> I thought the voltage of a battery only decreases if you try to draw 
> current faster than the chemical processes inside the battery can restore 
> it? (I.e., it's a flaw parculiar to chemical batteries.)

No, it decreases the instant start to draw any current.  Maybe trying to 
teach you about complex AC circuit theory and power electronics was a bad 
starting point :-)

When you connect a resistance, R, to a battery, the circuit you have made is 
identical to a true, fixed voltage source (say 12V), with two resistances 
connected in series.  One of the resistances is R, the one you connected, 
the other, called the internal resistance, Ri, is representing the resistive 
parts of the battery that you have no control over.

You can analyse this circuit easily.  You have a voltage, V of say 12 V, and 
a combined resistance of R+Ri.  So the current is found by Ohm's Law, and is 
equal to 12 / (R + Ri).

Now that you know the current in the circuit, you can work out the voltage 
across each resistor, again using Ohm's law.

For the resistor you just connected, R, the voltage across it will be given 
by I * R.  You know I because we just calculated it, so the voltage is 12*R 
/ (R + Ri).

If Ri is very small compared to R, then this is approximately just 12 volts. 
But when R gets small enough the voltage can no longer be approximated by 12 
volts.  And when R gets very much smaller than Ri, the voltage essentially 
becomes zero.

If the voltage R *is* zero, ie you have connected a thick wire or 
super-conductor between the terminals, then the voltage will be given by 
12*0/(0+Ri), ie zero volts.  *But* the current is still defined by 12 / 
(R+Ri), so that simply becomes 12/Ri.  This is the maximum current a battery 
can deliver.

This explains why on old cars the radio switches off momentarily as you 
start your car - due to the huge current drawn from the starter motor the 
battery voltage drops, often to as low as 6 or 8 V.  Also when charging the 
battery the opposite happens, and the voltage often goes up to 13 or 14 
volts.

I'll leave it as an exercise to work out the maximum power the battery can 
output...

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