On an Arduino, the 3.5V out has less noise than the 5V noise, so is preferable for sensors.
We connect a fixed resistor \(R_f\) to GND, then detection at the other side of the fixed resistor, \(V_o\) , then a sensor that generates a variable resistance, then the 3.5V =\(V_{cc}\) source.
The dectection is connection to an analog input, which is ADC with range 0 to 1023, based on voltage between 0 and 5V
We have hence
\(V_0=\frac{R_f}{R+R_f}V_{cc};\ ADC=\frac{V_0}{5}1023\)
We deduce
\(ADC=\frac{R_f}{R+R_f}1023\ \frac{3.5}{5}\)
We can obtain the variable resistor as
\(R=\left(\frac{1023}{ADC}\frac{3.5}{5}-1\right)R_f\)\(V_0=\frac{R_f}{R+R_f}V_{cc};\ ADC=\frac{V_0}{5}1023\)