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.