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• Strain Gages • - - - When a fine wire (25 μm)is strained within its elastic limit, the wire's resistance changes because of changes in the diameter, length, and resistivity. measure extremely small displacements on the order of nanometers Equations: R = PL length L (meters). A p (ohms meter) pdL dR = - PA-2L dA + L dp A A A (meters squared) • ΔΑ Δρ AR AL AA Ap = - A + ρ Dr. Shamekhi, Sahand University of Technology Displacement Meas. - Resistive Sensors - p3 Equation: Poisson's ratio u relates the change in diameter μ AD to the change in length, Substituting this: AD/D ======== -μAL/L AR AL Δρ === = (1 + 2μ)· + R L P Dimensional effect Piezoresistive effect Gage Factor: G= ARIR ALIL Aplp (1 + 2μ) + ALIL Changes in the lattice structure of the material, 6

• Strain Gages • - - - When a fine wire (25 μm)is strained within its elastic limit, the wire's resistance changes because of changes in the diameter, length, and resistivity. measure extremely small displacements on the order of nanometers Equations: R = PL length L (meters). A p (ohms meter) pdL dR = - PA-2L dA + L dp A A A (meters squared) • ΔΑ Δρ AR AL AA Ap = - A + ρ Dr. Shamekhi, Sahand University of Technology Displacement Meas. - Resistive Sensors - p3 Equation: Poisson's ratio u relates the change in diameter μ AD to the change in length, Substituting this: AD/D ======== -μAL/L AR AL Δρ === = (1 + 2μ)· + R L P Dimensional effect Piezoresistive effect Gage Factor: G= ARIR ALIL Aplp (1 + 2μ) + ALIL Changes in the lattice structure of the material, 6

Electricity for Refrigeration, Heating, and Air Conditioning (MindTap Course List)
Electricity for Refrigeration, Heating, and Air Conditioning (MindTap Course List)
10th Edition
ISBN:9781337399128
Author:Russell E. Smith
Publisher:Russell E. Smith
Chapter12: Electronic Control Devices
Section: Chapter Questions
Problem 14RQ
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Derive the equations in the picture using the Poisson ratio method.
• Strain Gages • - - - When a fine wire (25 μm)is strained within its elastic limit, the wire's resistance changes because of changes in the diameter, length, and resistivity. measure extremely small displacements on the order of nanometers Equations: R = PL length L (meters). A p (ohms meter) pdL dR = - PA-2L dA + L dp A A A (meters squared) • ΔΑ Δρ AR AL AA Ap = - A + ρ Dr. Shamekhi, Sahand University of Technology Displacement Meas. - Resistive Sensors - p3 Equation: Poisson's ratio u relates the change in diameter μ AD to the change in length, Substituting this: AD/D ======== -μAL/L AR AL Δρ === = (1 + 2μ)· + R L P Dimensional effect Piezoresistive effect Gage Factor: G= ARIR ALIL Aplp (1 + 2μ) + ALIL Changes in the lattice structure of the material, 6
Transcribed Image Text:• Strain Gages • - - - When a fine wire (25 μm)is strained within its elastic limit, the wire's resistance changes because of changes in the diameter, length, and resistivity. measure extremely small displacements on the order of nanometers Equations: R = PL length L (meters). A p (ohms meter) pdL dR = - PA-2L dA + L dp A A A (meters squared) • ΔΑ Δρ AR AL AA Ap = - A + ρ Dr. Shamekhi, Sahand University of Technology Displacement Meas. - Resistive Sensors - p3 Equation: Poisson's ratio u relates the change in diameter μ AD to the change in length, Substituting this: AD/D ======== -μAL/L AR AL Δρ === = (1 + 2μ)· + R L P Dimensional effect Piezoresistive effect Gage Factor: G= ARIR ALIL Aplp (1 + 2μ) + ALIL Changes in the lattice structure of the material, 6
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