Conductance and the siemens:
The better a molecule conducts, the less its resistance; the worst it conducts, the higher its resistance. Electrical engineers and Electricians sometimes refer to speak about the conductance of a substance, rather than about its resistance. The standard unit of conductance is the siemens, shows S. When a element has a conduc- tance of 1 S, its resistance is 1 ohm. If the resistance is increased, the conductance is cut in half, and vice-versa. Therefore, conductance is the reciprocal of resistance.
If you study the resistance in ohms, you may get the conductance in siemens by taking the quotient of 1 over the resistance. Also, if you know the conductance in siemens, you may get the resistance in ohms by taking 1 over the conductance. The relation may be written as:
siemens = 1/ohms, or
ohms = 1/siemens
Smaller units of conductance are necessary. A resistance of 1 kilohm is equal to 1 millisiemens. If resistance is megohm, conductance is 1 mi- crosiemens. You will hear about kilosiemens or megasiemens, representing resistances of 0.001 ohm and 0.000001 ohm respectively. Short lengths of heavy wire have conductance values in the range of kilosiemens. Heavy metal rods can have conductances in megasiemens range.
As an instance, suppose a component has a resistance of 50 ohms. Then its conductance, in siemens, is around 1⁄50, or 0.02 S. You can say that this is 20 mS. Or suppose a piece of wire having the conductance of 20 S. The resistance of it is 1/20, or 0.05, ohm. You will not hear the term "milliohm"; engineers do not, for some reason, speak of subohmic units. But you could say that this wire has a resistance of 50 milliohms, and you would be right technically.
Conductivity is trickier in nature. If wire has a resistivity of, say, 10 ohms per kilometer, you cannot just say that it has a conductivity of 1/10, or 0.1, siemens per kilometer. It is true that a kilometer of such type of wire will have a conductance of 0.1 S; but 2 km of wire will have a resistance of 20 ohms, and this is not twice the conductance, but half. If you say that the conductivity of wire is 0.1 S/km, then you might be invited to say that 2 km of the wire has 0.2 S of conductance. Wrong! Conductance reduces, rather than increasing, with wire length.
While dealing with the wire conductivity for various lengths of wire, it is best to convert to resistivity values, and then convert back to final conductance when you are all done calculating. Then there will not be any problems with mathematical semantics.