Wheatstone Bridge Calculator
Find the unknown resistance in a balanced Wheatstone bridge.
At balance: Rx = R3 × (R2 / R1). Enter the three known resistors to find Rx.
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A Wheatstone bridge circuit measures an unknown resistance precisely by comparing it against known reference resistors. When the bridge is balanced (no current through the galvanometer), the unknown resistance can be calculated exactly.
- Enter R1 and R2. These are the two known resistors that form the ratio arm of the bridge. Their ratio (R2/R1) determines the multiplier applied to R3.
- Enter R3. This is the known adjustable (or standard) resistor. In a real bridge, R3 is adjusted until the bridge balances (null reading on the galvanometer).
- Read Rx. The unknown resistance equals R3 × (R2/R1) at balance.
About the Wheatstone Bridge
The Wheatstone bridge was invented by Samuel Hunter Christie in 1833 and popularized by Sir Charles Wheatstone in 1843. The balance condition is: R1/R2 = R3/Rx, or equivalently Rx = R3 × (R2/R1). This circuit is the basis for precision resistance measurement and is still used in strain gauges, pressure sensors, temperature sensors (RTDs), and load cells.
In practical sensor applications, one or more resistors in the bridge are replaced by sensors whose resistance changes with the measured quantity. An amplifier replaces the galvanometer, and the unbalanced voltage is proportional to the measured parameter. This "bridge circuit" approach provides excellent common-mode rejection of temperature and supply voltage variations.
Frequently Asked Questions
What is the Wheatstone bridge formula?
At balance, the Wheatstone bridge satisfies R1/R2 = R3/Rx. Solving for the unknown: Rx = R3 × (R2/R1). The bridge is balanced when no current flows through the galvanometer connecting the midpoints of the two voltage dividers. At balance, the midpoint voltages are equal: Vin × R2/(R1+R2) = Vin × Rx/(R3+Rx).
Why use a Wheatstone bridge instead of a direct resistance measurement?
The null-balance method of the Wheatstone bridge is immune to errors from lead resistance, contact resistance, and galvanometer sensitivity. Because you are measuring a null condition (zero current), the exact value of the supply voltage does not matter. This makes the bridge extremely accurate for precision measurements. Modern bridges using operational amplifiers can measure resistance changes of parts per million.
How is a Wheatstone bridge used with strain gauges?
A strain gauge is a resistor whose resistance changes when deformed. In a bridge circuit, the strain gauge replaces one (quarter bridge), two (half bridge), or all four (full bridge) resistors. Mechanical strain changes the gauge resistance, unbalancing the bridge and producing a voltage proportional to strain. Load cells, pressure sensors, torque sensors, and accelerometers all use this principle. A full bridge configuration doubles sensitivity and cancels temperature-induced resistance changes.
What is a practical Wheatstone bridge measurement procedure?
Connect the unknown resistor (Rx) in one arm of the bridge. Set R1 and R2 to known ratio values (e.g., 1:1, 10:1, or 100:1). Adjust R3 (a calibrated decade resistance box) until the galvanometer reads zero. Read Rx = R3 × (R2/R1). For the best accuracy, use a ratio close to 1:1, choose R3 near the expected value of Rx, and ensure R1 and R2 are precision resistors with 0.1% or better tolerance.