The Wheatstone Bridge The Wheatstone bridge is a device used to measure an unknown resista...

The Wheatstone Bridge The Wheatstone bridge is a device used to measure an unknown resistance Rx by comparing it with known resistances R1, R2, and R3.5 The circuit diagram is shown in Fig. 3. The known resistances are adjusted so that no current from the cell with voltage E0 passes through the wire BD, in which there is an ammeter with resistance Rg.

Figure 3 Wheatstone bridge.

(a) Use Kirchoff’s Current Law6 that the algebraic sum of the currents at each junction must be zero to show that the unknown currents I, I1, I2, I3, and Ix satisfy the linear system

(b) Kirchoff’s Voltage Law states that the algebraic sum of all voltage drops around a closed circuit is zero.7 (Voltage equals resistance times current.) Use this law to show that

(c) Show that the bridge is balanced (that is, Ig = 0) when R1R3 = R2Rx.