Potentiometer Theory

[Jan Olligs]

I completely forgot two things:
1.) Unlike you, I refer with "X" to the resistance of the upper part of the poti, not the length and to the total resistance not as Rt but as R
2.) Because R=s*l/A where s is the specific resistant (constant for same material), l the length of the piece and A its area, ad because A and s are constant within the poti, you get R ~ l. Let's define a constant c so that R = c*l. Now R_total=c*l_total and X=c*l_X, so that

            X            c * l_X           l_X
U2 = U * ------- = U * ----------- = U * -------
         R_total       c * l_total       l_total

and thus, the voltage over the controller behaves to the total voltage as the length of the poti section parallel to the poti to the total length of the poti.

P.S.: poti should mean potentiometer