Lossy parallel coil resonance (${\omega }_r^2=1/(LC)-R^2/L^2$)

A series circuit comprising electrical resistance $R>0$ and inductance $L>0$, placed in a parallel circuit with capacitance $C>0$, has electrical admittance $Y=(R+i\omega L{)}^{-1}+i\omega C$. Vanishing imaginary part at nonzero angular frequency gives the displayed condition, requiring $L>R^{2}C$. It defines zero voltage-current phase difference, which need not coincide exactly with the maximum of impedance magnitude when loss is present. At this frequency the electrical impedance is real and equals $L/(RC)$.