Electronic – Inductor with AC source

Now since we always get an equal and opposite voltage across the inductor for each change in source voltage so it means that the current will never be able to flow in the inductor but yet current is always flowing in each text book. I am confused about it. Please guide me. I shall be grateful to you.

Think about what happens when you have 0 volts applied across an inductor. You might say that there isn't any current and that would be one truth from many other truths. The reality is that if there was 1 amp flowing through an inductor and the driving voltage was instantly brought to 0 volts, that 1 amp would continue to flow forever (assuming a perfect inductor).

What I'm trying to say is that you can't define the current through an inductor by the voltage across it even if the back-emf appears to make the "true" or "real" voltage zero at any particular instant in time. The current in an inductor is dependent on previous events in time.

Another way of looking at it: the back emf being equal to the driving voltage makes the effective voltage across the inductor equal to zero. But we're not talking about the external terminals of the inductor any more: -

^{simulate this circuit – Schematic created using CircuitLab}

We're talking about an invisible untouchable node. Given there is 0 volts across this "internal inductor" the impedance has to be zero (because it is also DC hence, current is 0/0 i.e. indefinable at any instant.

This means that there is nothing useful to know about current flow in a perfect inductor based on saying the back-emf equals the applied voltage

We are left with the old tried and tested relationship, that being: -

$$V = L\dfrac{di}{dt}$$

And back-emf tells us nothing about the current that flows.