Wheatstone Bridge Calculator
Calculate unknown resistance using the Wheatstone bridge balance equation. The classical method for accurate resistance measurement.
Wheatstone Bridge Guide
Balance Condition
A Wheatstone bridge consists of four resistors arranged in a diamond, with a galvanometer between two opposite corners and a battery between the other two. At balance, no current flows through the galvanometer. Balance condition: R₁/R₂ = R₃/Rₓ. Rearranged: Rₓ = R₂ × R₃ / R₁. The bridge is balanced by adjusting R₃ (a known variable resistor) until galvanometer reads zero. The unknown resistance is then calculated from the three known values. Charles Wheatstone popularised this technique in 1843 (
Why It's So Accurate
Conventional measurement (V/I): accuracy limited by the voltmeter and ammeter. ±1% typical for school instruments. Wheatstone bridge: accuracy limited only by the precision of the standard resistors. Modern precision standards: ±0.001%. Galvanometer detection: just needs to detect zero current — not measure it accurately. Modern null-balance bridges can resolve part-per-billion changes in resistance. Applications: precision resistance measurement. Strain gauges (small resistance changes detected
Unbalanced Bridge Sensitivity
When slightly unbalanced, current through galvanometer: I_g ≈ V × ΔR / (4 × R²) — for small imbalance. Maximum sensitivity: when all four resistors are approximately equal. Bridge with R₁ = R₂ = R₃ = Rₓ has maximum sensitivity. Far from balance: I_g approaches the bridge supply current. Used in transducers — the imbalance current is proportional to physical quantity being measured. Strain gauges: gauge resistance changes ~0.1% under strain. Bridge converts this to a measurable voltage. Foil stra
Variations and Modern Use
Slide-wire bridge: simple educational version using a uniform resistance wire. R₃ replaced by a slider along the wire. Length ratios replace resistance ratios. Kelvin bridge: for measuring very low resistances (microhms). Eliminates contact and lead resistance errors. Wien bridge: AC version for measuring capacitance and inductance. Also used as an oscillator (Wien bridge oscillator). Maxwell bridge: AC bridge specifically for inductance measurement. Modern digital multimeters and LCR meters use
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