For an inductive coil, the back emf produced is given by $ldi/dt$.
In a DC circuit, a power supply, a coil, and a resistance, all in series. when the switch is closed, the back emf becomes equal to emf of the source, then the back emf dissipates, as far as I understand, till the current becomes max.
now in an AC circuit, with a power supply and an inductive coil only, does the back emf ALWAYS equal to the emf of the source? if so, why doesn't it dissipate as in the first case? I can't understand how the back emf changes in the presence of a variable emf of the source.
Answer
KVL applies instantaneously. The sum of all voltages around a loop must be 0 at each instant.
In the switched circuit, the EMF of the inductor decreased over time because as the current increased the resistor started to take up more of the potential from the source.
In the AC circuit with no resistor, that doesn't happen. But since the source voltage eventually reverses itself, this doesn't lead to the inductor current continuing to increase toward infinity.
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