Chpater 18. Circuits. You don’t need resistance. You don’t need Ohm’s law. All you need is the fact that charged particles respond to electric fields created by other charged particles. It’s just that simple.
When I took my first electromagnetism course, I felt stupid becuase I never could just look at a circuit and tell what was in series and what was in parallel. And the cube of resistors…well I still have bad dreams about that. One thing I know now that I didn’t know then is that according to traditional textbooks, circuits simply should not work. Ideal wires don’t exist, and neither do ideal batteries nor ideal light bulbs. Fringe fields, however, do indeed exist and capacitors just wouldn’t work without them. So basically, I now know that the traditional textbook treatment of circuits is not just flawed, but deeply flawed to the point of being unrealistic.
Enter Matter & Interactions. M&I’s approach to circuits invokes the concept of a surface charge gradient to establish a uniform electric field inside the circuit, which drives the current. This was tough to wrap my brain around at first, but now I really think it should be the new standard mainstream explanation for circuits in physics textbooks. the concept of resistance isn’t necessary. It’s there, but not in its usual macroscopic form. M&I treats circuits from a purely microscopic point of view with fundamental parameters like mobile electron number density, electron mobility, and conductivity and geometry in the form of wire length and cross sectional area. Combine these with charge conservation (in the form of the “node rule”) and energy conservation per charge (in the form of the “loop rule”) and that’s all you need. That’s ALL you need. No more “total resistance” and “total current” nonsense either. In its place is a tight, coherent, and internally consistent framework where the sought after quantities are the steady state electric field in each part of the circuit and the resulting current in each part. No more remembering that series resistors simply add and parallel resistors add reciprocally. Far more intuitive is the essentially directly observable fact that putting resistors in series is effectively the same as increasing the filament length and putting resistors in parallel is effectively the same as increasing the circuit’s cross sectional area. It’s so simple, like physics is supposed to be.
Of course, in the next chapter (chapter 19) the traditional “Ohm’s law” model of circuits is seen to be emergent from chapter 18’s microscopic description, but honestly, I see no reason to dwell on this. Most of my students are going to become engineers anyway, and they’ll have their own yearlong circuit courses in which they’ll learn all the necessary details from the engineering perspective. For now, they’re much better off understanding how circuits REALLY work and if they do, they’ll be far ahead of me when I was in their shoes as an introductory student, and will have the deepest understanding of anyone else in their classes after transferring. That’s my main goal after all.