How a Balanced Bridge Measures an Unknown Resistance
A Wheatstone bridge measures an unknown resistance by comparing it against three known resistances arranged in a diamond configuration, with a voltage source across one diagonal and a measurement point across the other. When the bridge is balanced — meaning the ratio of resistances in one arm matches the ratio in the other — the differential voltage across the measurement diagonal is exactly zero, regardless of the actual supply voltage.
This balance condition (R1/R2 = R3/Rx) is what lets you solve for an unknown resistor Rx precisely, without needing to know the exact supply voltage at all — a genuinely elegant measurement technique, since it converts a resistance measurement into a null-detection problem, which can be made extremely sensitive. When the bridge is deliberately left unbalanced (as in strain gauge and sensor applications), the small differential output voltage becomes the actual measurement signal, proportional to how far the sensor's resistance has shifted from the balance point.
This is exactly the working principle behind strain gauges, load cells, and many temperature/pressure sensors — a small physical change alters one arm's resistance slightly, and the resulting bridge imbalance produces a measurable voltage proportional to that change.