Question #43451

A full-wave rectifier operates from a $50 \text{ Hz}$ AC mains supply and delivers a constant direct current $I_0 = 28 \text{ mA}$ to a load. The filtering circuit uses a parallel-plate capacitor with a non-linear ferroelectric dielectric. Due to the non-linear energy density locality in the dielectric, the total charge $q$ stored on the capacitor depends on the voltage $V$ across it as $q(V) = C_0 V + k V^2$, where $C_0 = 50 \text{ \mu F}$ and $k = 5 \text{ \mu F/V}$. The peak voltage reached by the capacitor during each charging cycle is $V_0 = 10 \text{ V}$. Assuming the discharge time is approximately equal to the time interval between consecutive voltage peaks, what is the peak-to-peak ripple voltage $\Delta V$ across the load?