# Siemens (unit)

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Siemens
Unit system SI derived unit
Unit of Electric conductance
SymbolS (= Ω−1)
Named after Ernst Werner von Siemens
In SI base units: kg −1 m −2 s 3 A 2

The siemens (symbol: S) is the derived unit of electric conductance, electric susceptance, and electric admittance in the International System of Units (SI). Conductance, susceptance, and admittance are the reciprocals of resistance, reactance, and impedance respectively; hence one siemens is redundantly equal to the reciprocal of one ohm, and is also referred to as the mho . The 14th General Conference on Weights and Measures approved the addition of the siemens as a derived unit in 1971.

SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.

In electrical engineering, susceptance (B) is the imaginary part of admittance, where the real part is conductance. The inverse of admittance is impedance, where the imaginary part is reactance and the real part is resistance. In SI units, susceptance is measured in siemens. Oliver Heaviside first defined this property in June 1887.

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. The SI unit of admittance is the siemens ; the older, synonymous unit is mho, and its symbol is ℧. Oliver Heaviside coined the term admittance in December 1887.

## Contents

The unit is named after Ernst Werner von Siemens. In English, the same form siemens is used both for the singular and plural. [1]

Ernst Werner Siemens was a German inventor and industrialist. Siemens's name has been adopted as the SI unit of electrical conductance, the siemens. He was also the founder of the electrical and telecommunications company Siemens.

## Definition

For a conducting element, electrical resistance R and electrical conductance G are defined as

The electrical resistance of an object is a measure of its opposition to the flow of electric current. The inverse quantity is electrical conductance, and is the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with the notion of mechanical friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S).

${\displaystyle G={\frac {1}{R}}={\frac {I}{V}}}$

where I is the electric current through the object and V is the voltage (electrical potential difference) across the object.

Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points. The difference in electric potential between two points in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named volt. In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule per 1 coulomb. The official SI definition for volt uses power and current, where 1 volt = 1 watt per 1 ampere. This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by V, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.

The unit siemens for the conductance G is defined by

${\displaystyle \mathrm {S} =\Omega ^{-1}={\dfrac {\mathrm {A} }{\mathrm {V} }}}$

where Ω is the ohm, A is the ampere, and V is the volt.

The ohm is the SI derived unit of electrical resistance, named after German physicist Georg Simon Ohm. Although several empirically derived standard units for expressing electrical resistance were developed in connection with early telegraphy practice, the British Association for the Advancement of Science proposed a unit derived from existing units of mass, length and time and of a convenient size for practical work as early as 1861. The definition of the ohm was revised several times. Today, the definition of the ohm is expressed from the quantum Hall effect.

The ampere, often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.

For a device with a conductance of one siemens, the electric current through the device will increase by one ampere for every increase of one volt of electric potential difference across the device.

The conductance of a resistor with a resistance of five ohms, for example, is (5 Ω)−1, which is equal to 200 mS.

## Mho

A name that is used as an alternative to the siemens is the mho, the reciprocal of one ohm. It is derived from spelling ohm backwards and is written as an upside-down capital Greek letter omega: ${\displaystyle \mho }$, Unicode symbol U+2127 (℧). According to Maver [2] the term mho was suggested by Sir William Thomson (Lord Kelvin). The ohm officially replaced the old "siemens unit", which was a unit of resistance, at an international conference in 1881. [3]

The Greek alphabet has been used to write the Greek language since the late ninth or early eighth century BC. It is derived from the earlier Phoenician alphabet, and was the first alphabetic script to have distinct letters for vowels as well as consonants. In Archaic and early Classical times, the Greek alphabet existed in many different local variants, but, by the end of the fourth century BC, the Eucleidean alphabet, with twenty-four letters, ordered from alpha to omega, had become standard and it is this version that is still used to write Greek today. These twenty-four letters are: Α α, Β β, Γ γ, Δ δ, Ε ε, Ζ ζ, Η η, Θ θ, Ι ι, Κ κ, Λ λ, Μ μ, Ν ν, Ξ ξ, Ο ο, Π π, Ρ ρ, Σ σ/ς, Τ τ, Υ υ, Φ φ, Χ χ, Ψ ψ, and Ω ω.

The Siemens mercury unit is an obsolete unit of electrical resistance. It was defined by Werner von Siemens in 1860 as the resistance of a mercury column with a length of one metre and uniform cross-section of 1 mm2 held at a temperature of zero degrees Celsius. It is equivalent to approximately 0.953 ohm.

NIST's Guide for the Use of the International System of Units (SI) refers to the mho as an "unaccepted special name for an SI unit", and indicates that it should be strictly avoided. [4]

The SI term siemens is used universally in science and often in electrical applications, while mho is still used in some electronic contexts. The inverted capital omega symbol, while not an official SI abbreviation, is less likely to be confused with a variable than the letter S when doing algebraic calculations by hand, where the usual typographical distinctions (such as italic for variables and Roman for unit names) are difficult to maintain. Likewise, it is difficult to distinguish the symbol S from the lower-case s where second is meant, potentially causing confusion. [5] So, for example, a pentode’s transconductance of 2.2 mS might alternatively be written as 2.2 ${\displaystyle m\mho }$ or 2200 ${\displaystyle \mu \mho }$ (most common in the 1930s) or 2.2 mA/V. A handwritten "S" can also be misread as the frequency space variable "s", commonly used in transfer functions.

## Notes and references

1. NIST Guide to the SI, Chapter 9: Rules and Style Conventions for Spelling Unit Names, National Institute of Standards and Technology, 2008, retrieved 2017-12-22
2. Maver, William: American Telegraphy and Encyclopedia of the Telegraph: Systems, Apparatus, Operation. 1903.
3. "Siemens (Unit of Electrical Conductance)". www.tech-faq.com.
4. NIST Guide to the SI, Chapter 5: Units Outside the SI, National Institute of Standards and Technology, 2008, retrieved 2017-12-22
5. Eugene R. Weiner, Applications of Environmental Aquatic Chemistry: A Practical Guide, p. 109, CRC Press, 2013 ISBN   1439853320