Question: We have a closed circuit composed of multiple DC sources and resistors. We also have a variable resistor in the circuit. Can we prove that the direction of current through this resistor will be the same, irrespective of the value of the resistor?
(The above fact may not even be true. It's just that I haven't been able to find a counterexample yet)
Inspiration: A highly ideal model of P-N junctions treats P-N junctions as constant resistance resistors when forward biased, and open junctions (resistance = infinity) when reverse biased. I was just curious if in this model it was possible to create a paradoxical circuit (of DC sources, resistors and P-N junctions) - as in one that has either no or more than one mathematical solution for the currents and potentials in the circuit.