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Let me return to the initial issue of the so-called
"internal resistance" of the battery. This concept
is extremely useful; a battery does behave as if an
emf was in series with a resistance. That resistance
does not have to remain constant; like in a filament
of a light bulb, it may depend on the current. But
the phenomenon (drop of DOP with the current)
might have nothing to do with the resistivity of
substances inside.
Here is another illustration. In many power
supplies the external resistance R2 is connected
to a charged capacitor C. That capacitor is charged,
for example 60 or 120 times per second, to keep
the DOP between the terminals constant. The
rate of charging is determined by the R1*C, where
R1 has to do with the transformer, with the diode,
etc. As long as R1*C << R2*C (small current)
the DOP is essentially constant. But the DOP
starts dropping rapidly with the current when
this condition is no longer satisfied. In the model
we can say that the internal resistance of the
source, r, becomes significant when the current
becomes excessive. But we can explain the
drop of DOP with I without introducing the
concept of r. We can say that the DOP drops
because the rate of charging is not able to
keep up with the rate of discharging.
Ludwik Kowalski
On Saturday, Mar 20, 2004 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. We do
observe that the DOP between the terminals
becomes smaller when the load current goes
up. And then we invent a model, an ideal
batterry in series with a resistor. In reality
the difference between the emf and the DOP
may be due to something else than limited
conductivities. The change of resistivity
of wires (due to ohmic heating) is small and
the same is probably true for the electrolyte,
unless the number of free carriers drops
significantely.
The invented model is very useful but it is
not an explanation. A real explanation must
deal with some current-induced processes
taking place inside a baterry. What are they?
Ludwik Kowalski