Editing Electrical impedance (section)

==== Inductive reactance ====
{{Main|Inductance}}

Inductive reactance <math>X_L</math> is [[Proportionality (mathematics)|proportional]] to the signal [[frequency]] <math>f</math> and the [[inductance]] <math>L</math>.

:<math>X_L = \omega L = 2\pi f L\quad</math>

An inductor consists of a coiled conductor. [[Faraday's law of induction|Faraday's law]] of electromagnetic induction gives the back [[Electromotive force|emf]] <math>\mathcal{E}</math> (voltage opposing current) due to a rate-of-change of [[magnetic flux density]] <math>B</math> through a current loop.

:<math>\mathcal{E} = -{{d\Phi_B} \over dt}\quad</math>

For an inductor consisting of a coil with <math>N</math> loops this gives:

:<math>\mathcal{E} = -N{d\Phi_B \over dt}\quad</math>

The back-emf is the source of the opposition to current flow. A constant [[direct current]] has a zero rate-of-change, and sees an inductor as a [[short-circuit]] (it is typically made from a material with a low [[resistivity]]). An [[alternating current]] has a time-averaged rate-of-change that is proportional to frequency, this causes the increase in inductive reactance with frequency.

==== Total reactance ====

The total reactance is given by

:<math>{X = X_L + X_C}</math> (<math>X_C</math> is negative)

so that the total impedance is

:<math>\ Z = R + jX</math>

== Combining impedances ==
{{Main|Series and parallel circuits}}

The total impedance of many simple networks of components can be calculated using the rules for combining impedances in series and parallel. The rules are identical to those for combining resistances, except that the numbers in general are [[complex number]]s. The general case, however, requires [[equivalent impedance transforms]] in addition to series and parallel.

=== Series combination ===

For components connected in series, the current through each circuit element is the same; the total impedance is the sum of the component impedances.

[[File:Impedances in series.svg]]

:<math>\ Z_{\text{eq}} = Z_1 + Z_2 + \cdots + Z_n \quad</math>

Or explicitly in real and imaginary terms:
:<math>\ Z_{\text{eq}} = R + jX = (R_1 + R_2 + \cdots + R_n) + j(X_1 + X_2 + \cdots + X_n) \quad</math>