Electrical
Wheatstone Bridge
Four-resistor circuit nulling small differences for precise resistance measurement
A Wheatstone bridge is a four-resistor diamond circuit used to measure unknown resistances precisely by balancing one branch against another. When the ratio R1/R2 equals R3/R4, no current flows through the galvanometer between the midpoints—the bridge is balanced. Adjusting a calibrated resistor until balance occurs gives the unknown value with high accuracy, independent of supply voltage. Modern strain gauges, RTDs, and pressure sensors use Wheatstone bridges in unbalanced mode, where the small voltage at imbalance is amplified to read tiny resistance changes.
- InventorChristie (1833), Wheatstone (1843)
- Balance conditionR1/R2 = R3/R4
- Balance currentZero through galvanometer
- Sensor modeUnbalanced, voltage out
- Accuracy0.01-0.1% typical
- Common useStrain gauges, RTDs
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Why Wheatstone bridges matter
- Strain measurement. Load cells, structural monitoring.
- Temperature sensing. RTDs in process control.
- Pressure transducers. Diaphragm-based gauges.
- Precision metrology. Resistance standards, calibration labs.
- Geological survey. Resistivity measurements of soil.
- Education. Classic example of null-balance and sensitivity.
- Industrial weighing. Truck scales, batching, packaging.
Common misconceptions
- Supply voltage must be precise. At balance, supply drops out; only ratios matter.
- Bridges always operate balanced. Sensors use unbalanced mode and amplify the imbalance.
- Lead resistance is irrelevant. For strain gauges, lead drops can cause errors—use 3- or 4-wire schemes.
- Galvanometer is essential. Modern null detectors are op-amps or ADCs.
- Linear with imbalance. Linear only for small deviations; full-scale bridges need correction.
- Temperature is automatically rejected. Only with appropriate gauge placement and dummy gauges.
Frequently asked questions
How does balance work?
When R1/R2 = R3/R4, the voltage at the midpoint of the R1-R2 branch equals the voltage at the midpoint of the R3-R4 branch. No current flows through the galvanometer between them. The unknown is found by adjusting a known calibrated arm until null. Balance is independent of supply voltage—any drift cancels because both branches see the same voltage.
Why is it more accurate than direct measurement?
Null detection. Instead of measuring an absolute voltage or current, you measure when a difference equals zero. A galvanometer or null detector can be very sensitive without needing absolute calibration. Supply voltage variations don't matter, lead resistances drop out, and the only critical quantities are the ratios of fixed resistors, which can be made very accurate.
How are strain gauges used?
A strain gauge changes resistance proportionally to strain (about 0.2% full-scale change). One or more gauges replace bridge arms. Under load, the gauge resistance changes, unbalancing the bridge by a few mV per V of supply. An instrumentation amplifier reads the imbalance. Quarter-, half-, and full-bridge configurations trade off cost, common-mode rejection, and temperature compensation.
What's a quarter bridge vs full bridge?
Quarter: one active gauge, three fixed resistors. Cheapest, but no temperature compensation. Half: two active gauges in opposite arms; cancels temperature drift if both see the same temperature. Full: four active gauges, one per arm; doubles sensitivity and rejects bending or temperature effects depending on configuration. Load cells almost always use full bridges.
What's a Kelvin bridge for?
Measuring very low resistances (under 1 ohm) where lead and contact resistance would dominate a standard Wheatstone reading. The Kelvin bridge adds extra arms and sensing connections to subtract out lead resistance. Used for shunts, motor windings, and copper bus bars where milliohm precision matters.
How does it handle AC?
Replace resistors with impedances and balance becomes Z1/Z2 = Z3/Z4 in both magnitude and phase. AC bridges measure capacitance (Schering bridge), inductance (Maxwell, Hay bridges), and dielectric loss. Phase-sensitive detectors replace the galvanometer. AC bridges are workhorses of precision impedance metrology before LCR meters made them obsolete for routine work.
What's a typical sensitivity?
For a Wheatstone bridge with all 350-ohm arms and 5 V excitation, a 1-ohm change in one arm produces about 3.5 mV imbalance—roughly 700 µV per 1% resistance change. Strain gauges yield 1-2 mV/V at full scale. Instrumentation amps with gain of 100-1000 and 24-bit ADCs let modern systems resolve nanostrain (parts per billion).