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 [1], and is equivalent to the now-obsolete mho. In English, it is siemens in both singular and plural.

Definition

For a device with electrical resistance R, the conductance G is defined as

$G = \frac1R = \frac{I}V,$

where

• G is the conductance,
• R is the resistance,
• I is the current through the device and
• V is the voltage "drop" (electrical potential difference) across the device.

The unit siemens for the conductance G is defined by 1 S = 1 A/V = 1 A²/W = 1 kg⁻¹•m⁻²•s³•A² =1 Ω⁻¹.

Example: The conductance of a resistor with resistance 6 ohms is G = 1/(6 Ω) = 0.16... S.

SI multiples

Multiple	Name	Symbol	Multiple	Name	Symbol
100	siemens	S
10¹	decasiemens	daS	10−1	decisiemens	dS
10²	hectosiemens	hS	10−2	centisiemens	cS
103	kilosiemens	kS	10−3	millisiemens	mS
106	megasiemens	MS	10−6	microsiemens	µS
109	gigasiemens	GS	10−9	nanosiemens	nS
1012	terasiemens	TS	10 −12	picosiemens	pS
1015	petasiemens	PS	10−15	femtosiemens	fS
1018	exasiemens	ES	10−18	attosiemens	aS
1021	zettasiemens	ZS	10−21	zeptosiemens	zS
1024	yottasiemens	YS	1024	yoctosiemens	yS

Mho

The siemens is equivalent to the now obsolete mho unit, which was derived from spelling ohm backwards and written with an upside-down capital Greek alphabet [2] letter Omega: $\mho$, Unicode symbol U+2127 (℧). The term siemens, as it is an SI unit, is used universally in science, 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 incorrectly write the symbol for second [3] as S instead of s, causing potential confusion.