Two beams with the gauges in the quarter-bridge configuration with strain gauges (GF=2.1, R=120 N) are used to measure strain. If the input voltage is 5v what is the output voltage when the system experiences 300 microstrain?

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**Transcription and Explanation for Educational Website:**

**Problem Statement:**

(a) Two beams with the gauges in the quarter-bridge configuration with strain gauges (Gauge Factor (GF) = 2.1, Resistance (R) = 120 Ω) are used to measure strain. If the input voltage is 5V, what is the output voltage when the system experiences 300 microstrain?

**Explanation of Diagrams:**

The image includes two diagrams representing the placement of strain gauges on beams for a quarter-bridge configuration. 

1. **Diagram on the Left:**
   - The diagram illustrates a beam with a strain gauge attached on the surface.
   - The strain gauge experiences a change in resistance denoted as R_d(1+ε), where ε represents the strain experienced.
   - There is an arrow indicating the direction of force applied, causing the strain.

2. **Diagram on the Right:**
   - Similar to the left diagram, this shows another beam with a strain gauge.
   - The resistance change is shown as R_t(1+ε), indicating another gauge experiencing strain.
   - Another arrow shows the direction of the applied force causing the strain in this setup.

**Educational Context:**

These diagrams and information illustrate the practical use of strain gauges for measuring mechanical deformation in structural elements. The quarter-bridge configuration shown is a fundamental concept in engineering for translating mechanical strain into electrical signals, which can then be measured and analyzed.

**Problem Solving Approach:**

- Use the given Gauge Factor (GF = 2.1), resistance (R = 120 Ω), and input voltage (5V).
- Calculate the change in resistance due to strain, and subsequently, determine the output voltage using the formulae for quarter-bridge strain gauge configuration.

This example is critical for students learning about basic strain measurement and its applications in fields like civil, mechanical, and aerospace engineering.
Transcribed Image Text:**Transcription and Explanation for Educational Website:** **Problem Statement:** (a) Two beams with the gauges in the quarter-bridge configuration with strain gauges (Gauge Factor (GF) = 2.1, Resistance (R) = 120 Ω) are used to measure strain. If the input voltage is 5V, what is the output voltage when the system experiences 300 microstrain? **Explanation of Diagrams:** The image includes two diagrams representing the placement of strain gauges on beams for a quarter-bridge configuration. 1. **Diagram on the Left:** - The diagram illustrates a beam with a strain gauge attached on the surface. - The strain gauge experiences a change in resistance denoted as R_d(1+ε), where ε represents the strain experienced. - There is an arrow indicating the direction of force applied, causing the strain. 2. **Diagram on the Right:** - Similar to the left diagram, this shows another beam with a strain gauge. - The resistance change is shown as R_t(1+ε), indicating another gauge experiencing strain. - Another arrow shows the direction of the applied force causing the strain in this setup. **Educational Context:** These diagrams and information illustrate the practical use of strain gauges for measuring mechanical deformation in structural elements. The quarter-bridge configuration shown is a fundamental concept in engineering for translating mechanical strain into electrical signals, which can then be measured and analyzed. **Problem Solving Approach:** - Use the given Gauge Factor (GF = 2.1), resistance (R = 120 Ω), and input voltage (5V). - Calculate the change in resistance due to strain, and subsequently, determine the output voltage using the formulae for quarter-bridge strain gauge configuration. This example is critical for students learning about basic strain measurement and its applications in fields like civil, mechanical, and aerospace engineering.
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