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A Wheatstone bridge is two voltage dividers fed from the same supply, with the output taken between their midpoints. When the two divider ratios are equal the bridge is balanced and the output is zero. Any small change in one arm — from a strain gauge, thermistor, or unknown resistor — unbalances the bridge and produces a measurable output voltage, which makes it superb for precise resistance and sensor measurements.
| Quantity | Formula |
|---|---|
| Left midpoint | VA = Vin × R2/(R1+R2) |
| Right midpoint | VB = Vin × R4/(R3+R4) |
| Output | Vout = VA − VB |
| Balance condition | R1R4 = R2R3 (Vout = 0) |
| Unknown at balance | Rx = R2 × R3/R1 |
Because the output at balance depends only on ratios (not the exact supply), the bridge is very accurate and largely immune to supply drift.
A circuit of four resistors arranged as two voltage dividers across a common supply, with the output measured between their midpoints. It is used to measure resistance and small changes very accurately.
The bridge is balanced (output zero) when the two divider ratios are equal: R1/R2 = R3/R4, or equivalently R1R4 = R2R3.
Adjust a known arm until the output is zero (null), then use Rx = R2×R3/R1. The null method is very precise because it does not depend on the exact supply voltage.
At balance the result depends only on resistor ratios, not on the supply voltage or its drift, and the null can be detected very sensitively — giving high precision.
Vout = Vin×(R2/(R1+R2) − R4/(R3+R4)), the difference between the two midpoint voltages.
A strain gauge changes resistance by a tiny fraction. Putting it in a bridge converts that small change into a differential voltage that an amplifier can read, while cancelling temperature effects.
How many of the four arms are active sensors: one (quarter), two (half), or all four (full). More active arms give a bigger, more linear, temperature-compensated output.
The balance point does not depend on it, but a higher excitation gives a larger output signal (and more self-heating). It is a trade-off between signal and sensor heating.
Because sensor resistance changes are tiny (often <1%), the unbalanced voltage is only millivolts. That is why bridges feed instrumentation amplifiers.
Yes — the sign shows which way the bridge is unbalanced (which arm increased). The magnitude shows how far from balance it is.
If all arms share the same temperature coefficient, their changes cancel and the bridge stays balanced — a key reason bridges are used for sensitive measurements.
A sensitive meter (galvanometer or amplifier) across the output used to detect when the bridge is exactly balanced while you adjust a known arm.
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