Resistance Inequalities

Abstract

IT is well known that the electrical resistance tensor r is symmetric in the absence of a magnetic field. It is the purpose of this communication to point out that this implies that certain inequalities exist between the diagonal and off-diagonal elements of r. To obtain these we note that since r is symmetric it can always be diagonalized by a rotation of co-ordinate axes, and the resulting diagonal tensor will have all its diagonal elements positive, since these will be the resistances along the ‘new’ axes. Hence r, considered as a matrix, is positive-definite and this implies that inequalities between its elements must exist of the form: