Question

For a strain gauge that measures an applied force, derive an equation that supports the following: a change in voltage is directly proportional to a change in APPLIED FORCE (NOT ELECTROSTATIC FORCE). show all work

Answer 1

Strain :

If a force is applied to a material , it undergoes some deformation. The strain is defined as change in length of the material to the original length.

= L/L

Strain guage :

As the name indicates , strain guage are used to measure the stain. If a force is applied to a wire , its length increases and diameter decreases. Hence strain increases. We know that resistance of any comductor is inversely proportional to the length. Hence if length imcreases , resistance decreases. Se can say, if we increase the applied force, resistance will be decreased.

To measure the changes in resistance , strain guage are configured in wheatstone bridge.

There are four resistance arms with an excitation voltage V . The output of the wheatstone bridge V₀ is measured between the middle nodes.

According to the combination , we have :

V₀ =

In balanced position , R₁/R₂ = R₄/R₃ , and V₀ =0

If we replace R₄ by strain guage , and apply a force , then resistance R₄ decreases , so the wheatstone bridge will be unbalanced and V₀ increases.

It means , the output voltage increases if we increase the applied force. Hence chnage in voltage is directly proportional to the applied force.