I'm back from the trip... a long one!
Yesterday, I tried to record ENERGY-IN and ENERGY-OUT from a JT-analog circuit, by using CAPACITORS to provide the input energy, and to collect the output energy. It worked, sort of. But the efficiency numbers came in around 70%, which was lower than what I had obtained using the MEAN Power calculations, using a Tektronix 3032. I would like to understand this result.
So, I recalled something about apparent non-conservation of energy when stored energy in one cap flows to another cap -- with energy loss being evident. I tried this experiment using two identical 10,000 uF caps. The first was charged to 2.66 volts. Stored energy is 1/2 CV**2.
Then I simply connected this cap to its twin. Then the voltage on each one was the same, 1.33 volts -- of course, by charge conservation:
V = Q/C so by doubling C, the voltage is halved.
BUT -- consider whether ENERGY was conserved:
E = 1/2 CV**2 -- so HALF of the initial energy was lost in the process of simply connecting the charged cap to a twin uncharged-cap! Work it out -- we have two caps in the end, but the voltage was down by 1/2, square that -- energy in each is 1/4 of the initial energy. Two of them, so 2 * 1/4 (Einitial) = 1/2 (Einitial) in the final situation.
What happened to the "missing" energy, or did I do something wrong? (HINT -- if you think I did something wrong, remember I conserved charge but not energy... it appears in this simple experiment, you can't have it both ways.)
OK -- prove the professor of physics wrong... OR if you agree with me that energy was lost, then tell me
HOW do we determine n (in a JT-analog circuit, say) using CAPS to provide the input energy, and to store output energy? That is, do we consider that energy will be LOST necessarily -- as is the case when we directly connect CAPS as in my test above.? (That is, is the n = 1/2 in this case due to the circuit "inefficiency", or simply due to the requirement of charge conservation coupled with the nature of capacitors? are direct-connecting wires really just 50% efficient? I don't think so...)
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