When I opened this thread, I suspected that I might also be opening a can of worms in so doing: and indeed, it looks like I was correct! Moreover, a subsequent trawl around the 'Net has shown me that this apparent paradox has received a wide audience and that various theories, ideas and suggestion are manifest: I did not know that this was such a much-debated issue when I opened this thread.
However, after reading all that has been written, here and on the 'Net, I have come to my own conclusions. Yes, there is an 'energy loss', but that energy loss is imaginary. The whole concept of the Conservation of Energy is solidly rooted in the concept of a 'closed system'. If we consider that system as only the capacitors and their zero-resistance connections, then the paradox arises. But regarding 'the system' as consisting only of those components is a fallacy: 'the system' includes the surrounding medium, and that is where the 'lost' energy goes: as electro-magnetic radiation. That radiation will meet a resistance and that provides the 'missing resistance' for that otherwise unaccounted energy to be dissipated.
Philosophically, the problem arises because with with the zero resistance scenario there is a step jump of current that goes to infinity, and mathematically, that causes a bit of a problem. Although having said that, even with a series resistance added, there is still a step of current, albeit less, so it would seem that some energy will still be radiated.
I now tender these thoughts of mine for consideration by our community here: all comments will be appreciated and read (as have been the ones previous to this post): thank you.
And a pleasant Easter to you all.
Al. / Skywave / March 30th., 2013
However, after reading all that has been written, here and on the 'Net, I have come to my own conclusions. Yes, there is an 'energy loss', but that energy loss is imaginary. The whole concept of the Conservation of Energy is solidly rooted in the concept of a 'closed system'. If we consider that system as only the capacitors and their zero-resistance connections, then the paradox arises. But regarding 'the system' as consisting only of those components is a fallacy: 'the system' includes the surrounding medium, and that is where the 'lost' energy goes: as electro-magnetic radiation. That radiation will meet a resistance and that provides the 'missing resistance' for that otherwise unaccounted energy to be dissipated.
Philosophically, the problem arises because with with the zero resistance scenario there is a step jump of current that goes to infinity, and mathematically, that causes a bit of a problem. Although having said that, even with a series resistance added, there is still a step of current, albeit less, so it would seem that some energy will still be radiated.
I now tender these thoughts of mine for consideration by our community here: all comments will be appreciated and read (as have been the ones previous to this post): thank you.
And a pleasant Easter to you all.
Al. / Skywave / March 30th., 2013