Tensile strain may be measured by the change in electrical resistance of a device called a strain gauge.

Question 1

Tensile strain may be measured by the change in electrical resistance of a device called a strain gauge. A strain gauge consists of folded fine metal wire mounted on a flexible insulating backing sheet. The strain gauge is firmly attached to the specimen.

When the strain in the specimen is increased, what happens to the resistance of the wire?

A It decreases, because the length decreases and the cross-sectional area increases.

B It decreases, because the length increases and the cross-sectional area decreases.

C It increases, because the length decreases and the cross-sectional area increases.

D It increases, because the length increases and the cross-sectional area decreases.

Reference: Past Exam Paper – November 2015 Paper 13 Q33

Solution:

Answer: D.

The strain gauge consists of a metal wire.

Resistance R of wire = ρL / A

As the strain in the specimen is increased, the wire is extended. Its length increases.

An increase in length results in an increase in resistance (from the formula above).

At the same time, the strain causes the cross-sectional area of the wire to become smaller (just like when a wire is extended by a force).

From the formula above, a decrease in cross-sectional area A also results in an increase in the resistance (as R is inversely proportional to the area).

 

So, as the strain in the specimen is increase, the resistance of the wire increases, because the length increases and the cross-sectional area decreases.