An ideal battery (with no internal resistance) has an EMF is connected to a supe

Question

An ideal battery (with no internal resistance) has an EMF is connected to a superconducting (resistantless) coil of inductance L. Find the current in the coil as a function of time, I(t), assuming zero current at time t=0.

I am thinking that the answer to this is the I(t) = for any t>0. The reasoning for this is that looking at relationship V=IR, we find that I is equal to V/R. Because the material is a superconductor, below the critical temperature the resistance is equal to zero. Knowing that there is voltage, we must assume that the current will reach an infinite amount. With no resistance in the circuit, whenever the circuit is closed the current will instantly approach infinity and the circuit will short-circuit.

Please let me know if this reasoning is true. Thank you!

Explanation / Answer

Since there is no resistance anywhere in the circuit the battery volatge directly appears accorss the inductor and current through it is infinity at that instant.

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