International System of Electrical and Magnetic Units
Encyclopedia
The International System of Electrical and Magnetic Units is an obsolete system of units used solely for measuring electrical and magnetic quantities. It was introduced by the Fourth International Electrical Congress (Chicago, 1893) and modified in 1908. It was rendered obsolete by the inclusion of electromagnetic units in the International System of Units
(SI) in 1948.
, mass
and time
was first demonstrated by Gauss
in 1832 with his measurement of the Earth's magnetic field, and the principle was extended to electrical measurements by Neumann
in 1845. A complete system of metric electrical and magnetic units was proposed by Weber
in 1851.Weber's original proposal was based on a millimetre–milligram–second system of units.
The development of the electric telegraph (an invention of Gauss and Weber) demonstrated the need for accurate electrical measurements. At the behest of Thomson
, the British Association for the Advancement of Science
(B.A.) set up a committee in 1862 to examine the options for standardizing electrical and magnetic units. After much discussion, the committee decided to adapt Weber's proposals to the CGS system of units: however the resulting "absolute" units were both difficult to realize
and (often) impractically small. To overcome these handicaps, the B.A. also proposed a set of "practical" or "reproduceable" units, which were not directly linked to the CGS system but which were, as near as experimental accuracy allowed, equal to multiples of the corresponding CGS units.It soon became apparent that the B.A. had developed two sets of CGS units. The practical units were based on the electromagnetic set of units rather than on the electrostatic set.
that could be repeated in different laboratories in different countries. The chosen method was based on the resistivity
of mercury
, by measuring the resistance of a column of mercury of specified dimensions (106 cm × 1 mm2): however, the chosen length of column was almost 3 millimetres too short, leading to a difference of 0.28% between the new practical units and the CGS units which were supposedly their basis.
The anomaly was resolved at another international conference, in Chicago in 1893, by a correction in the definition of the ohm. The units agreed at this conference were termed "international" units, to distinguish them from their predecessors.
The 1893 system had three base units: the international ampere
, the international ohm
and the international volt
.
The international units did not have the same formal legal status as the metre
and the kilogram
through the Metre Convention (1875), although several countries adopted the definition within their national laws (e.g., the United States, through Public Law 105 of July 12, 1894).
:
By Ohm's law, knowing any two of the physical quantities V, I or R (potential difference, current or resistance) will define the third, and yet the 1893 system defines the units for all three quantities. With improvements in measurement techniques, it was soon realized that
The solution came at an international conference in London in 1908. The essential point was to reduce the number of base units from three to two by redefining the international volt as a derived unit. There were several other modifications of less practical importance:
International Coulomb:the electric charge
transferred by a current of one international ampere in one second;The coulomb and the farad
had been used in earlier B.A. systems of electrical units with slightly different definitions, hence the need to add the qualifier "international".
International Farad
:the capacitance
of a capacitor
charged to a potential of one international volt by one international coulomb of electricity;
Joule
:107 units of work in the CGS system, represented sufficiently well for practical use by the energy expended in one second by an international ampere in an international ohm;
Watt
:107 units of power
in the CGS system, represented sufficiently well for practical use by the work done at the rate of one joule per second;
Henry:the inductance
in a circuit when an electromotive force induced in this circuit is one international volt, while the inducing current varies at the rate of one ampere per second.
and in quantity calculus
, it became apparent that a coherent absolute system of units could only include one electromagnetic base unit
. The first such system was proposed by Giorgi
in 1901: it used the ohm
as the additional base unit in the MKS system, and so is often referred to as the MKSΩ system or the Giorgi system.
An additional problem with the CGS system of electrical units, pointed out as early as 1882 by Heaviside
, was that they were not "rationalized", that is they failed to properly take account of permittivity
and permeability
as properties of a medium. Georgi was also a great proponent of rationalization of the electrical units.
The choice of electrical unit for the base unit in a rationalized system depends only on practical considerations, particularly the ability to realize
the unit accurately and reproducibly. The ampere
rapidly gained support over the ohm, as many national standards laboratories were already realizing the ampere in absolute terms using ampere balance
s. The International Electrotechnical Commission
(IEC) adopted the Giorgi system with the ampere replacing the ohm in 1935, and this choice of base units is often called the MKSA system.
