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I asked a similar question here some time ago, however I feel that this question is different and was not answered in the previous post, although it certainly is related.

My question here is, what happens when you charge an inductor from a battery?

Case 1: Battery and inductor only with no other significant resistance in the circuit

My thought is that the voltage across the inductor must match that of the battery by Kirchoff's voltage law, and so this will lead to a constantly rising current by $\epsilon = -L\frac{dI}{dt}$.

However then what happens? Would this continue happening indefinitely if we had an infinite energy battery until the current started becoming infinite (although no doubt some relativistic effects would come into play as the current started approaching the value of the speed of light). And if we had a normal battery, what would happen then? Would the emf across the inductor become zero when the battery ran out of energy (assuming this happened suddenly and there wasn't a 'tapering off'), but then what would happen to the energy? I can hazard a guess that the inductor would cause the current to start flowing in the opposite direction, and we would have the inductor charging up the battery?

However i'm not sure that this can be right. This is leading me to a scenario of a capacitor-inductor circuit. However here we have a battery and an inductor, not a capacitor and inductor. So surely you can't get the same scenario. Could it be that you get oscillations but rather than getting sinusoidal current as in an RLC circuit, you get a current that remains constant and then directly reverses each time the battery runs flat or the inductor runs flat?

Case 2: other non-negligable resistance in the circuit

The second part to my question is: what would happen if there was a circuit where an inductor is charging from a battery but there is another resistor in series in the circuit or the wires in the circuit have non-negligable resistance? I think then we would get sinusoidal current oscillations but with a decreasing amplitude as energy is dissipated over the resistor?

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Purely theoretically, if the circuit has no ohmic resistance, the battery would establish large current in the coil. Then current would then flow indefinitely in the circuit, the energy being stored as magnetic energy.

More realistic model is one where the circuit contains non-zero resistance. Resistance $R$ leads to voltage drop $RI$ so when the current gets high enough, $\epsilon = RI$ and the current stops increasing.

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