. 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?