If you were choosing between two strain gauges, one which has a single resistor in a bridge that varies and one that has two resistors that vary, one that increases and one which decreases, which would you expect to give a more linear voltage output (that is, a linear function of ‘x’, the position of the potentiometer)?

A strain gauge in which only one resistor varies is typically called a quarter bridge arrangement. The one in which 2 resistors vary, is called a half bridge arrangement, where the resistors showing opposite effects are mounted on either side of the flexing body. The figures and relationship between the output voltages and the change in resistance delta_R, is shown in the below diagram:

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