Electrical contacts to materials having distributed resistance

The phenomenon of the electrical contact between a sheet of material having distributed electrical resistance and an electrode having infinite conductivity, is examined from the circuit point of view. A theory is developed which demonstrates quantitatively that current passing between the electrode and the sheet tends to crowd to that edge of the electrode which faces the direction of current flow. This gives rise to the concept of a leading edge, and to a method of calculating the contact resistance of a given electrode. It is shown that the contact resistance can never drop below a certain minimum value, however wide the electrode is made, and this leads to the idea of electrode efficiency. Two definitions of efficiency are suggested, one based on comparison with the ideal electrode (that having uniform distribution of current density) and the other simply on contact resistance. For the special case of conducting rubber sheet which has a pressure-sensitive contact conductivity, it is shown that, with a constant clamping force, the contact resistance decreases with electrode width.