An ideal battery in a closed loop is connected in series with a resistor and a capacitor (with the resistor placed closest to the battery's positive terminal). There is a switch between the battery and the resistor. The switch closes at t = 0 s and, after a very long time, the capacitor is fully charged. Find expressions for (a) the total energy supplied by the battery as the capacitor is being charged, (b) total energy dissipated by the resistor as the capacitor is being charged, and (c) the energy stored in the capacitor when it is fully charged. Your expressions will be in terms of the emf, R, and C. (d) Do your results for parts a to c show that energy is conserved? Explain