Re: Capacitance problem

["Donald E. Simanek" <dsimanek@eagle.lhup.edu>]

On Sun, 30 Mar 1997, brian whatcott wrote:

> At 09:55 AM 3/30/97, Donald E. Simanek wrote:
> > ... Why does the result (half the energy goes
> > elsewhere) *not* depend on these particular details? If the only loss were
> > radiative, you'd get 1/2 for the energy loss. If the only loss were
> > resistive, you'd get 1/2. If it is a combination of both, you'd get 1/2.
> > I chose identical capacitors, which is one reason you get 1/2, but that
> > was only for convenience of discussion. The principle (if there is one)
> > could be applied to any pair of unequal capacitors, and the resulting
> > fractional energy loss would be a different value. 
> > ...
> > Dr. Donald E. Simanek
>
> I see the virtue of your complaint - and I scrabble for a handhold on
> the correct ledge. Here is one that may just be involved.
>
>    When the electrical engineer wants to transfer energy at the maximal rate
> he ensures that the source impedance matches the terminal impedance
> and accepts that in this case, half the available energy will be dissipated 
> in the transfer mechanism. He even assigns a name to this principle.
>
>      When the electrical engineer wishes to transfer energy efficiently,
> he ensures that the load represents a much higher impedance than the source 
> and interposes fuses to ensure this will remain the case.
>    An example of the maximum power theorem is the automobile starter: does 
> the battery voltage not sag to 6 volts?  

Well, yes, this is an example of the sort of general principle I was
fishing for. I'm not sure how we'll apply it to the capacitor problem.

Another example would be the Thevinin and Norton theorems which tell us
that a circuit will behave in a certain manner with respect to two
terminals *no matter what combinations of emfs and resistors* the circuit
is made up of.

I was really hoping that someone more math savvy than I knew already what
principle might apply to the capacitor problem, and jump in and enligten
us all. Maybe there is no such principle, and this thread will die.

It's one of those things that tantalizes, making one think that when a
precise result is *so independent of specific details*, then there *ought
to be* a general principle predicting that result. Maybe that's the
clearest statement of my concern that I've been able to state so far. When
I posted this I fully expected someone to say "What's the matter, Donald,
didn't you learn Schwartzengruber's Dissipative Energy Particition
Principle in college"? (I made that up.)

	-- Donald

......................................................................
Dr. Donald E. Simanek                            Office: 717-893-2079
Prof. of Physics                    Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745          CIS: 73147,2166 
Home page: http://www.lhup.edu/~dsimanek            FAX: 717-893-2047
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