Power as lenzs law states an inductor in a circuit opposes the flow of current through it because the flow induces an electromotive force emf that opposes it. In practice the inductor losses will be higher than calculated.

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In order to keep the current flowing against this induced emf the work has to be done by the external battery source.

Power dissipation inductor. This is because you have not accounted for the ac winding losses due to skin and proximity effects. The lr series circuit. The power dissipated in the inductor arises from two separate sources.
The current in this circuit is 0057a as i calclulated. The losses associated with the inductor core and those associated with the inductor windings. The resistance r is the dc resistive value of the wire turns or loops that goes into making up the inductors coil.
All three inductors have a power dissipation less than that required for a 400c rise. Real inductors have resistance too this is where power is dissipated in an inductor. In other words forming an lr series circuit.
Though determining these losses with precision can require complex measurements an easier alternative exists. Show that the power dissipated in the inductor is zero. A lr series circuit consists basically of an inductor of inductance l connected in series with a resistor of resistance r.
In rl ac circuit an ac source vst 220sin40000t 450 is connected to a 60mh inductor and a 3kw resistor. I know that inductor has no charging role in this circuit. Thus thermal performance should not be a problem in most applications.
In a real inductor the voltage leads the current but not by 900. The power dissipated in the winding resistance. Consider the lr series circuit below.

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