Editing Electrical impedance (section)

==== Inductor (in the steady state) ====
For the inductor, we have the relation (from [[Faraday's law of induction|Faraday's law]]):
:<math>v_\text{L}(t) = L \frac{\mathrm{d}i_\text{L}(t)}{\mathrm{d}t}</math>

This time, considering the current signal to be:
:<math>i_\text{L}(t) = I_p \sin(\omega t)</math>

it follows that:
:<math>\frac{\mathrm{d}i_\text{L}(t)}{\mathrm{d}t} = \omega I_p \cos \mathord\left( \omega t \right)</math>

This result is commonly expressed in polar form as
:<math>Z_\text{inductor} = \omega L e^{j\frac{\pi}{2}}</math>

or, using Euler's formula, as
:<math>Z_\text{inductor} = j \omega L</math>

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.