Siemens (unit)

The siemens (symbol: S) is the SI derived unit of electric conductance and electric admittance. Conductance and admittance are the reciprocals of resistance and impedance respectively, hence one siemens is equal to the reciprocal of one ohm, and is sometimes referred to as the mho. In English, the term siemens is used both for the singular and plural.^[1] 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 every SI unit whose name is derived from the proper name of a person, the first letter of its symbol is upper case (S). When an SI unit is spelled out in English, it should always begin with a lower case letter (siemens), except where any word would be capitalized, such as at the beginning of a sentence or in capitalized material such as a title. Note that "degree Celsius" conforms to this rule because the "d" is lowercase. —Based on The International System of Units, section 5.2.

Definition

For a conducting or semiconducting element with electrical resistance R, the conductance G is 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.

Example: The conductance of a resistor with resistance six ohms is G = 1/(6 Ω) ≈ 0.167 S ≈ 167 mS.

Historical/Deprecated

Since 1860 to the middle of 20th century, siemens or siemens mercury unit, was the unit of electrical resistance. It was defined as the resistance of a mercury column 1 meter long and uniform 1 mm² cross sectional area at 0 degrees Celsius. It was equivalent to 0.953 ohm approximately. Officially, it ceased usage after 1881, but was widely used in telegraph and telephone services until World War II.

Mho

Mho is an alternate, non-SI unit of conductivity which is equivalent to 1 siemens. Mho is derived from spelling ohm backwards and is written with an upside-down capital Greek letter Omega: , Unicode symbol U+2127 (℧). According to Maver^[2] the term mho was suggested by Sir William Thomson. The mho was officially renamed to the siemens, replacing the old meaning of the unit siemens, at a conference in 1881.^[3]

The term siemens, as it is an SI unit, is used universally in science and often in electrical applications, while mho is still used primarily in electronic applications. Two reasons are usually given for using mho instead of siemens in electronic applications:

• The inverted Omega and the mho, while not an official SI abbreviation, 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. Likewise, it is difficult to distinguish the symbol S from the lower case s where second is meant, potentially causing confusion.
• The term siemens could be confused with the large multinational electronics company Siemens.

References

1. ^ NIST Guide to SI Units - 9 Rules and Style Conventions for Spelling Unit Names, National Institute of Standards and Technology
2. ^ Maver, William: American Telegraphy and Encyclopedia of the Telegraph: Systems, Apparatus, Operation. 1903.
3. ^ http://www.tech-faq.com/siemens.html

• Brochure "The International System of Units" issued by the BIPM
• Different units named after Siemens