The International Committee for Weights and Measures
(CIPM) approved a new set of definitions for electrical units, based on the rationalized MKSA system, in 1946, and these were internationally adopted under the Metre Convention by the 9th General Conference on Weights and Measures
in 1948. Under this system, which would become the International System of Units
(SI), the ohm is a derived unit.The ohm is the electric resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere, the conductor not being the seat of any electromotive force.
The SI definitions of the electrical units are formally equivalent to the 1908 international definitions, and so there should not have been any change in the size of the units. Nevertheless, the international ohm and the international volt were not usually realized in absolute terms but by reference to a standard resistance and a standard electromotive force respectively. The realizations recommended in 1908 are not exactly equivalent to the absolute definitions: recommended conversion factors are
although slightly different factors may apply for individual standards in national measurement laboratories.Conversion factors for the U.S. national standards (NIST) are 1 Ωint = and 1 Vint = . As the international ampere was usually realized by means of an ampere balance rather than electrolytically, 1 Aint = 1 A. The conversion factor for the "electrolytic" ampere (Aelec) can be calculated from modern values of the atomic weight
of silver
and the Faraday constant:
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...
(SI) in 1948.
Earlier systems
The link between electromagnetic units and the more familiar units of lengthLength
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...
, mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
and time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
was first demonstrated by Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
in 1832 with his measurement of the Earth's magnetic field, and the principle was extended to electrical measurements by Neumann
Franz Ernst Neumann
Franz Ernst Neumann was a German mineralogist, physicist and mathematician.-Biography:Neumann was born in Joachimsthal, Margraviate of Brandenburg, located not far from Berlin. In 1815 he interrupted his studies at Berlin to serve as a volunteer in the Hundred Days against Napoleon, and was...
in 1845. A complete system of metric electrical and magnetic units was proposed by Weber
Wilhelm Eduard Weber
Wilhelm Eduard Weber was a German physicist and, together with Carl Friedrich Gauss, inventor of the first electromagnetic telegraph.-Early years:...
in 1851.Weber's original proposal was based on a millimetre–milligram–second system of units.
The development of the electric telegraph (an invention of Gauss and Weber) demonstrated the need for accurate electrical measurements. At the behest of Thomson
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...
, the British Association for the Advancement of Science
British Association for the Advancement of Science
frame|right|"The BA" logoThe British Association for the Advancement of Science or the British Science Association, formerly known as the BA, is a learned society with the object of promoting science, directing general attention to scientific matters, and facilitating interaction between...
(B.A.) set up a committee in 1862 to examine the options for standardizing electrical and magnetic units. After much discussion, the committee decided to adapt Weber's proposals to the CGS system of units: however the resulting "absolute" units were both difficult to realize
Realization
realization and realisation may be:* Realization , a sport climbing route in Ceüse, France* Realization , the pricing of security at market value* Realization , an actually observed value of random variable...
and (often) impractically small. To overcome these handicaps, the B.A. also proposed a set of "practical" or "reproduceable" units, which were not directly linked to the CGS system but which were, as near as experimental accuracy allowed, equal to multiples of the corresponding CGS units.It soon became apparent that the B.A. had developed two sets of CGS units. The practical units were based on the electromagnetic set of units rather than on the electrostatic set.
1893 system
The B.A. system of practical units gained considerable international support, and was adopted – with one important modification – by the First International Conference of Electricians (Paris, 1881). The British Association had constructed an artefact representation of the ohm (a standard length of resistance wire which had a resistance of 109 CGS units of electric resistance, that is one ohm) whereas the international conference preferred a method of realizationRealization
realization and realisation may be:* Realization , a sport climbing route in Ceüse, France* Realization , the pricing of security at market value* Realization , an actually observed value of random variable...
that could be repeated in different laboratories in different countries. The chosen method was based on the resistivity
Resistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...
of mercury
Mercury (element)
Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum...
, by measuring the resistance of a column of mercury of specified dimensions (106 cm × 1 mm2): however, the chosen length of column was almost 3 millimetres too short, leading to a difference of 0.28% between the new practical units and the CGS units which were supposedly their basis.
The anomaly was resolved at another international conference, in Chicago in 1893, by a correction in the definition of the ohm. The units agreed at this conference were termed "international" units, to distinguish them from their predecessors.
The 1893 system had three base units: the international ampere
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...
, the international ohm
Ohm
The ohm is the SI unit of electrical resistance, named after German physicist Georg Simon Ohm.- Definition :The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere,...
and the international volt
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...
