Simple circuits are not that simple

摘要

The teaching of basic circuits in early undergraduate physics courses is widespread and, to some extent, quite uniform. In most textbooks, the introduction of resistors, capacitors and inductors is followed by their assemblage into larger systems, together with mathematical calculations of charges and currents as functions of time. In this process, spatial features of circuits tend to be omitted. Here, we argue that this kind of omission is not 'natural' but, rather, should be justified in terms of internal time-scales operating in the system, in the framework of the continuity equation. When space is brought back to the discussion of circuits, a number of important physical features, absent in most textbooks, emerge. Among them, one has a spatial uniformity of currents, the existence of charges coating metallic surfaces, and the presence of charge distributions inside wires at the endings of resistors and coils. We believe that the discussion of these qualitative issues with students could foster a more mature and unified relationship with electromagnetism.