Parallel Resonance

At resonance, the parallel combination of the inductor and capacitor acts as an open circuit, causing the resistor to draw minimal current. Energy oscillates between the inductor's magnetic field and the capacitor's electric field. The imaginary part of the circuit's admittance becomes zero, resulting in purely resistive behavior.

The resonant frequency varies inversely with the square root of the product of inductance and capacitance. At this frequency, the net reactance is zero, meaning capacitive and inductive effects cancel each other out. This condition occurs when the circuit exhibits purely resistive behavior with maximum current flow through the resistor.

The quality factor indicates the sharpness of the resonance curve and the circuit's selectivity. A higher quality factor yields half-power frequencies symmetrically distributed around the resonant frequency and a narrower bandwidth. High-quality circuits with Q≥10 resonate strongly at a narrow range of frequencies, beneficial for filtering unwanted frequencies in radio communications.

At the half-power frequencies, the current is approximately 1.4142 times the minimum current at resonance, corresponding to 0.707 of the maximum current. These frequencies define the bandwidth, calculated as the difference between the higher and lower half-power frequencies. This bandwidth measurement characterizes the circuit's frequency selectivity and response width.

The frequency response indicates that current magnitude initially decreases, reaches a minimum at the resonance frequency, then increases as frequency continues to rise. This behavior reflects how the circuit's admittance changes with frequency. Understanding this frequency response of a circuit helps predict circuit behavior across different operating frequencies.

Parallel resonance circuits act as band-stop or notch filters, blocking a specific frequency range while allowing others to pass. This property makes them valuable in signal processing for eliminating unwanted frequencies or noise. The high selectivity of circuits with high quality factors enables precise frequency filtering in radio communications and interference reduction.

Admittance reflects the ease with which current can flow through the circuit. At resonance, the imaginary part of admittance is zero, resulting in purely resistive behavior. The circuit's total admittance determines how current distributes across the resistor, inductor, and capacitor elements connected in parallel.