Maximal relative error on Wheatstone Bridge
Step 1) Using the resistor value constraints specified in the question, select values for the bridge's resistors R1, R2, R3, and Rx so that (a) the bridge is balanced for the condition x=0 (\$R_{x}=1000\; \Omega\$) AND (b)&nbsp;the bridge exhibits maximum sensitivity for the x=0 case. (SENSITIVITY HINT)







simulate this circuit &ndash; Schematic created using CircuitLab

Step 2) Let x=10 (\$R_{x}=1100\; \Omega\$). Set the bridge's input voltage \$V_{in}\$ to a non-zero, constant (DC) voltage value \$V_{in}=k\$, and then solve for the bridge's output voltage \$V_{out}\$. (HINT: The solution will be a number times 'k'.)

FWIW, the system's sensitivity would be the ratio &Delta;Vout/&Delta;x, with units in terms of "Volts per distance" (e.g., 3 volts/millimeter).