### Conductance and the Siemens

Electricians and electrical engineers sometimes talk about the conductance of a material, rather than about its resistance. The standard unit of conductance is the siemens, abbreviated S. When a component has a conductance of 1 S, its resistance is 1 Ω. If the resistance is doubled, the conductance is cut in half, and vice versa. Therefore, conductance is the reciprocal of resistance.

If you know the resistance of a component or circuit in ohms, you can get the conductance in siemens: divide 1 by the resistance. If you know the conductance in siemens, you can get the resistance: divide 1 by the conductance. Resistance, as a variable quantity, is denoted by an italicized, uppercase letter R. Conductance, as a variable quantity, is denoted as an italicized, uppercase letter G. If we express R in ohms and G in siemens, then the following two equations describe their relationship:

G = 1/R
R = 1/G

Units of conductance much smaller than the siemens are often used. A resistance of 1 kΩ is equal to 1 millisiemens (1 mS). If the resistance is 1 MΩ, the conductance is one microsiemens (1 μS). You’ll sometimes hear about kilosiemens (kS) or megasiemens (MS), representing resistances of 0.001
Ω and 0.000001 Ω (a thousandth of an ohm and a millionth of an ohm, respectively). Short lengths of heavy wire have conductance values in the range of kilosiemens. Heavy metal rods can have conductances in the megasiemens range.

Suppose a component has a resistance of 50 Ω. Then its conductance, in siemens, is 1/50 S, which is equal to 0.02 S. We can call this 20 mS. Or imagine a piece of wire with a conductance of 20 S. Its resistance is 1/20 Ω, which is equal to 0.05 Ω. You will not often hear the term milliohm.
But you could say that this wire has a resistance of 50 mΩ, and you would be technically right.

Determining conductivity is tricky. If wire has a resistivity of 10 Ω/km, you can’t say that it has a conductivity of 1/10, or 0.1, S/km. It is true that a kilometer of such wire has a conductance of 0.1 S, but 2 km of the wire has a resistance of 20 Ω (because there is twice as much wire). That is not twice the conductance, but half. If you say that the conductivity of the wire is 0.1 S/km, then you might be tempted to say that 2 km of the wire has 0.2 S of conductance. That would be a mistake! Conductance decreases with increasing wire length.

Following figure illustrates the resistance and conductance values for various lengths of wire having a resistivity of 10 Ω/km. Resistance and conductance for various lengths of wire having a resistivity of 10 ohms per kilometer.