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Bridge circuits are widely used for the measurement of resistance, capacitance, and inductance. The resistive bridge, also known as Wheatstone bridge, is discussed in this section.

Basic Wheatstone Bridge Circuit

A basic Wheatstone bridge circuit contains four resistances, a constant voltage input, and a voltage gage, as illustrated below.

For a given voltage input Vin, the currents flowing through ABC and ADC depend on the resistances, i.e.,

The voltage drops from A to B and from A to D are given by,

The voltage gage reading Vg can then be obtained from,

Now suppose that all resistances can change during the measurement. The corresponding change in voltage reading will be,

Balanced Wheatstone Bridge Circuit

If the bridge is initially balanced, the initial voltage reading Vg should be zero. This yields the following relationship between the four resistances,

We can use this result to simplify the previous equation that includes the changes in the resistances. Doing so results in the solution for the change in Vg,

where h is defined by,

Moreover, when the resistance changes are small (< 5%), the second order term h is approximately zero and can be ignored. We then have,

which is the basic equation governing the Wheatstone bridge voltage in strain measurement. The coefficient is called the circuit efficiency.

Equal-Resistance Wheatstone Bridge Circuit

In practice, one often uses the same resistance value for all four resistors, R1 = R2 = R3 = R4 = R. Noting that r = 1 in this case, the change in voltage can be further simplified to,

By thoughtfully selecting the target and reference resistances, the Wheatstone bridge circuit can amplify small changes in resistance and/or compensate for changes in temperature.