Re: battery

[John Denker <jsd@AV8N.COM>]

Ludwik Kowalski wrote:
> The textbook I am using states:
> "The real battery, however, always has some
> internal resistance r. As a result, the terminal
> voltage is not equal to the emf."
>
> I do not like the "as a result" phrase.

I dislike several things about the quoted statement.

For starters, the thing they seem to be calling "emf"
has for the last jillion years or so been called the
"open-circuit voltage" or "Thevenin equivalent voltage"
or some combination of the two, such as "Thevenin
open-circuit voltage".

Also Ludwik is quite right to be suspicious of the alleged
origin of the observed Thevenin-equivalent impedance.
Batteries are remarkably tricky little creatures.  The
I/V characteristic is nowhere near linear.
 -- For small currents, the dominant effect has to do
with the chemical rate constants, and how much you shift
the rates by shifting the electrochemical potential.
 -- For larger currents, the dominant effect is diffusion
through the electrolyte.  Ionic mobility and all that.
 -- I suspect that in any halfway-well-designed battery,
ohmic losses in the metal parts is a quite small effect.

> The change of resistivity
> of wires (due to ohmic heating) is small

yes.

> and
> the same is probably true for the electrolyte,
> unless the number of free carriers drops
> significantely.

I disagree.  Ions move a lot slower than electrons.
The ionic conductivity of liquids is remarkably poor
compared to the electronic conductivity of ordinary
metals.