Electrical impedance
Inductor

For the inductor, we have the relation (from Faraday's law):

This time, considering the current signal to be:

it follows that:

This result is commonly expressed in polar form as

or, using Euler's formula, as

As in the case of capacitors, it is also possible to derive this formula directly from the complex representations of the voltages and currents, or by assuming a sinusoidal voltage between the two poles of the inductor. In the latter case, integrating the differential equation above leads to a constant term for the current, that represents a fixed DC bias flowing through the inductor. This is set to zero because AC analysis using frequency domain impedance considers one frequency at a time and DC represents a separate frequency of zero hertz in this context.
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