moment of a particle to that expected of a classical particle of the same charge and angular momentum. In nuclear physics, the nuclear magneton replaces the classically expected magnetic moment in the definition. The two definitions coincide for the proton.

<span class="mw-page-title-main">Kelvin</span> SI unit of temperature

The kelvin is the base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature, taken to be 0 K. By definition, the Celsius scale and the Kelvin scale have the exact same magnitude; that is, a rise of 1 K is equal to a rise of 1 °C and vice versa, and any temperature in degrees Celsius can be converted to kelvin by adding 273.15.

<span class="mw-page-title-main">2019 revision of the SI</span> Definition of the units kg, A, K and mol

In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artefacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.

In physics, natural unit systems are measurement systems for which selected physical constants have been set to 1 through nondimensionalization of physical units. For example, the speed of light c may be set to 1, and it may then be omitted, equating mass and energy directly E = m rather than using c as a conversion factor in the typical mass–energy equivalence equation E = mc2. A purely natural system of units has all of its dimensions collapsed, such that the physical constants completely define the system of units and the relevant physical laws contain no conversion constants.

<span class="mw-page-title-main">Alternative approaches to redefining the kilogram</span>

The scientific community examined several approaches to redefining the kilogram before deciding on a revision of the SI in November 2018. Each approach had advantages and disadvantages.

References

  1. "Resolution 1 of the 13th CGPM (1967) – SI unit of time (second)". Archived from the original on 11 April 2021. Retrieved 18 February 2019.
  2. "Resolution 1 of the 17th CGPM (1983) – Definition of the metre". Archived from the original on 29 March 2019. Retrieved 18 February 2019.
  3. "CIPM, 1988: Recommendation 1 – Representation of the volt by means of the Josephson effect". Archived from the original on 21 January 2021. Retrieved 18 February 2019.
  4. "CIPM, 1988: Recommendation 2 – Representation of the ohm by means of the quantum Hall effect". Archived from the original on 21 January 2021. Retrieved 18 February 2019.
  5. "Resolution 2 of the 19th CGPM (1991) – The Josephson and quantum-Hall effects". Archived from the original on 26 January 2021. Retrieved 18 February 2019.
  6. "CIPM, 2000 – use of the von Klitzing constant to express the value of a reference standard of resistance as a function of the quantum Hall effect". Archived from the original on 21 January 2021. Retrieved 18 February 2019.
  7. "26th CGPM Resolutions" (PDF). BIPM. Retrieved 18 February 2019.
  8. 1 2 Mohr, Peter J.; Newell, David B.; Taylor, Barry N. (2015). "CODATA recommended values of the fundamental physical constants: 2014". Zenodo. arXiv: 1507.07956 . doi:10.5281/zenodo.22826.
  9. "2022 CODATA Value: hyperfine transition frequency of Cs-133". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  10. "2022 CODATA Value: conventional value of Josephson constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  11. "2022 CODATA Value: conventional value of von Klitzing constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  12. "2022 CODATA Value: conventional value of volt-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  13. "2022 CODATA Value: conventional value of ohm-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  14. "2022 CODATA Value: conventional value of ampere-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  15. "2022 CODATA Value: conventional value of coulomb-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  16. "2022 CODATA Value: conventional value of watt-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  17. "2022 CODATA Value: conventional value of farad-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.
  18. "2022 CODATA Value: conventional value of henry-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 18 May 2024.