My question is why doesn't the current reach its peak a little earlier than π/2? When the voltage is at its peak I suppose the emf is smaller than the source voltage so the current keeps increasing, trying to flow through the inductor. The emf is big at this point based on what I know for the DC RL circuit and decreases through time. We can tell from the diagram that the current increases until π/2 when the inductor comes into play to oppose its decrease this time.
However, I can't understand why this is not happening earlier. I get the increase in current at first when voltage is at maximum value but when it gets really small the current has already reached the maximum value for that particular voltage. So won't the emf change polarity at that point?
In case I wasn't clear I give you this example. Say we have a DC LR circuit. Time has passed and the current has reached its maximum value given by Ohm's law. Now I disconnect the source and connect another source with a lower voltage(this happens instantly). The current will slowly decrease because the emf tries to keep it constant. So the decrease starts now and that is because the voltage is lower.
Isn't there a time before π/2 in the AC circuit when voltage is lower than the voltage given by Ohm's law for the current at that moment?