**Parallel RLC resonant circuit is also used to model a resonator in the resonance mode. Resonator is a system, that is experiencing the resonance phenomena. Resonance in RLC circuit occurs when power stored at inductor is equal to power stored at capacitor.**

The example of parallel RLC resonant circuit is depicted below.

In case of parallel connection ${Z}_{in}=\frac{1}{({\displaystyle \frac{1}{R}}+{\displaystyle \frac{1}{j\omega L}}+j\omega C)}$. So power delivered to resonator is ${P}_{tot}={\frac{\left|V\right|}{2}}^{2}(\frac{1}{R}+\frac{j}{\omega L}\u2013j\omega C)$.

Power stored at the inductor $L$ is ${P}_{L}=\frac{{\left|V\right|}^{2}}{4{\omega}^{2}L}$. Power stored at the capacitor $C$ is ${P}_{C}=\frac{{\left|V\right|}^{2}C}{4}$. And power that dissipates at the resistor ${P}_{R}=\frac{{\left|V\right|}^{2}}{2R}$.

So ${P}_{tot}=\frac{{\left|I\right|}^{2}{Z}_{in}}{2}={P}_{R}+2j\omega ({P}_{L}\u2013{P}_{C})$. Here we can find that ${Z}_{in}=\frac{{P}_{tot}+2j\omega ({P}_{L}\u2013{P}_{C})}{{\displaystyle \frac{1}{2}}{\left|I\right|}^{2}}$.

Resonance phenomena occurs when energy stored at inductor is equal to energy stored at capacitor, then ${Z}_{in}=\frac{2{P}_{tot}}{{\left|I\right|}^{2}}=R$.

The resonance frequency here is ${\omega}_{0}=\frac{1}{\sqrt{LC}}$ (the same as for series RLC resonant circuit). Quality factor for unloaded RLC circuit is ${Q}_{0}={\omega}_{0}RC$.

Let’s consider circuit behaviour near resonance frequency ${\omega}_{0}+\u2206\omega $, where $\u2206\omega \ll {\omega}_{0}$. So ${Z}_{in}\approx \frac{{\omega}_{0}}{{\omega}_{0}+2j{Q}_{0}\u2206\omega}$.