How can Current Flow through the Inductor in the AC Circuit? [duplicate]

Question

It's said that if the inductor is connected to the alternating voltage source, alternating current will be created in the circuit. Changing magnetic flux through the inductor will induce a voltage as given by the Faraday's law : $$ V(t) = L \frac {dI}{dt} $$

It seems that there are two voltages at the inductor, one of the source (as the inductor is connected to the voltage source) and the induced one. They are of the opposite polarities, but the same magnitude at every point in time. If so, how can current flow in such a circuit?

Answer 1

I apologise for not reading your question properly: this answer was first written for an inductor connected across an ideal dc supply. Nevertheless it deals with the paradox you have presented.

You are used to resistive circuits governed by $I=\frac {V_{resultant}}{R_{total}}$ in which a resultant voltage is needed in order for a current to flow. But you are now asking about an ideal circuit with no resistance. Here there is no such requirement, and solving $\mathscr E_{supply}-L\frac{dI}{dt}=0$ tells us what happens. For an ideal dc supply ($\mathscr E_{supply}=constant$) we have a current that increases linearly with time; for an ac supply ($\mathscr E_{supply}=\mathscr E_0 \sin \omega t$) we have a current of the same frequency as the supply voltage, but lagging by a quarter of a cycle.