If a superconductor has zero resistance, does it have infinite amperage?

In the world we live in, with the accuracies we can generate it is an observed fact the R=V/I.

Infinities need careful interpretation if they happen in the physical world.

In this form when there is no current one talks of infinite resistance ( seen also on the potentiometers sold) .

When one reverses the equation to the form I=V/R one has to be careful to see if there can be any material where R is 0. There are no such every day materials because they are composed by atoms tied together with electromagnetic forces which will always display some resistance to change of status at normal temperatures.

But there exist special materials under special conditions, superconducting materials and superconductivity, which take advantage of the quantum mechanical behavior of certain metals, and there one achieves practically zero resistance and very high currents indeed, according to the voltage applied.

The simplest method to measure the electrical resistance of a sample of some material is to place it in an electrical circuit in series with a current source I and measure the resulting voltage V across the sample. The resistance of the sample is given by Ohm's law as R = V/I. If the voltage is zero, this means that the resistance is zero.

Superconductors are also able to maintain a current with no applied voltage whatsoever, a property exploited in superconducting electromagnets such as those found in MRI machines. Experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a current lifetime of at least 100,000 years. Theoretical estimates for the lifetime of a persistent current can exceed the estimated lifetime of the universe, depending on the wire geometry and the temperature.

The current in the superconductors is not found by this simple formula, but theories have been developed and methods of measuring it use the magnetic fields generated.

The LHC uses high power superconducting magnets to achieve the high magnetic fields it needs. The problem is technological, keeping the superconductors cooled and the high power needed under control.

You can't put x volts over 0 ohms, the material must be at equal potential everywhere.