Siemens (unit)

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 (Ω−1) 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.[1]

For the deprecated "mercury unit", see Siemens mercury unit.
Siemens
Unit systemSI derived unit
Unit ofElectric conductance
SymbolS (Ω−1, ℧) 
Named afterErnst Werner von Siemens
In SI base units:kg−1⋅m−2⋅s3⋅A2

The unit is named after Ernst Werner von Siemens. In English, the same word siemens is used both for the singular and plural.[2]

Definition

For an element conducting direct current, electrical resistance R and electrical conductance G are defined as

where I is the electric 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

where Ω is the Ohm, A is the Ampere, and V is the Volt.

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 (/moʊ/), the reciprocal of one Ohm. It is derived from spelling Ohm backwards and is written as an upside-down capital Greek letter omega: ℧, Unicode character U+2127. According to Maver (1903)[3] 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.[4]

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.[5]

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 writing on a blackboard or doing algebraic calculations by hand. The usual typographical distinctions (such as italic for variables and roman for units) are difficult to maintain. Likewise, it is difficult to distinguish the symbol 'S' (siemens) from the lower-case 's' (seconds), potentially causing confusion.[6] So, for example, a pentode’s transconductance of 2.2 mS might alternatively be written as 2.2 m℧ or 2200 μ℧ (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. Minutes (PDF). 14th General Conference on Weights and Measures. 1971. p. 78.
  2. "Chapter 9: Rules and Style Conventions for Spelling Unit Names". NIST Guide to the SI (Report). National Institute of Standards and Technology. 2008. Retrieved 2017-12-22.
  3. Maver, William (1903). American Telegraphy and Encyclopedia of the Telegraph: Systems, apparatus, operation.
  4. "Siemens (unit of electrical conductance)". www.tech-faq.com.
  5. "Chapter 5: Units Outside the SI". NIST Guide to the SI (Report). National Institute of Standards and Technology. 2008. Retrieved 2017-12-22.
  6. Weiner, Eugene R. (2013). Applications of Environmental Aquatic Chemistry: A practical guide. CRC Press. p. 109. ISBN 1439853320.
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