9.8: Series Resonance
The RLC circuit impedance is defined as the ratio of the supply voltage to the circuit current. Resonance in such a circuit occurs when the imaginary part of this impedance equals zero. This specific condition means that the inductive reactance is exactly equal to the capacitive reactance. The frequency at which this happens is known as the resonant frequency. Mathematically, the resonant frequency is inversely proportional to the square root of the product of the inductance (L) and capacitance (C).
At this resonant frequency, the series combination of the inductor and capacitor behaves like a short circuit. Consequently, the circuit acts purely resistive, meaning the impedance is at its minimum, and the circuit allows maximum current flow. This also results in the voltage and current being in phase, achieving a unity power factor.
When resonance is achieved, the impedance reaches its minimum magnitude, allowing maximum current flow through the circuit. Additionally, at resonance, the voltage across the inductor and capacitor can greatly exceed the source voltage due to the quality factor of the circuit, which indicates the circuit's efficiency at its resonant frequency. This phenomenon is critical in applications like radio tuners and filters where signal strength for a selected frequency needs to be enhanced.
The series resonant circuit is characterized by the resonant frequency, where the circuit exhibits purely resistive behavior with maximal current. During the resonance condition, the inductive and capacitive reactance current increases many folds from its standard value. Still, this effect is not observed as inductive and capacitive reactance cancel out each other's effects. The resonant frequency is crucial in various applications, including tuning circuits in radio transmitters and receivers, where the ability to select or reject specific frequencies is essential.
