Wheatstone Bridge Calculator

Analyze a Wheatstone bridge circuit to find the unknown resistance. Calculate bridge balance conditions for precision resistance measurement.

UNKNOWN RESISTANCE (Rx)
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Rx for Balance (Ω)
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Bridge Ratio
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V_bridge at balance
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Total Current (mA)
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What Is a Wheatstone Bridge?

A Wheatstone bridge is an electrical circuit of four resistors in a diamond configuration, used to precisely measure unknown resistances. When balanced, no current flows through the galvanometer connecting the midpoints, and the unknown resistance can be calculated from the three known values.

Invented by Samuel Hunter Christie in 1833, this circuit is fundamental to precision measurement. Modern strain gauges, RTD temperature sensors, and pressure transducers all use Wheatstone bridge configurations for high-sensitivity detection of small resistance changes.

Balance Condition

Rx = R2 × R3 / R1

At balance, R1/R3 = R2/Rx. The measurement is independent of supply voltage, eliminating a major error source. Unbalanced bridges produce voltage proportional to resistance deviation.

Applications

  • Strain gauges: Detect 0.1% resistance changes to measure mechanical strain.
  • RTD sensors: Platinum resistance thermometers for precise temperature measurement.
  • Pressure transducers: Piezoresistive sensors with high linearity.
  • Gas detectors: Pellistor catalytic sensors for combustible gas detection.

Frequently Asked Questions

Why is a bridge more accurate than an ohmmeter?

Ohmmeters measure V and I to compute R, with errors in both propagating. A bridge compares ratios at null balance, independent of supply voltage. This null-measurement technique is inherently more precise.

What is quarter-bridge vs full-bridge?

Quarter-bridge: one active sensing element. Half-bridge: two active for temperature compensation. Full bridge: four active, maximizing sensitivity (4x output) with complete temperature compensation.

What happens when unbalanced?

Voltage V_g = Vs × (R2/(R1+R2) - Rx/(R3+Rx)) appears across the galvanometer. Small deviations produce nearly linear output, useful for sensor applications.