Like I said, there's a shared budget for temperature, magnetic field and current. If you're sufficiently close to the critical temperature, it only takes a sma

Like I said, there's a shared budget for temperature, magnetic field and current. If you're sufficiently close to the critical temperature, it only takes a small current to "blow the budget" which turns your material back into an ordinary conductor/resistor. If you remove the current or lower the temperature, there's a nonzero switching time before the material will return to its superconducting phase. There are some neat applications of this phenomenon in superconducting electronics. Cryotrons use transformers to produce large fields from small currents to switch a higher-current-capacity line from superconducting to normal. N-trons and other "current crowding" devices perform a similar trick using currents in a pinched region attached to the high current line. I can't remember the precise details, but different superconducting films are more or less inclined to "localize" the normal-phase region induced by local current/heat. Sadly, those neat devices are apparently quite finnicky because switching emits heat into their environment, and also depends on temperature of that same environment. As far as I know, cryotrons are used for high power electromagnets to rapidly and safely dump the energy -- they don't appear to be useful for superconducting computers, for example.