The values of inductance (L) and capacitance (C) determine the natural resonant frequency of an electrical circuit. Resonance occurs when the inductive and capacitive reactances become equal in magnitude, causing them to effectively cancel each other. The resonant frequency is given by fᵣ = 1/(2π√LC). Therefore, changing either the inductance or capacitance changes the resonant frequency. If a harmonic frequency in the system is equal or close to this resonant frequency, harmonic resonance can occur, potentially producing excessive voltage or current and stressing electrical equipment.
LC Resonance & Harmonic Resonance Simulation
The natural resonant frequency of an LC circuit depends on its inductance L and capacitance C. When the inductive reactance and capacitive reactance become equal in magnitude, resonance occurs. A harmonic frequency close to the resonant frequency can produce large current and voltage stresses in an electrical system.
1. Adjust Inductance and Capacitance
2. Calculated Electrical Parameters
Resonant Frequency
Harmonic Frequency
Frequency Difference
fr = 1 / (2π√LC)
3. LC Circuit Visualization
4. Reactance vs Frequency
5. What the Simulation Demonstrates
Inductive reactance: XL = 2πfL. It increases as frequency increases.
Capacitive reactance: XC = 1/(2πfC). It decreases as frequency increases.
At the resonant frequency:
XL = XC
The inductive and capacitive effects therefore cancel each other in the idealized series LC circuit. If a harmonic frequency approaches the resonant frequency, the circuit can experience a significant increase in current and voltage. In practical power systems, resistance, damping, transformer impedance, network configuration and other factors limit the actual amplification.