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An overview of complex impedance analysis in the frequency domain for passive circuits involving emfs, resistors, capacitors, and inductors. The technique allows for algebraic analysis of time-dependent circuits instead of solving differential equations. Complex algebra and notation, the generalization of ohm's law, and the combination of impedances.
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We now need to turn to the analysis of passive circuits (involving EMFs, resistors, capaci-
tors, and inductors) in frequency domain. Using the technique of the complex imp edance,
we will b e able to analyze time-dep endent circuits algebraically, rather than by solving dif-
ferential equations. We will start by reviewing complex algebra and setting some notational
conventions. It will probably not b e particularly useful to use the text for this discussion,
and it could lead to more confusion. Skimming the text and noting results might b e useful.
Let
V b e the complex representation of V. Then we can write
V ) = V e
{
= V [cos + { sin ]
where { =