Conductance and the siemens
The better a substance conducts, the less its resistance; the worse it conducts, the
higher its resistance. Electricians and electrical engineers sometimes prefer to speak 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 ohm. 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 in ohms, you can get the conductance in siemens by taking
the quotient of 1 over the resistance. Also, if you know the conductance in siemens,
you can get the resistance in ohms by taking 1 over the conductance. The relation can
be written as:
siemens = 1/ohms, or
ohms = 1/siemens
Smaller units of conductance are often necessary. A resistance of one kilohm is
equal to one millisiemens. If the resistance is a megohm, the conductance is one microsiemens.
You’ll also hear about kilosiemens or megasiemens, representing resistances
of 0.001 ohm and 0.000001 ohm (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 might sometimes have conductances in the
megasiemens range.
As an example, suppose a component has a resistance of 50 ohms. Then its conductance,
in siemens, is 1⁄50, or 0.02 S. You might say that this is 20 mS. Or imagine a
piece of wire with a conductance of 20 S. Its resistance is 1/20, or 0.05, ohm. Not often
will you hear the term “milliohm”; engineers do not, for some reason, speak of subohmic
units very much. But you could say that this wire has a resistance of 50 milliohms, and
you would be technically right.
Conductivity is a little trickier. If wire has a resistivity of, say, 10 ohms per kilometer,
you can’t just say that it has a conductivity of 1/10, or 0.1, siemens per kilometer. It is
true that a kilometer of such wire will have a conductance of 0.1 S; but 2 km of the wire
will have a resistance of 20 ohms (because there is twice as much wire), and this 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.
Wrong! Conductance decreases, rather than increasing, with wire length.
When dealing with wire conductivity for various lengths of wire, it’s best to convert
to resistivity values, and then convert back to the final conductance when you’re all
done calculating. Then there won’t be any problems with mathematical semantics.
Figure illustrates the resistance and conductance values for various lengths of
wire having a resistivity of 10 ohms per kilometer.
