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Wheatstone Bridge Calculator

The bridge measures resistance by comparison rather than by reading volts and amps, which is why it is far more accurate than Ohm's law with a multimeter. At balance the galvanometer reads zero and the supply voltage drops out of the answer entirely.

Wheatstone Bridge — P/Q = R/X at balance

Find the unknown resistance X when the bridge is balanced. P and Q are the ratio arms, R is the known (adjustable) arm.

Unknown resistance X
  1. 1.Given: P = 10 Ω, Q = 20 Ω, R = 15 Ω
  2. 2.At balance the galvanometer reads zero, so P ÷ Q = R ÷ X
  3. 3.FormulaX = Q × R ÷ PSubstituteX = 20 × 15 ÷ 10ResultX = 30 Ω
Common trap: Balance means zero current through the galvanometer, not zero current in the bridge — the two arms still carry current. The same principle powers the metre bridge: there P/Q is just the ratio of wire lengths ℓ/(100 − ℓ).

The formula

At balance: P / Q = R / X → X = (Q × R) / P

P, Q
the ratio arms (ohms)
R
the known variable arm at balance (ohms)
X
the unknown resistance (ohms)

Worked example

P = 1000 Ω, Q = 100 Ω, and the bridge balances at R = 4700 Ω.

  1. X = (Q × R) / P
  2. X = (100 × 4700) / 1000
  3. X = 470000 / 1000

X = 470 Ω, and the result does not depend on the supply voltage at all.

Where you'll use it

Precision resistance measurement, strain gauges, and thermistor bridges where a tiny resistance change becomes a null-referenced voltage. Its descendants — Kelvin, Maxwell and Schering bridges — extend the same idea to low resistances, inductance and capacitance.

The laws behind it

Parts this applies to

Potentiometer / Rheostat / TrimmerPhotoresistor (LDR)555 Timer ICRectifier DiodeZener DiodeBridge RectifierSCR (Thyristor)TRIAC

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