From conservation to Kirchhoff: getting started in circuits with conservation and accounting

This paper explores the connection between the general “conservation and accounting” approach to engineering science that forms the primary theme of the Foundation Coalition Sophomore Engineering Curriculum at Rose-Hulman Institute of Technology and the more specialized “Kirchhoff´s laws” techniques that are basic for understanding electric circuits. Circuit theory exists as a distinct discipline because of the set of specialized problem-solving techniques that apply to electric circuits. Conservation and accounting techniques provide a powerful set of tools for engineering problem solving, but conservation of charge and conservation of energy are not as useful as Kirchhoff´s laws for routine solution of electrical circuit problems. Kirchhoff´s laws are not wholly a consequence of the conservation principles. The laws also depend on the “lumped circuit” assumptions that restrict the class of problems to which circuit theory applies. The paper introduces the circuit variables current and voltage, and examines their relation to the conserved quantities of charge and energy. The lumped circuit model is discussed to illustrate the circumstances under which Kirchhoff´s laws apply