Engineering
Wheatstone Bridge Differential Voltage & Strain-Gauge Null Balance formulas
Calculate sensor bridge output Vout = Vex * (R3/(R1+R3) - R4/(R2+R4)) in millivolts and solve unknown resistance Rx = R3 * (R2 / R1) at null balance.
Two unloaded voltage dividers and a defined output polarity
R1 is the upper-left resistor, R3 lower-left, R2 upper-right and R4 lower-right. Apply Vex from the top node to the common bottom node. Vout is left midpoint minus right midpoint; reversing measurement leads reverses its sign. Assume ideal resistors and a high-impedance readout that does not load the bridge.
The balance condition is R1*R4=R2*R3 for nonzero excitation. Zero excitation also gives zero output for an unbalanced bridge, so it cannot establish resistance balance. The ideal balance ratio is independent of excitation amplitude; actual measurement accuracy is affected by component tolerances, lead resistance, heating, offsets and noise.
A1% resistance change does not specify strain without gauge factor and mechanical assumptions. The10V input is an arithmetic example, not an excitation recommendation for a particular gauge.
| Bridge Leg / Metric | Cell | 120-Ohm Quarter-Bridge | Electrical Output |
|---|---|---|---|
| Excitation Voltage Vex | B2 = 10 V | Precision DC reference | 5.0000 V midpoint at rest |
| Reference Legs R1, R2, R3 | B3:B5 = 120 Ohms | Left divider = 120 / 240 = 0.5000 | Fixed reference arms |
| Active Strain Gauge R4 | B6 = 121.2 Ohms (+1%) | Right divider = 121.2 / 241.2 | Vout = -24.88 mV |
| Null Balance Solve Rx | R3 * (R2 / R1) | Ideal ratio independent of nonzero Vex | Calculated balance resistance |
Wheatstone Bridge differential output in millivolts (mV)
Multiply volts by1000 for millivolts. This is output voltage, not normalized sensitivity in mV/V.
=IF(OR(COUNT(B2:B6)<>5,MIN(B3:B6)<=0),"Invalid inputs",ROUND(1000 * B2 * ((B5 / (B3 + B5)) - (B6 / (B4 + B6))), 2))Null-balance unknown resistance Rx = R3 * (R2 / R1) (Ohms)
Solve the R4 value that would balance the specified R1,R2,R3. A nonzero excitation and sufficiently sensitive detector are needed to identify a measured null.
=IF(OR(COUNT(B2:B5)<>4,B2=0,MIN(B3:B5)<=0),"Invalid inputs",ROUND(B5 * (B4 / B3), 2))Try the example
Use the original values or change them to test your understanding.