.
| Unit | 1893 ("international") definitionThe terminology of some of the definitions has been updated to modern usage. | CGS ("absolute") equivalent | Notes |
|---|---|---|---|
| Ampere Ampere The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics... |
the unvarying current Electric current Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire... which, when passed through a solution of silver nitrate Silver nitrate Silver nitrate is an inorganic compound with chemical formula . This compound is a versatile precursor to many other silver compounds, such as those used in photography. It is far less sensitive to light than the halides... in water, deposits silver Silver Silver is a metallic chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal... at the rate of per second |
the current produced in a conductor with a 1 ohm resistance when there is a potential difference of 1 volt between its ends | 0.1 cgs units of electric current |
| Ohm Ohm The ohm is the SI unit of electrical resistance, named after German physicist Georg Simon Ohm.- Definition :The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere,... |
the resistance offered to an unvarying electric current Electric current Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire... by a column of mercury Mercury (element) Mercury is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver or hydrargyrum... at the temperature of melting ice 14.4521 grams in mass, of a constant cross-sectional area and of the length of 106.3 centimetres |
109 cgs units of electric resistance | |
| Volt Volt The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the... |
of the electromotive force Electromotive force In physics, electromotive force, emf , or electromotance refers to voltage generated by a battery or by the magnetic force according to Faraday's Law, which states that a time varying magnetic field will induce an electric current.It is important to note that the electromotive "force" is not a... of a Clark cell Clark cell The Clark cell, invented by English engineer Josiah Latimer Clark in 1873, is a wet-chemical cell that produces a highly stable voltage usable as a laboratory standard.-Chemistry:... at a temperature of 15 °C |
the electromotive force produced in an electric circuit which cuts 108 magnetic lines of force per second | 108 cgs units of electromotive force |
The international units did not have the same formal legal status as the metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
and the kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...
through the Metre Convention (1875), although several countries adopted the definition within their national laws (e.g., the United States, through Public Law 105 of July 12, 1894).
Overdefinition and the 1908 modification
The 1893 system of units was overdefined, as can be seen from an examination of Ohm's lawOhm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...
:
- V = IElectric currentElectric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
R
By Ohm's law, knowing any two of the physical quantities V, I or R (potential difference, current or resistance) will define the third, and yet the 1893 system defines the units for all three quantities. With improvements in measurement techniques, it was soon realized that
- 1 Vint ≠ 1 Aint × 1 Ωint.
The solution came at an international conference in London in 1908. The essential point was to reduce the number of base units from three to two by redefining the international volt as a derived unit. There were several other modifications of less practical importance:
- the international ampere and the international ohm were formally defined in terms of the corresponding CGS electromagnetic units, with the 1893 definitions retained as preferred realizationRealizationrealization and realisation may be:* Realization , a sport climbing route in Ceüse, France* Realization , the pricing of security at market value* Realization , an actually observed value of random variable...
s; - the preferred realization of the international volt was in terms of the electromotive force of a Weston cellWeston cellThe Weston cell, invented by Edward Weston in 1893, is a wet-chemical cell that produces a highly stable voltage suitable as a laboratory standard for calibration of voltmeters...
at 20 °C (1.0184 Vint), as this type of cell has a lower temperature coefficient than the Clark cell; - several other derived units for use in electrical and magnetic measurements were formally defined:
International Coulomb:the electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
transferred by a current of one international ampere in one second;The coulomb and the farad
Farad
The farad is the SI unit of capacitance. The unit is named after the English physicist Michael Faraday.- Definition :A farad is the charge in coulombs which a capacitor will accept for the potential across it to change 1 volt. A coulomb is 1 ampere second...
had been used in earlier B.A. systems of electrical units with slightly different definitions, hence the need to add the qualifier "international".
International Farad
Farad
The farad is the SI unit of capacitance. The unit is named after the English physicist Michael Faraday.- Definition :A farad is the charge in coulombs which a capacitor will accept for the potential across it to change 1 volt. A coulomb is 1 ampere second...
:the capacitance
Capacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
of a capacitor
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...
charged to a potential of one international volt by one international coulomb of electricity;
Joule
Joule
The joule ; symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended in applying a force of one newton through a distance of one metre , or in passing an electric current of one ampere through a resistance of one ohm for one second...
