When a strain gauge is strained in its axial (grid line) direction, its resistance increases as thegrid length increases. Poisson's ratio predicts that the resistance will also change as a resultof transverse deformations. For a positive axial strain (tension), how does the gaugeresistance change as a result of the Poisson effect (increase, decrease, no change)? Pleasediscuss your answer

When a strain gauge is subjected to positive axial strain (tension), the length of the grid line increases, which in turn increases the resistance of the strain gauge. This is because resistance is directly proportional to the length of the conductor.

However, due to the Poisson effect, there is also a transverse deformation. Poisson's ratio is the ratio of the relative contraction strain (transverse, lateral or radial strain) normal to the applied load - to the relative extension strain (or axial strain) in the direction of the applied load.

When the material is stretched, it tends to contract in the directions orthogonal to the direction of stretching. This means that while the grid length increases (increasing resistance), the width of the grid decreases due to the Poisson effect.

The decrease in width (and therefore cross-sectional area) of the grid increases the resistance of the strain gauge, because resistance is inversely proportional to the cross-sectional area of the conductor.

So, in conclusion, as a result of the Poisson effect, the gauge resistance will increase due to the decrease in the cross-sectional area of the grid. This is in addition to the increase in resistance due to the increase in grid length.