Resonance in a parallel R-C-L circuit will occur when the reactive current in the inductive branches is equal to the reactive current in the capacitive branches (or when X_L = X_c). Because inductive and capacitive reactance currents are equal and opposite in phase, they cancel one another at parallel resonance.

If a capacitor and an inductor, each with negligible resistance, are connected in parallel and the frequency is adjusted such that reactances are exactly equal, current will flow in the inductor and the capacitor, but the total current will be negligible. The parallel C-L circuit will present an almost infinite impedance. The capacitor will alternately charge and discharge through the inductor. Thus, in a parallel R-C-L, as in Figure 10, the net current flow through the circuit is at minimum because of the high impendence presented by X_L and X_c in parallel.

Summary

Resonance is summarized below.

Resonance Summary

Resonance is a state in which the inductive reactance equals the capacitive reactance (X_L = X_c) at a specified frequency (f_Res).

Resonant frequency is:

R-C-L series circuit at resonance is when net reactance is zero and circuit current output is determined by the series resistance of the circuit.

R-C-L parallel circuit at resonance is when net reactance is maximum and circuit current output is at minimum.