Resonance in an AC Circuit

At resonance frequency, the inductive and capacitive reactances cancel each other completely, so impedance equals only the resistance value. This occurs when the inductor's reactance and capacitor's reactance are equal. As a result, the current and voltage are exactly in phase, and current reaches its maximum amplitude. Lower resistance produces sharper current peaks at resonance.

At high frequencies, inductive reactance dominates while capacitive reactance becomes negligible. At low frequencies, the capacitor offers high reactance while the inductor offers minimal reactance. At the resonance frequency, both reactances are equal. This frequency-dependent behavior determines the circuit's phase difference and overall impedance characteristics.

The quality factor is the ratio of resonance frequency to bandwidth. A higher quality factor indicates a sharper resonance peak and narrower bandwidth, meaning power is concentrated more tightly around the resonance frequency. Lower resistance values produce higher quality factors and sharper peaks, while higher resistance broadens the resonance response.

Resistance dissipates power as thermal energy during every cycle of oscillation. This energy loss dampens the circuit's response, reducing the current amplitude at resonance and broadening the resonance peak. The greater the resistance, the lower the current amplitude at resonance frequency and the less sharp the power versus frequency curve becomes.

At frequencies above resonance, inductive reactance exceeds capacitive reactance, so voltage leads current with positive phase difference. Below resonance, capacitive reactance exceeds inductive reactance, so current leads voltage with negative phase difference. At exactly the resonance frequency, current and voltage are in phase with zero phase difference.

Resonance bandwidth is the range of angular frequencies over which average power exceeds half the maximum power value. It is calculated as the ratio of resistance to inductance (R/L). A narrower bandwidth indicates a sharper resonance peak, while a wider bandwidth shows a broader power distribution around the resonance frequency.

By adjusting capacitance, inductance, and resistance values, circuits can be tuned to dissipate power selectively at different frequencies. This tuning capability is essential for radio frequency transmission and reception, allowing systems to isolate and amplify signals at specific frequencies while rejecting unwanted frequencies.