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 increaseby AR while R2 and R4 are compressed with their resistance decreased by the same amount AR. The four strain gauges are connected into a bridge circuit with an excitation voltage of Vpc of 5 volts as shownin figure 2 below.Strain GaugeR1 R3R2 R4R1R2VdcVaSignalConditioningVoltageOutputCircuitVbForce RodR4R3Figure 1Figure 2Diaphragm1. Show that the output of the bridge, Vpa = (AR/R ) Vdc where R is the initial resistance of each wire. (Hint : Let R1=R3 = R + AR, R2=R4= R- AR and use voltage divider rule to solve for Vpa = 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 factorof 2.0.3. If the initial resistance of the unstrained gauges is 10KO, determine the change in resistance of the resistor, AR

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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 AR while R2 and R4 are compressed with their resistance decreased by the same amount AR. The four strain gauges are connected into a bridge circuit with an excitation voltage of Voc of 5 volts as shown in figure 2 below. Strain Gauge R1 R3 R2 R4 R1 R2 Vdo Va Signal Conditioning Circuit Voltage Output Vb Force Rod R4 R3 Figure 1 Figure 2 Diaphragm 1. Show that the output of the bridge, Vpa = (AR/R ) Vdc where R is the initial resistance of each wire. (Hint : Let R1=R3 = R + AR, R2=R4= R- AR and use voltage divider rule to solve for Vba = Vp -Va) 2. If the maximum stress gauge wire is limited to 30OMPA 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 10KO, determine the change in resistance of the resistor, AR

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 AR while R2 and R4 are compressed with their resistance decreased by the same amount AR. The four strain gauges are connected into a bridge circuit with an excitation voltage of Voc of 5 volts as shown in figure 2 below. Strain Gauge R1 R3 R2 R4 R1 R2 Vdo Va Signal Conditioning Circuit Voltage Output Vb Force Rod R4 R3 Figure 1 Figure 2 Diaphragm 1. Show that the output of the bridge, Vpa = (AR/R ) Vdc where R is the initial resistance of each wire. (Hint : Let R1=R3 = R + AR, R2=R4= R- AR and use voltage divider rule to solve for Vba = Vp -Va) 2. If the maximum stress gauge wire is limited to 30OMPA 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 10KO, determine the change in resistance of the resistor, AR

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Power Measurement

According to Blondel's theorem, the total power is measured with one less number of wattmeters than the number of wires present in the system. So, a single-phase and two-wire system will require one wattmeter and a single-phase and the three-wire system will require two wattmeters, and a three-phase and the three-wire system will also require two wattmeters and a three-phase and the four-wire system will require three wattmeter devices. The wattmeter is a device that measures power using one voltage and one current input as shown in the above figure. Multiple current or voltage input pair cables are used by many power analyzers and digital storage oscilloscopes (DSOs) for measuring watts, in effect within a single instrument acting as multiple wattmeters. It is possible to measure three-phase and four-wire power with one correctly specified power analyzer.

Question

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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 AR while R2 and R4 are compressed with their resistance decreased by the same amount AR. The four strain gauges are connected into a bridge circuit with an excitation voltage of Vpc of 5 volts as shown
in figure 2 below.
Strain Gauge
R1 R3
R2 R4
R1
R2
Vdc
Va
Signal
Conditioning
Voltage
Output
Circuit
Vb
Force Rod
R4
R3
Figure 1
Figure 2
Diaphragm
1. Show that the output of the bridge, Vpa = (AR/R ) Vdc where R is the initial resistance of each wire. (Hint : Let R1=R3 = R + AR, R2=R4= R- AR and use voltage divider rule to solve for Vpa = 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 10KO, determine the change in resistance of the resistor, AR

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