Chapter Summary

• X_L and X_C have opposing effects in an RLC circuit.
• In a series RLC circuit, the larger reactance determines the net reactance of the circuit.
• In a parallel RLC circuit, the smaller reactance determines the net reactance of the circuit.

Series Resonance

• The reactances are equal.
• The impedance is minimum and equal to the resistance.
• The current is maximum.
• The phase angle is zero.
• The voltages across L and C are equal in magnitude and, as always, 180° out of phase with each other and thus they cancel.

Parallel Resonance

• The reactances are approximately equal for Q 10.
• The impedance is maximum.
• The current is minimum and, ideally, equal to zero.
• The phase angle is zero.
• The currents in the L and C branches are equal in magnitude and, as always, 180° out of phase with each other and thus they cancel.
• A band-pass filter passes frequencies between the lower and upper critical frequencies and rejects all others.
• A band-stop filter rejects frequencies between its lower and upper critical frequencies and passes all others.
• The bandwidth of a resonant filter is determined by the quality factor (Q) of the circuit and the resonant frequency.
• Cutoff frequencies are also called –3 dB frequencies or critical frequencies.
• The output voltage is 70.7% of its maximum at the cutoff frequencies.