Walker, Halliday & Resnick — Electromagnetic Oscillations and Alternating Current: Problem 16

16 In a series oscillating RLC circuit, $R = 12.0\ \Omega$, $C = 31.2\ \mu\text{F}$, $L = 9.20\ \text{mH}$, and $\mathcal{E} = \mathcal{E}_m \sin \omega_d t$ with $\mathcal{E}_m = 45.0\ \text{V}$ and $\omega_d = 3000\ \text{rad/s}$. For time $t = 0.442\ \text{ms}$ find (a) the rate $P_g$ at which energy is being supplied by the generator, (b) the rate $P_C$ at which the energy in the capacitor is changing, (c) the rate $P_L$ at which the energy in the inductor is changing, and (d) the rate $P_R$ at which energy is being dissipated in the resistor. (e) Is the sum of $P_C, P_L,$ and $P_R$ greater than, less than, or equal to $P_g$?