Averagesupernova said:
My first thought on this was if the OP needs to ask about voltage division, a potentiometer is not the place to start. No disrespect intended. After all, at one time all of us didn't know 'where to start'.
I rather think a potentiometer would be a very good start. Let me explain:
During circuit analysis we very often apply Ohms law in the form V=I*R. That means: We treat the voltage V as it would be "created" (developed) across R by the current I. This works well and all the calculations are correct. However - physically spoken - it is wrong. Vice versa - it is the voltage (and the associated E-field within the conducting material) that allows the movement of charges (current I).
A current through the resistor R can never produce the corresponding voltage V across the resistor R.
This can be best explained (visualized) by one single resistance Rtot (like the total potentiometer path) with a wiper which divides the total resistance Rtot into two parts.
It is clear that the voltage between A and B (see the figure in the original question) creates a corresponding E-field within the material - and allows the current I=V_AB/Rtot. Now - it is obvious that between A and W (and also between W and B) we have smaller voltages because of V=E*L (E-field E constant, L=length between A and W or W and B, respectively). And - of course - the sum of both again is V_AB.
For my opinion, this explains best the principle of voltage division.
If we would start with the other alternative - two discrete resistors - the explanation based on the E-field would be not so clear and we would use instead the relation V=I*R.
As mentioned above, this would work - however, on the basis of a physically wrong assumption.
Not to forget - here we are in a "Physics Forum" and each good electronic engineer should know the physical background of the equations he is using.
(Remark: Some similar considerations apply in connection with the use of the relation Ic=beta*Ib, and some people derive from this equation that Ib would control Ic - but this is not the case. But according to my experience - a very "critical" question).
Remark: Rather often I can read that the voltage-current relation would be a chicken-egg problem. I think, this is not the case and such a wrong view results probably from a wrong interpretation of Ohms law (as explained above). Therefore: No current without a driving voltage - voltage first and current as a result. As a consequence - in reality, there are no real current sources.