The resonance of an AC circuit refers to the condition where the inductive reactance ( ) and capacitive reactance ( ) in the
circuit are equal in magnitude but opposite in phase. Mathematically, the resonance condition is expressed by the
equation:In an AC circuit with inductors (L) and capacitors (C), the reactances are frequency-dependent. The inductive
reactance is given by:
f is the frequency of the AC signal,L is the inductance of the coil.
The capacitive reactance is given by:where:f is the frequency of the AC signal,C is the capacitance of the capacitor.
At the resonance frequency (resf es? ), the inductive reactance is equal to the capacitive reactance:Solving for ?
At resonance, the impedance of the circuit becomes purely resistive, and the circuit exhibits certain characteristics:
Maximum Current: The current flowing through the circuit is at its maximum because the impedance is minimized.
Unity Power Factor: The power factor of the circuit is 1 at resonance, meaning the current is in phase with the voltage.
Maximum Power Transfer: In certain applications, such as in antenna design and signal processing, resonance is used to
achieve maximum power transfer.
Resonance is an important phenomenon in AC circuits, and it is often exploited in the design and operation of various
electronic systems, including inductive-capacitive (LC) and resonant RLC circuits.