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This is more a theoretical question: Let's say we use a potentiometer as a variable resistor. We can set it from 0% (0Ω) to 100% (let's say 1Ω for simplicity).

Using this pot we can reduce the total range of resistances covered by the 0% to 100% by adding a resistor in parallel. (This results in a non-linear relationship between the position of the wiper and the resistance, but that is fine.) For instance adding 1 ohm resistor we get a maximum of 0.5Ω.

Now I was wondering, is it possible to have a circuit using only resistors to control a larger range of resistances with this potentiometer? (Having 0Ω at 0% is not a requirement!)

My gut feeling is that this is not possible, but I did not manage to prove it.

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  • \$\begingroup\$ @Hearth thanks for pointing out, I put the A at the wrong spot! \$\endgroup\$
    – flawr
    Jan 10, 2021 at 17:23
  • \$\begingroup\$ Exactly how do you define "range"? If the pot (ideally) goes from 0 to x ohms then the range R(max)/R(min) is quite large. \$\endgroup\$ Jan 10, 2021 at 17:25
  • \$\begingroup\$ @SpehroPefhany I'm interested in the "range" defined by the difference between R(max) and R(min). (And yes, we do assume ideal resistors/pots.) \$\endgroup\$
    – flawr
    Jan 10, 2021 at 17:29
  • \$\begingroup\$ Yes you can, and this is how D/A’s work in small steps or digital pots. There are also partial log pots for audio. \$\endgroup\$ Jan 10, 2021 at 18:09
  • \$\begingroup\$ Can you use a spreadsheet and plot the inverse or nonlinear or asymptotic relationship compared to a linear pot. Then try it with a sig gen and DC biased AC with a common emitter instead of a pot \$\endgroup\$ Jan 10, 2021 at 18:16

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Generally not. You could switch in series resistors to the combination to make the rheostat a "fine" adjustment control but that requires switches which are out of scope.

One of the practical problems you would encounter is that the power dissipation of the pot may be exceeded at low values. Remember that the power rating is for the whole track. If you use only a fraction of the resistance track then the maximum power dissipation decreases to that fraction of the pot's power rating. Think of it as power rating per unit length or per degree of rotation.

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