**Impedance and Phase Angle of Series Resonant Circuit:**

The impedance of a Series Resonant Circuit is

The variation of X_{C} and X_{L} with frequency is shown in Fig. 8.4.

At zero frequency, both X_{C} and Z are infinitely large, and X_{L} is zero because at zero frequency the capacitor acts as an open circuit and the inductor acts as a short circuit. As the frequency increases, X_{C} decreases and X_{L} increases. Since X_{C} is larger than X_{L}, at frequencies below the resonant frequency *f*_{r}, Z decreases along with X_{C}.

At resonant frequency *f*_{r}, X_{C} = X_{L}, and Z = R. At frequencies above the resonant frequency *f*_{r}, X_{L} is larger than X_{C}, causing Z to increase. The phase angle as a function of frequency is shown in Fig. 8.5.

At a frequency below the resonant frequency, current leads the source voltage because the capacitive reactance is greater than the inductive reactance. The phase angle decreases as the frequency approaches the resonant value, and is 0° at resonance.

At frequencies above resonance, the current lags behind the source voltage, because the inductive reactance is greater than capacitive reactance. As the frequency goes higher, the phase angle approaches 90°.