• $summary_{type}$: concept
• $word_{count}$: 170

At resonance, $X_L$ = $X_C$, giving $omega_0$ = 1/sqrt(LC) and $f_0$ = $\frac{1}{2*pi*sqrt(LC}$). The impedance reduces to Z = R (minimum), current reaches maximum I = $\frac{V}{R}$, and the phase angle is zero (purely resistive). The quality factor Q = $omega_0$*L/R = $\frac{1}{R}$sqrt$\frac{L}{C}$ determines the sharpness of the resonance peak. Higher Q means narrower bandwidth ($Delta_{omega}$ = $\frac{R}{L}$ = $\frac{omega_0}{Q}$) and greater voltage magnification: $V_L$ = $V_C$ = QV at resonance. These voltages can greatly exceed the source voltage — this is not an error but a real physical phenomenon. The energy oscillates between L (magnetic) and C (electric) with no net dissipation in the reactive elements. Changing R affects the peak height and width but not the resonant frequency. Changing L or C shifts the resonant frequency. Radio tuning uses a variable capacitor to adjust $f_0$.