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| where does 1/2 come from in capacitor energy calculation |
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| hamster_nz:
--- Quote from: NANDBlog on July 13, 2018, 03:11:17 pm ---And where does the energy go with the two capacitor paradox. https://en.wikipedia.org/wiki/Two_capacitor_paradox --- End quote --- It is because energy isn't the conserved unit in electronics, current is (unless you are keeping track of lost energy, such as heat, light, EM radiation and stray electrons) It is like momentum (mass * speed) is the conserved unit in collisions, not kinetic energy ( energy = 1/2 * mass & velocity ^2) If you have a slow noise to tail, with a car of equal weight then your car will stop, and the other car will roll off with the approximately same speed - as long as the energy is transferred efficiently (much like Newton's Cradle https://en.wikipedia.org/wiki/Newton%27s_cradle). In this case momentum and energy are conserved - it has just been moved to the other car. This is like the energy transfer in a switch mode power supply - it transforms the voltage and current to ensure a good match between the source and load, allowing for efficient transfer (usually by moving energy in and out of an inductor). However, if you have a more energetic crash nose to tail crash, one where the structure of the car cannot transfer the energy efficiently both cars will tend to stick together and move off at half the original speed. In this case only momentum is conserved, but half the energy is missing (as twice the mass is moving at half the speed) - much like the energy in the two capacitor 'paradox'. So where does the missing energy go? Humm, I don't know, but just maybe that big bang and the crumpled metal had something to do with it... |
| SparkyFX:
--- Quote from: woodchips on July 13, 2018, 04:03:15 pm ---You have two caps, each 1F 10V, one fully charged, one not. Energy 1/2CV^2 is 1/2x1x10^2 = 50J. Connect in parallel, now have two caps total of 2F at 5V, Energy 1/2CV^2 is 1/2x2x5^2 = 25J. To me, 25 is half of 50? --- End quote --- Sorry to answer 2 years later, but (1/2x2x5)^2 = 25J. (1/2x1x10)^2 = 25J. |
| Nominal Animal:
--- Quote from: SparkyFX on March 16, 2020, 05:55:27 am ---Sorry to answer 2 years later, but (1/2x2x5)^2 = 25J. (1/2x1x10)^2 = 25J. --- End quote --- True, but irrelevant in this context. The energy E stored in a capacitor with capacitance C and voltage V across the capacitor is E=0.5CV2, not (0.5CV)2. |
| SparkyFX:
Right, the problem is the assumption of half voltage, while the charge curve indicates an exponential function per energy stored. The voltage in the new parallel system will be 7.07V, given the same energy is stored, then it will match the new capacity. I started from the wrong end of the wrong statement in the wrong way, sorry :) |
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