The paper presents the analytical computation of the electric constriction resistance for a two coaxial cylindrical-shaped pole used as main current path in a large variety of power switchgears and electrical apparatus. The analyse relies on the accurate solution of the homogeneous second-order PDE (Partial Differential Equation) that describes the steady-state regime of the electric field strength inside the domain limited by the upper cylinder’s boundary (Laplace’s equation). Finally, the total electromagnetic power is obtained by means of Poynting’s vector flux, thereby allowing the constriction resistance formula to be also derived.

Keywords: Constriction resistance, Separation of variables method, Fourier- Bessel series decomposition.