You don't need any theorems to explain this.
It is a classic example of internal resistance of the battery. This is a factor in any electrical component and has the formal title of
Equivalent Series Resistance - or
ESR. Understanding this is extremely important in understanding how components actually work in the real world......
(There are also capacitance and inductance parameters you should get to know - but you won't need to worry about those for this exercise.)What you have created is a simple voltage divider that uses the internal resistance of the battery (
which, from the conditions mentioned, appears to be somewhere around 28ohm {This is indicative only. Failing battery chemistry, variable usage and rest cycles will result in this varying significantly during experiments}) and the potentiometer, which you have wired as a simple variable resistor (only using the wiper and one end terminal).
This rough sketch shows the circuit you have constructed, in two different layouts. In both cases, the dotted line represents the physical case of the battery, which is absolutely irrelevant in assessing the electrical circuit.
The layout on the left is how it is commonly viewed, but the layout on the right makes it much more clear for seeing the voltage divider at work.
When the pot
R is turned to minimum resistance (ie zero) there will be no voltage across it and the full voltage drop will occur across the internal resistance
r of the battery. The resulting power loss will heat up the battery (how much will depend on how fresh the battery is).
When the pot is turned to maximum (10K), then the pot will have a far greater resistance than the internal resistance of the battery - and will, therefore, have the greatest voltage drop.
At points along the potentimeter's rotation, there will be a smooth but non-linear voltage change. This is what you have observed.
On the point of burning the pots - let me guess.... At 10K, they survive. At zero, they survive. But when you move them just off from zero, the magic smoke appears...?