>> Yes, more exactly, there are devices which do not have constant 
>> resistance/impedance.
>
> Are you saying the resistence doesn't determine the current? Or are you 
> just saying that the current can cause the resistence to change?

If you want to look at it like that, yes, the resistance will depend on what 
the applied voltage is, rather than always being constant.  Nobody really 
talks of "resistance" with such devices though, it's just accepted that V is 
not linearly proportional to I, and that for any given V you can look up the 
I from the chart.

> Now, see, I always thought electricity just takes *every* path, with the 
> current being determined by Ohm's law.

It does, and if use Ohm's law to work out the voltage at a point that is 
connected to 0V with a 1kOhm resistor and to 5V with a 1Mohm resistor, you 
will see the voltage is essentially 0V.  OK so it will actually be very 
slightly above 0V, but that's why there is a tolerance range on the input of 
such devices.

> So, if you have a high-resistence path from A to B, and then you add a 
> second, lower-resistence path from A to B, does the current flowing 
> through the first path change? Or does it remain the same?

It remains the same because neither the voltage across the high value 
resistor, nor the resistance of the resistor itself have changed, and then 
I=V/R.  Of course you get some additional current flowing through the lower 
resistance path now, but still the same amount through the high resistance.

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