I have some questions about the energy stored in capacitors. Looking in Physics books, there are two equations which govern the amount of energy stored in capacitors: Energy in Joules (Watt*Seconds) = .5 * Q^2/C Where Q is the charge in couloumbs and C is the capacitance in Farads. Energy in Joules (Watt*Seconds) = .5 * V^2 * C Where V is the voltage. Now, if you were to take a 100F capacitor and charge it to 2.5 volts, the energy would be .5 * 2.5*2.5 * 100 = .5 * 6.5 * 100 = 312.5 Joules If you take the very same capacitor and double the voltage. This time you charge it to 5 volts... energy would be .5 * 5*5 * 100 = .5 * 25 * 100 = 1250 Joules So, if you raise the voltage by 2, you get 4 times the stored energy? What kind of magic is that? How can you get a four-times increase of energy just by doubling the voltage? Wouldn't that be cold fusion or perpetual motion if I could do that? In theory, if you could get a four times increase in energy just by increasing the voltage twice, couldn't you increase the voltage to 10,000 volts, put a bunch of high-capacitance capacitors together and store 500,000,000 joules of energy? If that were the case, we could harness the power of chain letter math. Something has to give if you increase the voltage on the same capacitance. You can't get four times the amount of energy out just by raising the voltage twice, can you? And, if so, where did that power of two come from anyways? What combination of two other equations gives you the V squared? The secret can't be with charge, because charge is also linear. You raise the voltage by two, the charge increases by two. Secret can't be the capacitance, because you're using the very same capacitor in both cases. Equation that governs charge, and capacitors. Q = CV Or, swapped around... V = Q/C So, what am I missing? What goes down to compensate as the apparent energy goes up? The capacitance is staying the same. The voltage is doubling. The charge is doubling. where does the 'four times more energy' come from? I can envision that possibly the answer might be time. Could the extra energy be allowable because time is the secret missing variable? Could the time it takes to charge it up that extra amount be the answer to the hidden 'where did the energy come from?. If not, then what compensates by dropping to balance out that four-times-the-energy value? You can't really get four times the energy just by doubling the voltage, can you? And, if you can get four times each time you double the voltage, why can't you just charge up capacitors to a couple hundred volts, then drop them back down to a lower voltage when you want to use them?