Series and parallel circuits

Impedance in a series circuit is the orthogonal sum of resistance and reactance:
Z =(R2 + (X2L− X2C)) ^1/2
Equivalent series and parallel circuits are circuits that have the exact same total impedance
as one another, one with series-connected resistance and reactance, and the other with parallelconnected
resistance and reactance. The resistance and reactance values of equivalent series and
parallel circuits may be expressed in terms of those circuits’ total impedance:

If the total impedance of one circuit (either series or parallel) is known, the component values of
the equivalent circuit may be found by algebraically manipulating these equations and solving for
the desired R and X values:
Z2 = RseriesRparallel


Z2 = XseriesXparallel