:107 units of work in the CGS system, represented sufficiently well for practical use by the energy expended in one second by an international ampere in an international ohm;
Watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
:107 units of power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
in the CGS system, represented sufficiently well for practical use by the work done at the rate of one joule per second;
Henry:the inductance
Inductance
In electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...
in a circuit when an electromotive force induced in this circuit is one international volt, while the inducing current varies at the rate of one ampere per second.
SI units
With advances in the theory of electromagnetismElectromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
and in quantity calculus
Quantity calculus
Quantity calculus is the formal method for describing the mathematical relations between abstract physical quantities. Despite the name, it is more analogous to a system of algebra than calculus in the mathematical sense of the term. Measurements are expressed as products of a numeric value with a...
, it became apparent that a coherent absolute system of units could only include one electromagnetic base unit
Fundamental unit
A set of fundamental units is a set of units for physical quantities from which every other unit can be generated.In the language of measurement, quantities are quantifiable aspects of the world, such as time, distance, velocity, mass, momentum, energy, and weight, and units are used to describe...
. The first such system was proposed by Giorgi
Giovanni Giorgi
Giovanni Giorgi was an Italian electrical engineer who invented the Giorgi system of measurement, the precursor to the International System ....
in 1901: it used the ohm
Ohm
The ohm is the SI unit of electrical resistance, named after German physicist Georg Simon Ohm.- Definition :The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere,...
as the additional base unit in the MKS system, and so is often referred to as the MKSΩ system or the Giorgi system.
An additional problem with the CGS system of electrical units, pointed out as early as 1882 by Heaviside
Oliver Heaviside
Oliver Heaviside was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations , reformulated Maxwell's field equations in terms of electric and...
, was that they were not "rationalized", that is they failed to properly take account of permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
and permeability
Permeability (electromagnetism)
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...
as properties of a medium. Georgi was also a great proponent of rationalization of the electrical units.
The choice of electrical unit for the base unit in a rationalized system depends only on practical considerations, particularly the ability to realize
Realization
realization and realisation may be:* Realization , a sport climbing route in Ceüse, France* Realization , the pricing of security at market value* Realization , an actually observed value of random variable...
the unit accurately and reproducibly. The ampere
Ampere
The ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...
rapidly gained support over the ohm, as many national standards laboratories were already realizing the ampere in absolute terms using ampere balance
Ampere balance
The ampere balance is an electromechanical apparatus used for the precise measurement of the SI unit of electric current, the ampere. It was invented by William Thomson, 1st Baron Kelvin....
s. The International Electrotechnical Commission
International Electrotechnical Commission
The International Electrotechnical Commission is a non-profit, non-governmental international standards organization that prepares and publishes International Standards for all electrical, electronic and related technologies – collectively known as "electrotechnology"...
(IEC) adopted the Giorgi system with the ampere replacing the ohm in 1935, and this choice of base units is often called the MKSA system.
The International Committee for Weights and Measures
International Committee for Weights and Measures
The Interglobal Committee for Weights and Measures is the English name of the Comité international des poids et mesures . It consists of eighteen persons from Member States of the Metre Convention...
(CIPM) approved a new set of definitions for electrical units, based on the rationalized MKSA system, in 1946, and these were internationally adopted under the Metre Convention by the 9th General Conference on Weights and Measures
General Conference on Weights and Measures
The General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures . It is one of the three organizations established to maintain the International System of Units under the terms of the Convention du Mètre of 1875...
in 1948. Under this system, which would become the International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...
(SI), the ohm is a derived unit.The ohm is the electric resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere, the conductor not being the seat of any electromotive force.
The SI definitions of the electrical units are formally equivalent to the 1908 international definitions, and so there should not have been any change in the size of the units. Nevertheless, the international ohm and the international volt were not usually realized in absolute terms but by reference to a standard resistance and a standard electromotive force respectively. The realizations recommended in 1908 are not exactly equivalent to the absolute definitions: recommended conversion factors are
- 1 Ωint ≈ 1.000 49 Ω
- 1 Vint ≈ 1.000 34 V
although slightly different factors may apply for individual standards in national measurement laboratories.Conversion factors for the U.S. national standards (NIST) are 1 Ωint = and 1 Vint = . As the international ampere was usually realized by means of an ampere balance rather than electrolytically, 1 Aint = 1 A. The conversion factor for the "electrolytic" ampere (Aelec) can be calculated from modern values of the atomic weight
Atomic weight
Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12...
of silver
Silver
Silver is a metallic chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal...
and the Faraday constant:
- 1 Aelec = 1.000 022(2) A