The Determination of Pressure Coefficients of Capacitance for Certain Geometries

The electrical capacitance between two conductors separated by a dielectric is a quantity which can be calculated with ease only in certain geometrical arrangements of high symmetry. Even the classic example of parallel plates presents major difficulties as one may only perform the calculation exactly for the case of plates of infinite area or vanishing separation. The approximation becomes poor when (area)V(separation) becomes small and the theoretical treatment of edge effects is sufficiently difficult that it has not been solved though the solution would greatly facilitate dielectric constant measurement. When pressure enters into the situation as a variable the difficulties are enhanced as one must be able to describe the geometry effects as well as the change in dielectric constant. The engineers responsible for designing submarine cables are confronted with the necessity of knowing the manner in which capacitance depends upon pressure as may be illustrated in the following way. A submarine telephone cable is composed of a central copper conductor surrounded by a sheath of dielectric material. Due to the extreme length repeaters must be placed at intervals, the separation being determined by the attenuation of the cable. The attenuation, a, of a coaxial telephone cable may be written « = (G/2)(L/Cf + {R/2){C/Lf where G is the conductance of the dielectric per unit length, C the 485