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Question:

why don't inductors generate heat even though they oppose current flow?

Has it something to do with the number of windings? I am not sure?

Answer:

They don't oppose current flow with resistance but with an opposed voltage. An ideal inductor has no resistance. And it's not the current itself that is opposed but any change in the current. When an inductor is connected to a battery, the current does not rise instantaneously; it's limited to a certain rise rate because the opposing voltage reduces the net voltage driving the the rise. Increasing current in the windings creates an increasing magnetic field which in turn induces an opposing voltage proportional to the field increase rate. This results in an equilibrium between current increase rate and net voltage across the inductor.

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