Siemens (unit)

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The siemens (symbol: S) is the SI unit of electric conductance.

Contents 1 Definition 2 SI multiples 3 Origin 4 Explanation 5 SI electricity units

Definition

1 S = 1 A/V = 1 A²/W = 1 kg⁻¹·m⁻²·s³·A²

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		10–24	yoctosiemens	yS

Origin

It is named after Werner von Siemens.

Explanation

Mho is a now eccentric name for this unit of electrical conductance, equal to 1 Ω⁻¹. It is derived by spelling ohm backwards. Its symbol is a greek letter omega turned upside down <math>\mho</math> ℧ (U+2127). The term siemens is used universally in science and primarily in electrical applications, while mho is used primarily in electronic applications. The upside down ohm symbol has the advantage of being less likely to be confused with a variable than the letter S when doing algebraic calculations by hand where fine typographical distinctions (such as italic for variables and roman for unit names) are hard to maintain.

Siemens are related to other units as follows

<math>\mathrm{S} = \mho = \frac\mathrm{A}\mathrm{V} = \frac1\Omega</math>

• S = siemens
• ℧ = mho
• A = amperes
• V = volts

The formula for computing conductance is as follows:

<math>G = \frac1R = \frac{I}V </math>

• G = Conductance (in siemens)
• R = Resistance (in ohms)
• I = Current (in amperes)
• V = Voltage (in volts)

Example: G = 1 / 6 Ω = 0.1667 S

SI electricity units

SI electromagnetic units edit
Quantity	Name	Symbol	Dimensions
Current	ampere (SI base unit)	A	A
Electric charge, Quantity of electricity	coulomb	C	A·s
Potential difference	volt	V	J/C = kg·m2·s−3·A−1
Resistance, Impedance, Reactance	ohm	Ω	V/A = kg·m2·s−3·A−2
Resistivity	ohm metre	Ω·m	kg·m3·s−3·A−2
Electrical power	watt	W	V·A = kg·m2·s−3
Capacitance	farad	F	C/V = kg−1·m−2·A2·s4
Elastance	reciprocal farad	F−1	kg·m2·A−2·s−4
Permittivity	farad per metre	F/m	kg−1·m−3·A2·s4
Conductance, Admittance, Susceptance	siemens	S	Ω−1 = kg−1·m−2·s3·A2
Conductivity	siemens per metre	S/m	kg−1·m−3·s3·A2
Magnetic flux	weber	Wb	V·s = kg·m2·s−2·A−1
Magnetic flux density	tesla	T	Wb/m2 = kg·s−2·A−1
Magnetic induction	ampere per metre	A/m	A·m−1
Reluctance	ampere-turns per weber	A/Wb	kg−1·m−2·s2·A2
Inductance	henry	H	Wb/A = V·s/A = kg·m2·s−2·A−2
Permeability	henry per metre	H/m	kg·m·s−2·A−2
Magnetic susceptibility	(dimensionless)	χ	-