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Super conductor cables are supposed to be the cables having zero resistance/impedance, so that it carries infinite current capacity which will further lead to v=0 since v=ir and r is 0 therefore v=0 how could current flow when potential difference is zero
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I think the current flow of a dc superconductor coil is limited by internal resistance of power supply circuit .
No voltage is required as the resistance is zero. This is for static conditions only. In order to change the current, i.e. ac condition, a voltage is needed due to inductance, since v = L * di/dt. When a superconductor connects a power source, which is generally constant voltage, to a load resistance, then the current is simply Vsource/Rload, with all the voltage dropped across the load, and none dropped across the superconductor. In the ac domain, however, the superconductor contributes some inductance. There is a non-zero voltage due to inductance. Claude USA
I think we debate about the validation of circuits laws (KCL & KVL) when the circuit will be included of superconductor. The circuit current just limited by source internal resistance in DC condition.
For AC condition, you can suppose a current transformer with super conductor secondary winding. When secondary side of this CT is shorted without any additional load, as Claude said, the leakage inductance of current transformer limits the secondary current. In this case we front the inductance drop voltage ( L*di/dt ) against secondary induced voltage as emf of super conductor closed ring which made induced secondary current. 
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