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Resistance and Dimensions of a Wire

We have seen that if two conductors be joined in series the resistance of the combination is the sum of the resistances of the parts. Let the conductor be a long wire of uniform material and cross-section. Then it follows from the above (p. 422) that the resistance is proportional to the length; for if we take two pieces of the same length they will have the same resistance, and if connected end to end the resistance of the double length is double that of the single. Thus the resistance is proportional to the length.

Again, we may show that the resistance is inversely proportional to the area of the cross-section. For suppose two points, A and B, are connected by a single wire, the resistance of which is R. Introduce a second connecting wire of the same length and thickness, and therefore of the same resistance as the former. The resistance will now be R/2, and since it was found by Ohm that the resistance depends on the area of the cross-section and not on its form, we may without altering the result suppose the two wires, which have been laid side by side, welded into one, having a cross-section double of that of either wire.

Thus, by doubling the cross-section the resistance is halved. The resistance, therefore, varies inversely as the area of the cross-section.

Last Update: 2011-03-15