The Determination of Pressure Coefficients 

 of Capacitance for Certain Geometries 



By D. W. McCALL 



(Manuscript received Februarj^ 15, 1955) 



Expressions are derived for the pressure coefficients of capacitance of 



parallel plate capacitors subjected to one-dimensional and hydrostatic 



pressures and of cylindrical capacitors subjected to radial compression. The 



derivations apply to systems in which the dielectrics are isotropic, elastic 



solids. 



I. INTRODUCTION 



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) '/(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 con- 

 fronted 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 deter- 

 mined by the attenuation of the cable. The attenuation, a, of a coaxial 

 telephone cable may be written 



a = {G/2)(L/Cf + (R/2)(C/Lf 



where G is the conductance of the dielectric per unit length, C the 



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