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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.