Beyond the model of conductor with fixed cross-section and length: Exactly and numerically solvable problems

In this paper we present an overview of methods of resistance finding for the conductor with variable cross-section or (and) length. First, we consider the cases of the finite size resistors and an infinite homogeneous weakly conducting medium with two electrodes. Next, we continue the Romano and Price analysis about the truncated cone problem by means of comprehensive numerical calculations done for the trapezoid plates. We conclude that in general case of a conductor with variable cross-section the homogeneous electric field approximation gives only the lower limit estimation for the resistance value. This fact can be explained on the basis of the minimum electric power principle. The issues outlined in this article will be useful for advanced undergraduates, who study methods for solving electrostatic problems.Keywords: problem solving, electrical resistance, trapezoid plate problem.

Problem solving; Electrical resistance; Trapezoid plate problem