My book says that current has to be constant throughout a simple series electrical circuit consisting of wires, a cell and few resistors, and hence resistors have higher potential difference across them than the rest of the wire with lower resistance.
How does the circuit "know" that it has to maintain a constant current? How does it know that it has to increase the potential difference across it? I know that potential difference in a circuit is the energy dissipated in the resistance, and with more resistance, more is the potential difference due to Ohms Law. But why does the current not just flow through the resistor, experience same potential difference as any other two points in the circuit with lower resistance, meaning that it will have less current flowing through it?
Best Answer
(a) "How does the circuit "know" that it has to maintain a constant current?"
If the current (rate of flow of charge) wasn't the same all round the circuit, then electric charge would be piling up at some point or points. This couldn't go on happening for long because the piled-up charge (negative, let's say) would prevent (by repulsion) further charge charge from joining the pile. In a very short time after completing the circuit, the current will be the same all round the circuit, so the charge going into a segment of conductor per second will be the same as the charge leaving it.
This steady-state current will be determined by the pd provided by the power supply, and the resistance of the circuit. [You seem to be happy with this.]
(b) "How does [the circuit] know that it has to increase the potential difference across [a component with higher resistance]?
In my opinion this is quite a deep question – if you don't want simply to be told that $V=IR$. I believe that the answer is along these lines... When I talked in (a) about piling up of charge, I didn't say that the piles went away, just that they were self-limiting. I think that (surface) charges on the conductor are responsible for the different pds across the different components. But we are in territory into which few venture, least of all writers of textbooks.