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- . A copper metal wire is used as a strain gauge. The resistivity is 1.68x10 -8 Ω.m at 20. The length and cross-sectional area of the wire are 5mm and 4*10 -4 m2.

# . A copper metal wire is used as a strain gauge. The resistivity is 1.68x10 -8 Ω.m at 20. The length and cross-sectional area of the wire are 5mm and 4*10 -4 m2.

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1. A copper metal wire is used as a strain gauge. The resistivity is 1.68x10 -8 Ω.m at 20. The length

and cross-sectional area of the wire are 5mm and 4*10 -4 m2. The material elongates by an

amount of 0.2mm in 0.2mm increments until it reaches 6mm in length. Assuming the volume

remains constant, calculate the resistance at each length. You should use the standard equation

for the resistance of a metal. What is that equation? Fill in the table below. Show all calculations.

Calculate the difference in resistance between the resistance at each length and the resistance

before strain is added. Also, calculate the change in resistance using the approximation found in

equation 5.12 of your text. How does the change in length change the resistance of the gauge? Is

it linear? Why or why not? (You can use Excel to create a plot and paste it in your submission if

you want?) How good is the approximation?

R0=ρ(l0/A0)

Length CrossResistanc

sectional area e Initial resistance

(at 5mm) Change in the

resistance Change in resistance

using Eq.5.12 5mm

5.2m

m

5.4m

m

5.6m

m

5.8m

m

6mm

2. A tensile force of 2150 N is applied to a 12 m steel beam with a cross-sectional area of 5.2 x 10 -4

m2. Find the strain on the beam.

3. A strain gauge has a GF (Gauge factor) = 2.03 and R = 120 ohms and is made from wire with =

0.0034/℃ at 25℃. The dissipation factor is given as PD = 25mW/℃. What is the maximum

current that can be placed through the strain gauge to keep self-heating errors below 1u (1

micro) of strain?