An approximate expression for constriction resistance of electrical contacts having multiple contact areas

Many experiments using the electrolytic bath have been performed to simulate the constriction resistance of electrical contacts. These correspond to cases where the contact area consists of multiple true contact areas dispersed on the apparent contact area. An approximate expression must be calculated to satisfy the characteristics of constriction resistance from the experiments and minimize the error. Therefore, the current study investigates is the expression as a function of normalized n-th order moment of the sectional areas, for example, 2nd order moment of figure of inertia. The influence of the figure on the contact area in relation to constriction resistance is discussed based on the "form factor" introduced by R. Helm. Errors caused by the approximation are examined for the known form factors of figures for an ellipse, a triangle, a square and two separated circles.