When the input frequency of an RLC circuit matches the resonant frequency, a phenomenon called resonance occurs. An RLC circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series or parallel. The resonant frequency of the circuit is determined by the values of the inductance and capacitance:
Resonant Frequency (f_res) = 1 / (2 * π * √(L * C))
When the input frequency matches the resonant frequency (f_input = f_res), the following effects are observed:
Maximum Current: The current flowing through the circuit reaches its maximum value. This occurs because at resonance, the inductive and capacitive reactances cancel each other out, leading to an overall decrease in impedance. Consequently, more current can flow for a given voltage.
Voltage Across Components: The voltage across the capacitor and inductor will be out of phase by 180 degrees. At resonance, the voltages across these components are at their maximum. The voltage across the resistor will also be at its maximum.
Minimum Impedance: The total impedance of the RLC circuit is at its minimum value at resonance. This is due to the cancellation of inductive and capacitive reactances, leaving only the resistance as the dominant component of impedance.
Energy Exchange: Energy oscillates between the inductor and capacitor continuously at resonance. The inductor stores energy in its magnetic field, while the capacitor stores energy in its electric field. As the cycle repeats, the energy is exchanged between the two components.
Phase Shift: At resonance, the phase shift between the current and voltage across the resistor is zero, meaning they are in phase. However, the voltage across the capacitor and inductor will be 180 degrees out of phase with the current.
Maximum Amplitude in Series Circuit: In a series RLC circuit, the voltage across the entire circuit is maximized at resonance. This is because the voltage drop across each component (resistor, inductor, and capacitor) reaches its maximum value.
Resonance has significant practical applications, such as in tuning radio receivers and in various filtering and signal processing applications. However, it's essential to handle resonance with caution, as it can lead to high currents and voltages, potentially causing damage to components if not properly managed. Engineers often incorporate resonance control techniques to prevent unwanted resonance effects in circuits.