Resonance

Từ vựng

English	Ý nghĩa
resonance/ˈrezənəns/	cộng hưởng
bandwidth/ˈbændwɪdθ/	băng thông

English

Resonance: the imaginary parts cancel

At resonance $ω_{0} = 1/\sqrt{LC}$ the series impedance drops to pure $R$ (its minimum) and current peaks; the bandwidth between the half-power points is $BW = R/L = ω_{0}/Q$, and each reactive element holds Q times the source voltage — check the magnification on both elements.
The parallel tank is the dual: maximum impedance, circulating branch currents Q × the line current that cancel at the terminals.

Example

$R = 5$ Ω, $L = 0.1$ H, $C = 10$ µF: $ω_{0} = 1000$ rad/s, $Q = ω_{0}L/R = 20$. A 10 V source drives 2 A, so $V_{L} = 200$ V and $V_{C} = 2/0.01 = 200$ V — equal, 180° apart. $BW = 1000/20 = 50$ rad/s with half-power frequencies 975.3 and 1025.3 rad/s (difference 50.0, machine-verified). One bandwidth away at 900 rad/s the current is $10/|5 + j(90 - 111)| = 0.45$ A — under a quarter of the peak: that selectivity is what a tuner sells.