Abstract
Does it ever bother you that emfs, resistors, and inductors add in series, but capacitors add in parallel? Does it bother your students? The AP Physics C syllabus for electricity and magnetism specifies the mathematical models students are expected to not merely memorize but to understand. Over time, my students' questions have made me rethink my conceptual and mathematical understanding of this material to help them efficiently develop reasonable conceptual and mathematical models of E&M. In this paper I describe aspects of this pedagogical rethinking related to four ideal circuit elements. I specify the end state of understanding that I want students to develop, but do not attempt to detail the pedagogical path to that understanding.
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