I think the difference between AC, steady state and step response is being confused.

Under steady state conditions, i.e. once the inductor has been left connected to the power supply for long enough for the current to stabilise, the inductance is unimportant. The current is simply proportional to the series resistance of the inductor. If it's an ideal inductor, the current will be infinite, which is obviously impossible.

When a voltage is suddenly applied, i.e. the inductor is subjected to a step change in voltage, the initial current is zero, then it slowly rises to the steady state value, limited only by the series resistance. In an ideal inductor, the current will linearly increase towards infinity, with the rate of change proportional to the applied voltage and inversely proportional to the inductance. In a real world inductor, the current will logarithmically increase towards the value limited by the series resistance.

When the current through the inductor is suddenly interrupted, the voltage across the inductor, at that instant will be infinite.** In a non-ideal inductor, the series resistance actually makes no difference to the voltage**. It's the parallel resistance which limits the voltage and the capacitance too. In real life, an arc will form across the switch contacts or the semiconductor driving it will undergo avalanche breakdown, which can be destructive, hence the need for a transient suppressor or fly-back diode.

In an AC circuit, the current through the inductor depends on its impedance, which is simply Z = 2pi*LF, in an idea conductor, where: Z = impedance in Ohms, L = inductance in henries and F = frequency in Hz. In an ideal inductor, the always current lags the voltage by 90^{o}. The current can be calculated using Ohm's law: I = V/Z. In a non-ideal inductor, the impedance is Z = ((2pi*LF)^{2}+R^{2})^{0.5}.