Voltage divider ratio limitation applied to potentiometer
If your 2k pot is to give you a span of 20% from 50% to 70% then you need \$ \frac {2k}{20} = 100 \ \Omega \$ per %.

So the bottom, 50%, resistor will be 50 x 100 = 5k.

The top, 30%, resistor will be 30 x 100 = 3k.



Generally you will be constrained by the available potentiometer values. Pick one that suits and calculate the other resistors afterwards.




  I'm trying to find the general formula or more like understanding of how to choose resistor values to limit the voltage ratio when using a potentiometer.








simulate this circuit &ndash; Schematic created using CircuitLab

Using min and max in percentage form:

$$ R_1 = \frac {R_2 \cdot (100 - max)}{max - min} $$

$$ R_3 = \frac {R_2 \cdot min}{max - min} $$

Testing for your example with a 2k pot and a 50% to 70% adjustment range:

\$ R_1 = \frac {R_2 \cdot (100 - max)}{max - min} = \frac {2k \cdot (100 - 70)}{70 - 50} = 3k \$

\$ R_3 = \frac {R_2 \cdot min}{max - min}= \frac {2k \cdot 50}{70 - 50} = 5k \$

Obviously, min can be set as low as 0% and max to 100% which will result in R3 or R1 being 0 Ω.