LCR Resonance

Series LCR resonance: at f₀ = 1/(2π√(LC)), the inductive and capacitive reactances cancel and impedance is minimum (= R).

Current is MAXIMUM at resonance: I_max = V_rms/R, regardless of L or C separately.

At resonance, V and I are IN PHASE — circuit looks purely resistive even though L and C are present.

Quality factor Q = (1/R)√(L/C) = ω₀L/R = 1/(ω₀RC). Higher Q ⇒ sharper resonance, narrower bandwidth.

Bandwidth Δf = f₀/Q = R/(2πL). Wide R (resistance) ⇒ broad resonance peak. Low R ⇒ sharp, selective.

Resonance is the principle of RADIO TUNING — varying C tunes Q-circuit to the broadcast frequency.

V across L and V across C can each be Q × V_source — much larger than the source. This is voltage MAGNIFICATION at resonance.

Parallel (anti-)resonance behaves OPPOSITELY: impedance is MAXIMUM, current minimum (for ideal components).