RLC Parallel CircuitFinding the impedance of a parallel RLC circuit is considerably more difficult than finding the series RLC impedance. This is because each branch has a phase angle and they cannot be combined in a simple way. The impedance of the parallel branches combine in the same way that parallel resistors combine:

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RLC Parallel: Complex Impedance MethodWhen the complex impedances of the branches of the parallel RLC circuit are combined, the equivalent impedance is of the form
then the impedance in ohms and the phase can be determined. By setting the = 0, the resonant frequency can be calculated. The expressions for these calculations are quite lengthy. 
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RLC Parallel ExpressionsThe complex impedances of the parallel RLC circuit takes the form when rationalized, and the components have the form

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