Why did you have to create another thread?
It's about this right?
https://www.eevblog.com/forum/beginners/controlling-an-lm317/msg417819/#msg417819If you didnt understand something, why dont you ask again?
There's two simple rules you can take advantage of:
Resistors in series : Total resistance = R 1 + R 2 + ... R n
Resistors in parallel : 1 / Total Resistance = 1 / R1 + 1 / R2 + 1 / R3
For two resistors, the last formula becomes 1/R = 1/R1 + 1/R2 = (R1 + R2)/R1xR2 so then R = R1xR2 / (R1+R2)
Now let's imagine you have a 1kohm resistor and that 10 kohm potentiometer. What happens when you put them in parallel?
When the pot is at 0, the potentiometer acts as a jumper, shorting the 1kohm resistor, so R = 0 ohm.
When the pot is at 100 ohm: R = 100 x 1000 / 1100 = 90.9 ohm
When the pot is at 1k: R = 1000 x 1000 / 2000 = 500 ohm
When the pot is at 2k: R = 2000 x 1000 / 3000 = 666 ohm
When the pot is at 3k: R = 3000 x 1000 / 4000 = 750 ohm
[..]
When the pot is at 5k then R = 820 ohm , at 7k R will be 875 ohm , at 10k R will be 910 ohm
So just by putting a 1kohm resistor in parallel with a 10kohm potentiometer, you have a 0-910 ohm potentiometer. Now by turning the potentiometer you'll get a much finer resistance change.
Now you can put this in series with a second 10k potentiometer and you basically have the rough adjust (change from a resistance value to another) and when you adjust the second potentiometer you can fine tune the resistance.
For example, if you put both potentiometers at the middle of the rotation, you'd get 5000 ohm (rought adjust) + 820 ohm ( the 1kohm and 5000 ohm of pot in parallel gives you 820 ohm) so now you have a 5820 ohm resistor.
Want an even finer adjustment? Do the math for a 470 ohm fixed resistor and see what happens.
edit: corrected the error, thanks for mentioning it.