When an electric current (I) flows through an inductor and a capacitor connected in series, the voltage at the terminals of this LC circuit is zero (0) for some frequency fo of the applied signal.
This only happens when the voltage at the terminals of the inductor L and the voltage at the terminals of the capacitor C are equal in magnitude but opposite in phase.
In other words:
VL = VC
Where: VL = IXL, VC = IXC
Since these two elements are in series, the electric current flowing through them is the same (I). Then: XL = XC
We know that: XL = 2πfoL = woL and XC = 1/(2πfoC) = 1/(woC). Where: wo = 2πfo
Equating the absolute values of XL and XC;
fo is called the resonant frequency.
Similar condition exists when an inductor and a capacitor are connected in parallel.
The series LC circuit and the parallel LC circuit are called resonant circuits.
