Constriction resistance and the real area of contact

The relation between the area of contact and the constriction resistance which holds for a single circular contact spot is widely used in electric contact theory, although the normal mode of contact is by a large number of microcontacts. A method of finding the resistance of a cluster of microcontacts is derived, and it is shown that the resistance may be regarded as the sum of the parallel resistance of the microcontacts and an interaction term often related to the extent of the cluster and not to the number or size of the individual contacts. The resistance is often close to that found by assuming that the entire area covered by the cluster is a single conducting spot. The known agreement between areas of contact found from resistance measurements and by other methods is therefore puzzling - until it is realized that the other methods also give only an apparent area: the real area of contact in, for example, a Brinell indentation is a small fraction of the area of the indentation. Thus from the point of view of electric contact theory the system is self-consistent, although the real area of contact is now seen to play no part in it: the implications for the theory of friction are more profound.