# Using a potentiometer to control greater resistance

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.

• @Hearth thanks for pointing out, I put the A at the wrong spot! Jan 10, 2021 at 17:23
• 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. Jan 10, 2021 at 17:25
• @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.) Jan 10, 2021 at 17:29
• 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. Jan 10, 2021 at 18:09
• 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 Jan 10, 2021 at 18:16