« on: 21/11/2023 21:58:00 »
Imagine a simple circuit of a battery, a switch, a lamp and a piece of superconducting wire in a loop. What happens when the switch is closed is the question and is a little more complex than it initially appears. Since any piece of wire has both inductance and resistance it therefore has a time constant, l/r which defines the time it takes for the current to rise to ~63% of the value v/r, where v is the applied voltage. In the case of the superconducting wire this time constant will be infinite and hence no current will flow! This scenario will also involve a potential across the piece of superconducting wire which is obviously impossible. Ok, you say maybe we cannot model a superconductor as having a time constant but we can look at limits: as the resistance is artificially lowered the time constant will be valid and each time it is lowered the time constant will increase until we approach zero resistance where the current will flow but at such a slow rate that it appears to be non-conducting. In this situation I am just looking at the piece of superconducting wire in isolation. There has to be some error in this analysis but I can't find it.