Halliday, Resnick & Walker — Circuits: Problem 29

29 In Fig. 27-37, \(R_s\) is to be adjusted in value by moving the sliding contact across it until points \(a\) and \(b\) are brought to the same potential. (One tests for this condition by momentarily connecting a sensitive ammeter between \(a\) and \(b\); if these points are at the same potential, the ammeter will not deflect.) Show that when this adjustment is made, the following relation holds: \(R_x = R_s R_2 / R_1\). An unknown resistance (\(R_x\)) can be measured in terms of a standard (\(R_s\)) using this device, which is called a Wheatstone bridge.