How a Wheatstone bridge measures an unknown resistor
The circuit behind the balance formula, why the null method is so accurate, and where Wheatstone bridges are used in real instruments.
Two dividers and a detector
A Wheatstone bridge is built from four resistors arranged as two voltage dividers across a single supply. The first divider is R1 stacked over R2, and the second is R3 stacked over the unknown Rx. Each divider produces a voltage at its midpoint that depends on the ratio of its two resistors. A galvanometer or sensitive voltmeter connects the two midpoints and measures the difference between them, which is what the whole circuit is designed to drive to zero.
Why balance gives Rx = R2 R3 / R1
The midpoint of the first divider sits at a fraction R2 / (R1 + R2) of the supply, and the second midpoint at Rx / (R3 + Rx). When those two fractions are equal the detector sees no voltage difference and reads zero, the balanced condition. Setting the fractions equal and simplifying gives R1 / R2 = R3 / Rx, which rearranges to Rx = R2 * R3 / R1. Notice the supply voltage has vanished from the equation, so the balance point depends only on the resistor ratios.
Why the null method beats direct reading
Reading resistance directly with an ohmmeter relies on the meter's own accuracy and a stable test current. A bridge instead compares the unknown against known resistors and looks for the moment the detector reads exactly zero, where even a tiny imbalance is easy to spot. Because the measurement is a comparison at a null rather than an absolute reading, it can be extremely precise and is limited mainly by the tolerance of the reference resistors. This is why bridges were the standard for accurate resistance measurement long before digital multimeters.
Where bridges show up in practice
Beyond textbook resistance measurement, the bridge topology is the heart of many sensors. Strain gauges, load cells, and pressure transducers place a variable resistor in one arm so that a small resistance change unbalances the bridge into a measurable output voltage. Resistance temperature detectors use the same idea to turn temperature into a readable signal. Understanding the balance equation makes it easier to see how these instruments convert a physical quantity into an electrical one.