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# siemens (mho)

Contributor(s): Gary Marcantoni

(Siemens AG is a German company engaged in electrical engineering and electronics.)

The siemens (symbolized S) is the Standard International (SI) unit of electrical conductance. The archaic term for this unit is the mho (ohm spelled backwards). Siemens are also used, when multiplied by imaginary numbers, to denote susceptance in alternating current (AC) and radio frequency (RF) applications. Reduced to base SI units, 1 S is the equivalent of one second cubed ampere squared per kilogram per meter squared (1 s3 · A2 · kg-1 · m-2). The siemens is also the equivalent of an ampere per volt (A/V).

In a direct current (DC) circuit, a component has a conductance of 1 S when a potential difference of one volt (1 V) produces a current of one ampere (1 A) through the component. Thus, one siemens is the equivalent of one ohm. But mathematically, resistance and conductance are reciprocals of each other. If R is the resistance of a component in ohms and G is the conductance in siemens,

R = 1 / G

and

G = 1 / R

In AC and RF circuits, conductive siemens behave the same as they do in DC circuits, provided the root-mean-square (rms) AC voltage is specified. In AC and RF circuits, susceptance exists only when there is a net capacitance or inductance. Capacitive susceptances have positive imaginary number values; inductive susceptances have negative imaginary-number values. The susceptance of a particular capacitor or inductor depends on the frequency.

Conductances and susceptances are sometimes expressed in units representing power-of-10 multiples or fractions of 1 S. A kilosiemens (1 kS) is equal to one thousand (103) siemens. A megasiemens (1 MS) is equal to one million (106) siemens. A millisiemens (1 mS) is equal to one-thousandth (10-3) of a siemens. A microsiemens (1 uS) is equal to one-millionth (10-6) of a siemens.

Also see conductance, Ohm's Law, prefix multipliers, resistance, reactance, ohm, and Standard International (SI) system of units.

This was last updated in February 2008

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