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# Siemens (unit)

The siemens (symbol: S) is the SI derived unit of electric conductance. It is named after the German inventor and industrialist Ernst Werner von Siemens, and is equivalent to the previously used designation of this unit, the mho. In English, the term siemens is used both for the singular and plural. The 14th General Conference on Weights and Measures approved the addition of the siemens as an SI derived unit in 1971.

 This SI unit is named after Ernst Werner von Siemens. As with all SI units whose names are derived from the proper name of a person, the first letter of its symbol is uppercase (S). But when an SI unit is spelled out, it should always be written in lowercase (siemens), unless it begins a sentence or is the name "degree Celsius". — Based on The International System of Units, section 5.2.

## Definition

SI multiples for siemens (S)
Submultiples Multiples
Value Symbol Name Value Symbol Name
10–1 S dS decisiemens 101 S daS decasiemens
10–2 S cS centisiemens 102 S hS hectosiemens
10–3 S mS millisiemens 103 S kS kilosiemens
10–6 S µS microsiemens 106 S MS megasiemens
10–9 S nS nanosiemens 109 S GS gigasiemens
10–12 S pS picosiemens 1012 S TS terasiemens
10–15 S fS femtosiemens 1015 S PS petasiemens
10–18 S aS attosiemens 1018 S ES exasiemens
10–21 S zS zeptosiemens 1021 S ZS zettasiemens
10–24 S yS yoctosiemens 1024 S YS yottasiemens
Common multiples are in bold face.

For a physical object, typically an electronic device, with electrical resistance R, the conductance G is defined as $G = \frac{1}R = \frac{I}V,$

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

The unit siemens for the conductance G is defined by $\mbox{S} = \Omega^{-1} = \dfrac{\mbox{A}}{\mbox{V}} = \dfrac{\mbox{C}^2 \cdot \mbox{s}}{\mbox{kg} \cdot \mbox{m}^2} = \dfrac{\mbox{A}^{2} \cdot \mbox{s}^3}{\mbox{kg} \cdot \mbox{m}^2}$

Note that the last term is in SI base units where A is the symbol for ampere, the unit of electric current; kg is the symbol for kilogram, the unit of mass; m is the symbol for metre, the unit of length; and s is the symbol for the time unit second. C is the symbol for the SI derived unit of electric charge, the coulomb; V is the symbol for the SI derived unit of voltage, the volt; and Ω is the symbol for the SI derived unit of electrical resistance, the ohm.

So for a device with conductance one siemens, then the electric current through it with one volt across it is one ampere, and for each extra volt across it the electric current through it increases by one ampere.

Example: The conductance of a resistor with resistance six ohms is G = 1/(6 Ω) $\approx$ 0.167 S.

## Mho

The siemens is equivalent to the previously used term mho unit, which was derived from spelling ohm backwards and written with an upside-down capital Greek letter Omega: $\mho$, Unicode symbol is U+2127 (℧). The term siemens, as it is an SI unit, is used universally in science and primarily in electrical applications, while mho is still used primarily in electronic applications. The upside down ohm symbol, while not an official SI unit, has the advantage of being 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. Furthermore, in some industries (like electronics) it is common to write the symbol for second incorrectly as S instead of s, causing potential confusion.

## References

• Brochure "The International System of Units" issued by the BIPM