Resonance

At resonance inductive and capacitive reactances cancel — the basis of tuned circuits and filters.

Intermediate

$f_0 = \frac{1}{2\pi\sqrt{LC}}$

Series resonance: impedance is minimum ( $Z = R$ ), current is maximum. The voltage across L or C can be $Q$ times the supply voltage!
Parallel resonance: impedance is maximum, line current is minimum.

Quality factor and bandwidth (series):

$Q = \frac{1}{R}\sqrt{\frac{L}{C}} = \frac{\omega_0 L}{R} \qquad BW = \frac{f_0}{Q}$

High-Q circuits are sharply selective (radio tuning); unwanted resonance in power systems can cause dangerous over-voltages with harmonics.

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