The Wheatstone Bridge

1. The Wheatstone Bridge Using Kirchhoff’s Voltage Law: Using Kirchhoff’s Current Law: Figure 4.10

2. Rx • What is the Wheatstone • bridge equation if another • resistor, Rx, is added in • parallel with R1 ?

3. Rx • One advantage of using two resistors in parallel in • one leg of the WB is that the added resistor can be • located remotely from the actual WB, such as in a flow. • Here, that resistor can serve as a sensor.

4. When Eo = 0, the WB is said to be ‘balanced’ → • When the WB is balanced and 3 of the 4 resistances • are known, the 4th (unknown) resistance can be found • using the balanced WB equation. The is called the null • method.

5. Now consider the case when all 4 resistors are the • same initially and, then, one resistance, say R1, is changed • by an amount dR. This is called the deflection method. • Often, dR is associated with a change in a physical variable.

6. In-Class Example Figure 4.18 RTD: aRTD = 0.0005 / ºC; R = 25 W at 20.0 ºC Wheatstone Bridge: R2 = R3 = R4 = 25 W; Ei =5 V Amplifier: Gain = G Multimeter: 0 V to 10 V range (DC) Experimental Operating Range: 20 ºC to 80 ºC

7. Cantilever Beam with Four Strain Gages • From solid mechanics, for a cantilever beam, both the elongational strain, eL, and the compressive strain, eC, are directly proportional to the applied force, F. Figure 4.11 Figure 6.2 • When F is applied as shown (downward), R1 and R4 • increase by dR (due to elongation), and R2 and R3 • decrease by dR (due to compression). Here, dR is directly proportional to the strains.

8. The Cantilever Beam with Four Gages • The WB equation becomes • This instrumented cantilever beam system is the basis for many force measurement systems (like force balances and load cells.