Analytical calculation of the constriction resistance for a switchgear pole of particular shape

The paper provides a better evaluation of the electrical resistance in the case of a particular pole shape, common in many different power switchgears (circuit breakers, contactors, and isolators etc.), used for both low and high voltage installations use. Currently, the dimensioning, design and optimization of these devices relies mostly on empirical procedures and determinations. Our proposed analytical approach provides a more accurate relationship for the constriction resistance, method based on the solution of Laplace´s equation verified by the electric field inside the pole´s conductive domain, in the steady-state regime formulation. Separations of variables method was used, leading to an accurate expression for pole´s electric resistance which takes into consideration the electric current constriction phenomenon. This precise relationship becomes particularly useful in various important design and dimensioning computations, e. g., the prospective value of short-circuit current, at a the specific level of the electric net, where these electrical apparatus are placed.