Complex Impedance

Use of Complex Impedance The handling of the impedance of an AC circuit with multiple components quickly becomes unmanageable if sines and cosines are used to represent the voltages and currents. A mathematical construct which eases the difficulty is the use of complex exponential functions. The basic parts of the strategy are as follows: Euler relation Polar form of complex number Impedance combinations Phasor diagrams RL and RC combinations Example for parallel elements

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Complex Impedance for RL and RC Using complex impedance is an important technique for handling multi-component AC circuits. If a complex plane is used with resistance along the real axis then the reactances of the capacitor and inductor are treated as imaginary numbers. For series combinations of components such as RL and RC combinations, the component values are added as if they were components of a vector. Shown here is the cartesian form of the complex impedance. They can also be written in polar form. Impedances in this form can be used as building blocks for calculating the impedances of combination circuits like the RLC parallel circuit. Impedance AC behavior of inductor AC behavior of capacitor

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Complex Impedance for RL and RC This depicts the phasor diagrams and complex impedance expressions for RL and RC circuits in polar form. They can also be expressed in cartesian form. Impedance Polar form of complex number	Index AC circuit concepts
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