Past exam of the physics 2 paper of the University of Oxford / 2016 / 11 / i / a / Solution

A series connection has the same electric current through each element, so complex impedances add:For $R>0$, define $\varphi =\arg \tilde{V}-\arg \tilde{I}=\arg Z_{\mathrm{s}}$. ThenAbove resonance, the circuit is inductive and electric potential difference leads current; below resonance it is capacitive and electric potential difference lags current. Atthe inductive and capacitive reactances cancel and $Z_{\mathrm{s}}=R$ is purely resistive. The same resonance condition holds for an ideal series circuit independent of the drive amplitude.