The oldest bridge in Electronics

The very old, but very famous Wheatstone bridge is an electrical circuit that has been widely used in many applications all around the world.  Originally invented by Samuel Christie in 1833 as a means of comparing the resistance of wires and metals, the invention was eventually popularized by Charles Wheatstone in 1843.  Wheatstone provided a mathematical formula that displayed the relationship of currents, voltages, and resistances by applying the principles of Ohm's law.  The Wheatstone bridge is frequently used in resistance measuring applications, such applications include resistance thermometer, strain gauge, and even soil analysis.

 Let's say for example we are trying to measure the resistance of a soil type.  Of course the soil's resistance value is variable, as the resistance changes when the soil is watered.  For experimental purposes, we decide we want to measure the resistance when the soil is dry, and also when the soil is moist after watering. The circuit of the Wheatstone bridge is displayed in Figure 1, note how there are a total of 4 resistors, with two branches in parallel, where each branch has two resistors in series.  Three of the resistors are usually known, while the other is unknown.  In this case, the unknown resistor element is soil that is squeezed between two electrodes.

Applying KCL, we can derive the expressions below:

Figure 1.  Wheatstone bridge VOUT vs R_SENSOR