John Larkin wrote:
On Sat, 17 Jul 2010 02:42:20 -0400, ehsjr
wrote:


Paul Hovnanian P.E. wrote:

My solution for the missing energy.


But John's puzzle stated that energy *is* conserved,
so there is no missing energy in his puzzle.

He said _charge_ was not conserved, in some cases.

Or maybe it's a different puzzle? What I recall was a 4F cap
that was charged to .5 volts, therefore Q=2 coulombs. He magically
cut in half. (I don't know why he didn't start with 2 caps, 2F
each, in parallel.)

The resultant 2F caps each retained the .5V charge
for Q=1 coulomb per cap.

He then puts them in series resulting in
*a 1F cap charged to 1 volt* which is Q=1 coulomb,
and claims there's 1 coulomb missing.

That's the fallacy. The result is NOT a 1F cap.
The result is 2 2F caps, in series. Each cap
has Q=1 coulomb - there is no missing coulomb.
Doesn't matter that total circuit C = 1 F.

Ed


But every 1F cap is, internally, two 2F caps in series. Just draw a
dotted line midway through the dielectric. Play that game all you
want.

That "game" leads nowhere.
It implies that all capacitors are internally a series string of
infinitely small (physical) capacitors and infinitely large
capacitance for each.

This all reminds me of the 3 men rent a hotel room puzzle.
The clerk tells them it will be 30 dollars, so each hands
him a 10 dollar bill. Later, the clerk realizes he's made
an error, the rate is only $25. So he gives 5 ones to the
bellhop & instructs him to give the money back to the men.
The bellhop can't divide it equally, so he goes to their
room and hands each man a dollar, and pockets the other 2
bucks. Now, each man has gotten a dollar back, so each
has given a total of $9 to the clerk. That's $27, and the
bellhop has 2 bucks in his pocket.
Where is the other dollar?




After the two 1F caps are separated and rearranged in series, if you
discharge them through a resistor, you will recover 1 coulomb.

My point all along is that, in actual circuit design, the generalism
"charge is conserved" is dangerous, given that "charge" is
ampere-seconds that you can actually measure and use.

Well, I don't see any inconsistancy in putting "stuff" in at
one rate, and getting that "stuff" out at another, whether it's
water into bottles, cookies into bags, electrons into conductors,
whatever. You get the same amount of "stuff" out as you put in
(assuming you empty the container), but the time taken to do it
is different.

Ed


John