resonance

Resonance occurs in an AC circuit when the inductive reactance (XL) and capacitive reactance (XC) are equal in magnitude, causing them to cancel each other. At this frequency, called the resonant frequency, the impedance of the circuit drops to its minimum value, determined only by resistance. The current through the circuit reaches its maximum possible level for the applied voltage. This is a real and often powerful effect that operators and designers must either exploit or contain, depending on the application.

The resonant frequency depends on the inductance (L) and capacitance (C) in the circuit. For a series LC circuit, it is found using the formula f = 1 / (2π√LC), where f is in hertz, L is in henries, and C is in farads. A small capacitor paired with a large inductor resonates at a low frequency; a small inductor and large capacitor resonate at a high frequency. In practice, resistance is always present in real components, which dampens the resonance and widens the frequency range around resonance where the effect is noticeable.

Resonance in AC power systems and machine design

In electrical power distribution and industrial machinery, resonance can be beneficial or destructive. Series resonance is used intentionally in tuning circuits, induction heating, and impedance matching. Parallel resonance, where inductors and capacitors are arranged in parallel, creates a high impedance at resonant frequency and is used in filter circuits and frequency selection. However, unintended resonance in motors, transformers, cables, and switchgear can lead to excessive currents, voltage rise, component overheating, and insulation failure. Capacitor banks installed for power factor correction sometimes create resonance conditions with the inductance of the supply network, a problem mitigated by detuning reactors or impedance analysis before installation.

The sharpness of a resonance peak is described by the quality factor, or Q. High-Q circuits (low resistance) have a sharp, narrow peak and strong resonant effect. Low-Q circuits (high resistance) have a broad, shallow peak. In motors and generators, Q is determined by copper and iron losses; in capacitor banks, by the internal resistance of the capacitors and connecting conductors. Technicians measure or calculate Q to predict how strongly a circuit will respond at resonance.

Identifying resonance in the field requires careful measurement. A frequency sweep using a signal generator and monitoring voltage or current across the reactive components reveals the resonant peak. In power systems, harmonic analysis equipment detects resonance by revealing where specific harmonics from variable frequency drives or rectifiers match natural circuit frequencies. Once identified, resonance is managed through impedance matching, detuning, filtering, or damping with resistors. The phenomenon is unavoidable in AC systems; control lies in predicting it and designing circuits to operate safely away from resonant frequencies or to exploit resonance where intended.