Resonance in an AC Circuit

Let a resistor, an inductor, and a capacitor in series be supplied with a sinusoidal voltage. The circuit's impedance depends on the source's angular frequency. The inductor's reactance increases with the frequency, whereas the capacitor's reactance decreases.

The current is maximum if these reactances are equal. On equating them, the source's frequency which permits this is obtained.

This phenomenon is called the resonance in a series R-L-C circuit. At this frequency, the phase difference between the current and voltage, proportional to the difference between the inductor and capacitor's reactances, is zero.

At the resonance frequency, the impedance is simply the resistance. Hence, the current peaks sharply if the resistance is lower.

The resonance bandwidth is defined as the range of angular frequencies over which the average power is more than half of the maximum value, which is the ratio R over L.

The quality factor is defined as the ratio of the resonance frequency and the bandwidth. The higher the quality factor, the sharper the resonance.