What is the role of capacitive reactance and inductive reactance in an LCR circuit at resonance?

In an LCR circuit at resonance, the role of capacitive reactance and inductive reactance is that they become equal. At this specific frequency, known as the resonant frequency, the reactive components of the circuit interact in such a way that the effects of the inductance and capacitance balance each other out.

When the inductive reactance (which opposes changes in current) equals the capacitive reactance (which opposes changes in voltage), the overall impedance of the circuit is minimized, allowing maximum current to flow. This condition is crucial for the resonant behavior of the circuit, as it leads to the phenomenon where the circuit can oscillate with maximum amplitude at the resonant frequency.

This relationship is fundamental in the design and analysis of resonant circuits, such as in radio transmitters, where tuning to resonance allows for the selective amplification of certain frequencies. Understanding that at resonance, the two types of reactance are equal enables one to predict and manipulate the circuit behavior effectively.