(Solved):   An unbonded strain gauge shown in figure 1 is used to measure pressure. As the pressure is ...

 

An unbonded strain gauge shown in figure 1 is used to measure pressure. As the pressure is applied to the diaphragm, the upper strain wires R1 and R3 are stretched and the resistance in each wire increase by DR while R2 and R4 are compressed with their resistance decreased by the same amount DR. The four strain gauges are connected into a bridge circuit with an excitation voltage of VDc of 5 volts as shown in figure 2 below. Strain Gauge R1 R3 Signal Voltage Conditioning Circuit Output Vb R4 Figure 1 Figure 2 Diaphragm 1. Show that the output of the bridge, = Vba (DR/R) Vdc where Ris the initial resistance of each wire. (Hint : Let R1=R3 = R + DR, R2=R4= R- DR and use voltage divider rule to solve for Vba = Vb -Va) 2. If the maximum stress gauge wire is limited to 300MPa and the Elastic modulus of the material is 210GPa, calculate the range of voltage output from the bridge. Assume the strain gauges have a gauge factor of 2.0. 3. If the initial resistance of the unstrained gauges is 10KW, determine the change in resistance of the resistor, DR R2 Force Rod