The strain € is given in terms of 8R, R₁ (the unstrained strain gauge resistance) and GF y SR GF-R₁ Determine an expression for the uncertainty in & in terms of A(8R), AGF and AR1. Call this AE.
The strain € is given in terms of 8R, R₁ (the unstrained strain gauge resistance) and GF y SR GF-R₁ Determine an expression for the uncertainty in & in terms of A(8R), AGF and AR1. Call this AE.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![### Strain Calculation and Uncertainty
#### Strain Formula
The strain \( \epsilon \) is calculated using the formula:
\[
\epsilon = \frac{\delta R}{GF \cdot R_1}
\]
Where:
- \( \delta R \) is the change in resistance.
- \( R_1 \) is the unstrained resistance of the strain gauge.
- \( GF \) is the gauge factor.
#### Uncertainty in Strain
To determine the expression for the uncertainty in strain \( \epsilon \), in terms of the uncertainties \( \Delta(\delta R) \), \( \Delta GF \), and \( \Delta R_1 \), denote this uncertainty as \( \Delta \epsilon \).
Calculate \( \Delta \epsilon \) by considering the propagation of uncertainties involved in the measurements of \( \delta R \), \( GF \), and \( R_1 \).
This explanation would be accompanied by mathematical expressions and an example calculation to demonstrate the process clearly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa487fd1f-659d-4c4f-ad85-f8cf24cc282d%2Fb8304cbd-c02f-40a9-8526-46a60e5e0bf7%2F0ppriqk_processed.png&w=3840&q=75)
Transcribed Image Text:### Strain Calculation and Uncertainty
#### Strain Formula
The strain \( \epsilon \) is calculated using the formula:
\[
\epsilon = \frac{\delta R}{GF \cdot R_1}
\]
Where:
- \( \delta R \) is the change in resistance.
- \( R_1 \) is the unstrained resistance of the strain gauge.
- \( GF \) is the gauge factor.
#### Uncertainty in Strain
To determine the expression for the uncertainty in strain \( \epsilon \), in terms of the uncertainties \( \Delta(\delta R) \), \( \Delta GF \), and \( \Delta R_1 \), denote this uncertainty as \( \Delta \epsilon \).
Calculate \( \Delta \epsilon \) by considering the propagation of uncertainties involved in the measurements of \( \delta R \), \( GF \), and \( R_1 \).
This explanation would be accompanied by mathematical expressions and an example calculation to demonstrate the process clearly.
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