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A wound coil in general is a series LR circuit. If the coil has N turns, will there be a capacitance in between consecutive turns of the coil? If there is a capacitance, is it parallel to L and R or is it parallel to L? Also what will be the range of this capacitance?

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There's capacitance parallel to each individual winding and there is capacitance between layers of windings. There is also capacitance between isolated coils (as in a transformer). There is also capacitance to the core of the device which may or may not be earthed or somehow connected to ground

There is no simple generic answer but you can reduce each turn to a series R and L all in parallel with C.

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