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

What is the Wheatstone bridge equation if another resistor, R x, is added in parallel with R 1 ? RxRx

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. RxRx

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

Now consider the case when all 4 resistors are the same initially and, then, one resistance, say R 1, is changed by an amount  R. This is called the deflection method. Often,  R is associated with a change in a physical variable.

In-Class Example Figure 4.18 RTD:  RTD = / ºC; R = 25  at 20.0 ºC Wheatstone Bridge: R 2 = R 3 = R 4 = 25  E i =  5 V Amplifier: Gain = G Multimeter: 0 V to 10 V range (DC) Experimental Operating Range: 20 ºC to 80 ºC

Cantilever Beam with Four Strain Gages When F is applied as shown (downward), R 1 and R 4 increase by  R (due to elongation), and R 2 and R 3 decrease by  R (due to compression). Here,  R is directly proportional to the strains. Figure 4.11 From solid mechanics, for a cantilever beam, both the elongational strain,  L, and the compressive strain,  C, are directly proportional to the applied force, F. Figure 6.2

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