Variational alternatives to Kirchhoff's loop theorem in dc circuits

Problems involving the flow of direct current in circuits are typically sol ved through the use of Kirchhoff's rules-the junction theorem and the loop theorem. Since students typically find the meaning and use of the junction theorem straightforward, but are prone to conceptual and computational diff iculties with the loop theorem, we present here a little-known alternative method for solving de circuit problems. In this method, the junction theore m is retained, but the use of the loop theorem is replaced by the minimizat ion of a single global variational quantity for the circuit. In this paper, the variational method is described and its use is illustrated, and its eq uivalence to standard methods is proved by vector calculus from the steady- state limit of Maxwell's equations. (C) 1999 American Association of Physic s Teachers.