A capacitor is not an ideal energy storage medium, and it's VERY non linear over time voltage and current drop at an exponential rate. A 480 farad capacitor at 12 volts is not practical, aside from the non linear nature, high farad capacitors are usually only in the 2.5 volt range and even then 480 farads would require one hell of an array. The price would probably make you crap your pants as I have 1 farad 5 volt cap's that cost 2.50 each, your equations are direct energy relation equations and don't take into account the real world nature of energy and it's conversion efficiency.