10 Consider a simple, one-loop RC circuit made of a capacitor C, a resistor R, and an ideal battery which provides a emf \( \epsilon \). After waiting a very long time, the capacitor is fully charged. Find the total energy provided by the battery throughout the charging process, the total energy stored in the capacitor, and the total energy delivered to the resistor. Does conservation of energy hold? Hint: \( P = \frac{dU}{dt} \) or \( dU = Pdt \). Battery: \( P_B = \frac{dU_B}{dt} = \epsilon i(t) \); capacitor: \( P_C = \frac{dU_C}{dt} = \frac{d}{dt}\frac{1}{2C}q^2(t) \); resistor: \( P_R = \frac{dU_R}{dt} = Ri^2(t) \).