The study examined the knowledge of the functional relations between potential difference, magnitude of current, and resistance among seventh graders, ninth graders, 11th graders (in technical schools), and college students. It also tested the efficiency of a learning device named "functional learning" derived from cognitive psychology on the knowledge of these relations. A total of 73 participants were confronted with pictorial electrical circuits. Their task was to learn to infer resistance from potential difference and magnitude of current information, without any recourse to formal computations. It was possible to characterize, in a simple way, each student's initial conceptualizations about the relationships between potential difference, magnitude of current and resistance. These initial conceptualizations were very diverse, from the correct one to completely different ones to completely opposite ones. Learning was, to a certain extent, possible; but the learning sessions were more effective among students that had already been exposed to Ohm's law at school. Learning had durable effects, at least in the medium term (5 weeks), and mainly among the older students. There was a good correspondence between the state of learning of the relationships and the ability to solve classical physics problems related to these relationships.