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# Appendix F: Quality Factor of RLC Circuits

This appendix is added for those readers who might need it for other application than electric circuits, such as in communications. For parallel and series circuits a quality factor Q can be defined using the values of the three components. Q is a ratio; so it is a number without any unit. Here R is the resistance of a resistor that is part of the RLC and must not be confused with the internal resistance of a coil as an inductor.

For a parallel RLC circuit the quality is

 $Q=R\sqrt{\frac{C}{L}}$ (F.1)

At the resonance frequency, for which XC = XL, C can be substituted in terms of L and Equation F.1 assumes the form

 $Q=\frac{R}{{X}_{L}}$ (F.2)

Because XC = XL, Q can also be written as Q =

For a series RLC the quality is XC

 $Q=\frac{1}{R}\sqrt{\frac{L}{C}}$ (F.3) ...

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