Demonstration of R fixe = Square root of Rmax* Rmin(Voltage divider with resistance varaible)

Community General Discussion
1

WhatsApp Image 2021-04-27 at 17.57.37
WhatsApp Image 2021-04-27 at 17.57.371237×1600 73.8 KB

Hello everyone, I hope you are well. I am working on a voltage divider bridge with a variable resistance and I could you please have the demonstration of the formula which says the fixed resistance is equal to the square root of Rmax * Rmin!

Resistance fixe = Square root (Rmax * Rmin)
Someone has the demonstration please?? thank you

2

you can have the resistor you want... Not sure I get the question

Partitore-di-tensione Resistor-R2-voltage-divider-equation

(you might want to qualify what resistance you want to optimize something for example, like getting the max voltage range for Vout ?)

3

The Resistance named Temp is a variable resistance. Resistance Temp goes from [600k- 4 MegaOhm ]. 600k is the Rmin and 4 MegoOhm is the Rmax.

Now, i need the value of Fixe Resistance named R.
I found on the arduino forum that says that the resistance fixe (R) = square root (Rmax * Rmin).

I want please the demonstration of this formula. How we can demonstrate that Resistance fixe = Square root(Rmax*Rmin).

I don't speak english very well, sorry if you don't understand me.

4

what I'm saying is that the fixed Resistance R can be what you want... unless you set a constraint on what you want to obtain.

5

The Resitance R1 on your schema is my resistance variable on mine.

6

There is no constraint. The resistance R is exactly what i want.

7

Yes. and whatever R2 you choose, the voltage you'll see is Vout = Vin . R2 / (R1 + R2)

unless you put some contraints on what you want Vout to be, any R2 will do something

you can pick sqrt(R2max - R2min) if you want or something else like sqrt (Rmax * Rmin) (which is probably what you get if you try to complete the math you were doing and maximizing ∆Vout) or if you want just 1mΩ

8

Yes, I want to maximize ∆Vout. We have to do the derivative and I am stuck at this level. I don't know how they came up with the final formula.

9

the derivative work is kinda trivial, you only need to know that (U/V)' = (U'V - UV')/V2 and (U-V)' = U' - V'
if you want to find an optimum for the function this is where the derivative will be 0

and you'll get to R2 = RminRmax
(with a few assumptions that Vin is not null, all R are non null and Rmin is different than Rmax)

give it a try... at some point you'll get

Rmin(R+Rmax)2 - Rmax(R+Rmin)2 = 0. (assuming the denominator is non null based on earlier assumptions)
and if your remember that (a + b)2 is a2 + b2 + 2 ab and distribute and factor by (Rmin-Rmax) you will get

(Rmin-Rmax)(R2 - RminRmax) = 0

as you know (Rmin-Rmax) is not null, then you get R2 = RminRmax

10

Thank you very much!!!!!!!

Thank you!!!!!!

11

This topic was automatically closed 120 days after the last reply. New replies are no longer allowed.