• Tags: resonance, frequency, Q-factor
• Difficulty: Advanced

Resonance occurs when X_L = X_C, i.e., omega_0L = 1/(omega_0C). Solving: omega_0 = 1/sqrt(LC), f_0 = 1/(2pisqrt(LC)). At resonance: (1) Z = R (minimum possible impedance), (2) I = V/R (maximum current), (3) phi = 0 (purely resistive behavior), (4) V_L = V_C = QV (can exceed source voltage). The quality factor Q = omega_0L/R = 1/(omega_0CR) = (1/R)*sqrt(L/C) measures sharpness of resonance. High Q means a narrow, tall resonance peak — the circuit is highly selective (used in radio tuning). Bandwidth Delta_omega = omega_0/Q = R/L is the frequency range where current exceeds I_max/sqrt(2). Increasing R broadens the peak and reduces I_max. The resonant frequency is independent of R. JEE often asks: how does changing L, C, or R affect the resonance curve?