This post continues this series into second semester introductory calculus-based physics, usually electromagnetic theory. This question addresses basic DC circuits. In a traditional introductory e&m course, circuits are presented with so many idealizations that according to such treatments simple circuits shouldn’t work at all! Two of the most important idealizations are that potential differences along wires are neglected so there are effectively no wires, and that fringe fields associated with real capacitors are neglected so capacitors effectively don’t work. These same treatments are also based on the concepts of potential difference and resistance, which is fine for an engineering perspective. However, all of DC circuit analysis can be done more realistically by adopting a surface charge gradient model that emphasizes some deceptively fundamental physics: charged particles act in response to local electric fields. That’s the whole story really.
Here are some conceptual questions that may be quite difficult for students of the traditional approach to circuits.
(a) Two circuits have identical wires, identical batteries, and identical light bulbs. The only difference between the circuits is that one has two bulbs in series with the battery and the other has only one bulb in series with the battery. Why does the single bulb glow brighter than either of the two bulbs in the other circuit? Do not invoke the concept of resistance (traditional treatments say that adding a second identical bulb doubles the circuit’s effective resistance, but do not use this concept in your explanation).
(b) Two circuits have identical wires, identical batteries, and identical light bulbs. The only difference between the circuits is that one has two bulbs in parallel with the battery and the other has only one bulb in parallel (really in series I suppose) with the battery. Why does the single bulb glow with the same brightness as either of the two bulbs in the other circuit? Do not invoke the concept of resistance (traditional treatments say that adding a second identical bulb doubles the circuits effective resistance, but do not use this concept in your explanation).
(c) What effect on a circuit does adding two identical bulbs in series, compared to having just one bulb in series, have?
(d) What effect on a circuit does adding two identical bulbs in parallel, compared to having just one bulb, have?
(e) What effect on a circuit does adding two identical capacitors in series, compared to having just one capacitor in series, have?
(f) What effect on a circuit does adding two identical capacitors in parallel, compared to having just one capacitor, have?
Have fun!