Question #42024

A primary coil is driven by an alternating current $I_1(t) = I_0 \sin(\omega t)$. A secondary coil with self-inductance $L$ and negligible resistance is magnetically coupled to the primary with a mutual inductance $M > 0$. The secondary coil is connected in series with a load $Z$. The reference direction for the secondary current $I_2(t)$ is chosen such that positive $I_1$ and positive $I_2$ produce magnetic flux in the same direction in the core. Let $\Delta \phi$ be the phase difference such that the steady-state secondary current is $I_2(t) = I_{20} \sin(\omega t + \Delta \phi)$ with $I_{20} > 0$. If $\Delta \phi_L$ is the phase difference when $Z$ is an ideal inductor $L_0$, and $\Delta \phi_C$ is the phase difference when $Z$ is an ideal capacitor $C_0$ (where $\frac{1}{\omega C_0} > \omega L$), what are the values of $\Delta \phi_L$ and $\Delta \phi_C$ respectively?