Past exam of the physics 2 paper of the University of Oxford / 2013 resit / 10 / ii / Solution

The source figure has a series capacitor followed by $R$ in parallel with $L$. Its complex impedance isThe imaginary part vanishes at a finite positive frequency only if $R^{2}C>L$, in which caseAt that frequency, substituting $R^2+{\omega }_{\ast }^2{L}^2={\omega }_{\ast }^{2}L{R}^{2}C$ into the real part givesIf $R^{2}C\le L$, no finite positive-frequency cancellation exists; the impedance merely tends toward its high-frequency limit.