Some didactical suggestions for a deeper embedding of DC circuits into electromagnetism

Undergraduate students often encounter great difficulties in understanding Ohm's law and electrical circuits. Considering the widespread students' beliefs and their common mistakes, as they come out from the literature and our teaching experience, we think that a relevant source of these problems comes from the fact that electrical circuits are generally treated separately from the other topics of electromagnetism, with poor reference to the circulation of the electric field. We present here a way to deal with electrical circuits that could help students to overcome their difficulties. In our approach, the electric field is the protagonist and the mathematical tool the students are asked to use is its circulation. In the light of the circulation of the electric field, the experimental Ohm's law is revisited, the concept of electromotive force is discussed and some suggestions to eliminate common misconceptions about the role of a battery in a circuit are presented.