Heres a simple explanation why the contact doesn't interpolate... no doubt you still won't get it. It doesn't involve any math.
Voltage A +-----+-----+-----+ | | | | R R R R | | | | V---L1--+--L--+--L--+--L--+---L2---GND V1 V2
How the hell can the voltage A a be any different no matter what L is(the inductance of one turn) and what R is? Your telling me as you move the contact it "interpolates"? So if we move the contact to the left it now somehow interpolates between the voltages?
The above is identical to
Voltage A +-----+-----+-----+ | | | | R R R R | | | | V---L1--+--L--+--L--+--L--+--L--+--L---L2---GND V1 V2
Where now the contact as moved to the left. It hasn't interpolated between any voltages. It has simply been shifted and the voltage reduced. It would be exactly(almost anyways) the same as if the contact had 20 points of contact or just 1.
A is basically The average voltage across the contacts and this average voltage shifts exactly by the same amount as if it were just one point of contact.
YOU CAN ONLY CHANGE IN DISCRETE STEPS!!!!. But when you move the contact you do not add any current paths!
But it doesn't matter. All the resistors have the high side at the same f****ng potential. As you move the contact one turn to the left or right you have increased or decreased that by a constant discrete amount. Each time you do it you move it in a discrete step. There is no damn interpolating.
Yet I guess that is even too hard for you to understand?
How can the contact be at different potentials?
Now for all the f****ng genius that believe the contact interpolates heres the f****ng reason for a contact - It makes contact wtih more than 1 turn so that the contact will always have a voltage on it. It can't get stuck between two turns and not output a voltage. It also smooths voltage as you turn. (that is not interpolating)
e.g., As you turn you might add a turn and loose a turn but because the turns are not spaced perfectly you might add a turn and have the voltage jump up before the other turn is added. (basically changing the contact size as it connects to N then N+1 then back to N causing the voltage to change)
In any case you all are morons... ever single person that replied and agreed with larkin was wrong. Thats what you get for jumping on the bandwaggon. Maybe learn to think for yourselfs next time... assholes.
The reason for the resistance is obvious... It's so A won't be at different potentials. This is basic electronics... Maybe these expert engineers are not so expert?
Of course I expect the usual responses...