Re: There's work, and then there's work

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 20:22 -0800 2/2/03, David Rutherford wrote:
> Then how do the charges continue on to the other plate of the capacitor,
> in order to equalize the potentials of the plates, if they've expended
> all of their kinetic energy in the resistor? If what you say is true,
> you could install a galvanometer downstream from the resistor and it
> would show zero current during the discharging of the capacitor. I
> assume that's not what's observed.
Well, for one thing, the charges don't get all the way to the other
plate. The charges that get to the other plate to neutralize the
capacitor are in the wire near the plate they end up on. Think of a
garden hose full of water. If you turn on the faucet for just a brief
time, the water that comes out of the business end of the hose is not
the same water that just came out of the faucet. The drift speed of
the electrons in the wire (and the resistor) is only a fraction of a
millimeter per second (you can figure that out by calculating the
number of electrons that must cross a line in the wire per second to
maintain the necessary current. Almost all of their kinetic energy is
thermal, or due to the random nature of the electron motion.

But that aside, it is not the kinetic energy that the electrons give
up in passing through the resistor (actually, they may even gain a
tiny bit, since the resistor is getting warmer as a result of the
current). What the electrons are losing is their electrical potential
energy. Imagine a ball rolling down the hill through tall grass. Its
speed will be pretty much constant, but at the bottom of the hill it
will have less energy than it did at the top--in this case,
gravitational potential energy. The electrons are rolling down an
electrical hill through tall electrical grass. At the bottom they
still have whatever kinetic energy they had at the top but now they
have less electrical potential energy.

Please, get yourself an introductory physics text and read it. All of
this is well described there.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

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