Impedance and phase angle of resonant circuit

Impedance and phase angle of series resonant (also known as series variable frequency resonant) circuit:

The impedance of a series resonant circuit is

The variation of XC and XL with frequency is shown in Figure 8.4.

At zero frequency, both XC and Z are infinitely large, while XL 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, XC decreases while XL increases. Due to XC being greater than XL, Z decreases with XC at frequencies lower than the resonant frequency fr.

At the series resonant frequency fr, XC = XL,Z =R。 At frequencies higher than the resonant frequency fr, XL is greater than XC, resulting in an increase in Z. The relationship between phase angle and frequency variation is shown in Figure 8.5.

At frequencies below the resonant frequency, the current will lead the power supply voltage because the capacitance reactance is greater than the inductance reactance. As the frequency approaches the resonance value, the phase angle decreases and reaches 0 ° during resonance.

At frequencies higher than resonance, the current lags behind the power supply voltage because the inductance reactance is greater than the capacitance reactance. As the frequency increases, the phase angle approaches 90 °.

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By hvhipot