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.
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