A Wheatstone bridge is used to measure an unknown resistance by balancing two legs of a 'bridge circuit', one leg of which includes the unknown component.
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If the ratio of the two resistances in the known leg (R2/R1) is equal to the ratio of the two in the unknown leg (Rx/R3), then the voltage at the two midpoints will be equal and no current flows between the two midpoints. R2 is varied until this condition is reached. The current direction indicates if R2 is too high or too low.
Detecting zero current can be done to extremely high accuracy (see Galvanometer). If R1, R2 and R3 are known to high precision, then Rx can be measured to high precision. Very small changes in Rx disrupt the balance and are readily detected.
The Wheatstone bridge illustrates the concept of a difference measurement, and how it allows extremely accurate measurements to be made.