Parallel LC circuit

An ideal inductor and capacitor in parallel have electrical admittance $1/Z=1/(j\omega L)+j\omega C$ for phasors with time dependence $e^{j\omega t}$. The branch currents cancel at angular frequency ${\omega }_0=1/\sqrt{LC}$, giving zero total electrical admittance and an infinite limiting electrical impedance. Below this resonance its electrical reactance is positive; above it the electrical reactance is negative. Losses make the peak finite.