# Where did the energy go?

Discussion in 'Homework Help' started by Heavydoody, Feb 28, 2010.

1. ### Heavydoody Thread Starter Active Member

Jul 31, 2009
140
11
"A capacitor of capacitance C is charged to a potential difference Vo. The terminals of the charged capacitor are then connected to those of an uncharged capacitor of capacitance C/2. Compute: a) the original charge of the system; b) the final potential difference across each capacitor; c) the final energy of the system; d) the decrease in energy when the capacitors are connected; e) Where did the "lost" energy go?"

Here's what I get:

I believe this to all be accurate. I am having difficulty with the last part: Where does the energy go? I suspect it leaves the system as heat, but that is just a guess, and I cannot seem to locate the answer in my textbook. Can anyone answer this for me?

Apr 20, 2004
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3. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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This is a 'conundrum' that has been discussed for many years.

If this is a purely theoretical problem in which it is assumed there are no switching [spark / arc], resistive or dielectric loss allowed in the circuit then a likely explanation is that the energy is lost as an electromagnetic wave which propagates from the circuit during the instantaneous charge redistribution.

In a real physical circuit it is probably a combination of many factors which you would include in a realistic circuit model.

Also, keep in mind that a physically realizable circuit would have some inductance as well.

Last edited: Feb 28, 2010
4. ### Heavydoody Thread Starter Active Member

Jul 31, 2009
140
11
This seems like a logical explanation. It's particularly confusing to me since none of the calculations account for any "friction" due to resistance in conductors (my heat theory). Nor does the type of dielectric seem to matter (note the lack of permittivity in the equations). Interaction with external fields is likewise neglected. It is like the frictionless ramp problems...except that here, even though this is an optimized, theoretical problem, we still wind up losing energy from our "isolated" system.