Tuning an LRC circuit

A short notepad on some electronic stuff I have been reading up on via Electronics Demystified: this time about tuning an LRC (series) circuit (i.e. one with capacitance, inductance and resistance).

In these circuits, the resonant frequency is found when the effects of capacitance and inductance cancel each other out.

Inductive reactance is given by 2\pi\textit{f}L (where \textit{f} is the AC frequency and L is the inductance), while capacitive resistance is \frac{1}{2\pi\textit{f}C} where C is the capacitance.

So to cancel these out: 2\pi\textit{f}L = \frac{1}{2\pi\textit{f}C} ,  and as we may assume L and C are fixed this requires finding the resonant frequency \textit{f}_{r} :

\frac {1}{2\pi\sqrt{LC}}

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