A singularity in Kirchhoff’s circuit equations

Abstract

Students often have difficulty in understanding qualitatively the behavior of simple electric circuits. In particular, as different studies have shown, they find multiple batteries connected in multiple loops difficult to analyze. In a recent paper, Sree Harsha et al (2015 Phys. Educ. 50 568), we showed such an electric circuit, which consists of ideal batteries connected in parallel, that could not be solved by the existing circuit analysis methods. In this paper, we shall introduce a new mathematical method for solving simple electric circuits from the solutions of more general circuits and show that the currents, in this particular circuit, take the indeterminate 0/0 form. We shall also present some of the implications of teaching the method. We believe that the description presented in this paper should help instructors in teaching the behavior of multiple batteries connected in parallel.