Question #43338

This question tests the fundamental energy-based definition of the Quality Factor (Q-factor) and the physical reality of core losses in AC circuits.

Students are heavily conditioned to blindly apply the lumped-parameter formula $Q = \frac{1}{R}\sqrt{\frac{L}{C}}$, which yields $Q = 100$ (Option D).

This formula assumes that all energy dissipation is purely ohmic.

However, in a real inductor with a ferromagnetic core, the hysteresis loop area represents an additional, frequency-dependent energy loss per cycle.

To solve this correctly, the student must abandon the standard formula, calculate the total energy dissipated per cycle (ohmic + hysteresis), and use the foundational definition $Q = 2\pi (E_{\text{stored}} / E_{\text{dissipated}})$.

This effectively models the hysteresis as an equivalent series resistance $R_{\text{eff}} = R_{\text{ohmic}} + \frac{\omega_0 A_h V}{\pi I_0^2}$.