Mode 1 — Find Rx from R1, R2, R3
Mode 2 — 4-Way Solver (each resistor from the other three)
Mode 3 — Galvanometer Voltage When Unbalanced
Mode 4 — Sensitivity & Null Conditions
Verified example
R1 = 100 Ω, R2 = 200 Ω, R3 = 150 Ω → Rx = 200 × 150 ÷ 100 = 300 Ω (exact). With a 12 V source and Rx = 310 Ω (unbalanced): Vg = 12 × (100/300 − 150/460) = 86.9565 mV. Sensitivity at the balance point: dVg/dRx = 8.8889 mV/Ω.
Frequently asked questions (FAQ)
When the bridge is balanced (zero galvanometer), R1/R2 = R3/Rx applies, so Rx = R2 × R3 ÷ R1. Example: R1 = 100 Ω, R2 = 200 Ω, R3 = 150 Ω → Rx = 200 × 150 ÷ 100 = 300 Ω.
Enter the three known resistor values, choose which resistor is unknown (R1, R2, R3, or Rx), then press Calculate. The calculator uses the balance condition R1/R2 = R3/Rx and solves all four directions: Rx = R2·R3/R1, R3 = R1·Rx/R2, R2 = R1·Rx/R3, R1 = R2·R3/Rx.
The bridge is balanced when the products of opposite resistors are equal: R1 × Rx = R2 × R3. Example: R1 = 100 Ω, R2 = 200 Ω, R3 = 150 Ω, Rx = 300 Ω → 100 × 300 = 30,000 and 200 × 150 = 30,000, so the galvanometer reads zero.
Vg = V × (R1/(R1+R2) − R3/(R3+Rx)). Example: V = 12 V, R1 = 100 Ω, R2 = 200 Ω, R3 = 150 Ω, Rx = 310 Ω → Vg = 12 × (100/300 − 150/460) = 0.08696 V ≈ 86.9565 mV. The sign of Vg indicates the needle deflection direction.
Using Vg = V×(R1/(R1+R2) − R3/(R3+Rx)): if Vg is positive, current flows from the right node (R3–Rx) to the left node (R1–R2); if negative, the reverse. If Rx is larger than its balance value, Vg is positive.
Voltage sensitivity is the derivative dVg/dRx = V × R3/(R3+Rx)², i.e. the galvanometer voltage change per ohm of Rx change. Example: V = 12 V, R3 = 150 Ω, Rx = 300 Ω → dVg/dRx = 12 × 150/450² = 8.8889 mV/Ω.
Minimum ΔRx = galvanometer current resolution ÷ (dIg/dRx), where dIg/dRx = (dVg/dRx)/(Rg + Rth). Example: V = 12 V, R1 = 100 Ω, R2 = 200 Ω, R3 = 150 Ω, Rx = 300 Ω, Rg = 50 Ω, 100 nA resolution → minimum ΔRx = 2.4375 mΩ.
Rth = (R1‖R2) + (R3‖Rx), i.e. the parallel sum of each arm. Example: R1 = 100 Ω, R2 = 200 Ω, R3 = 150 Ω, Rx = 300 Ω → Rth = 66.6667 + 100 = 166.6667 Ω. This value is used to compute the galvanometer current Ig = Vg/(Rg + Rth).
Sensitivity is maximum when all four resistors are of the same order (R1/R2 ratio near 1) and the source voltage V is as large as possible within the resistors' power limits. An extreme arm ratio (e.g. R1/R2 = 1000) makes dVg/dRx small, making it hard to detect small imbalances.
Measuring unknown resistors with high precision, measuring small resistance changes in sensors (strain gauges, RTD/thermistors, pressure sensors), and instrument calibration. The null principle makes the result independent of source voltage accuracy.
Yes. Modes 1 and 2 solve bridge balance problems (finding Rx or another resistor), mode 3 computes galvanometer voltage when unbalanced along with deflection direction, and mode 4 computes sensitivity and null conditions — with the formula shown in every result.
All resistors in ohms (Ω) — you may use kΩ or MΩ as long as you are consistent across all four resistors, since the formula uses ratios. Source voltage in volts (V), Vg results are auto-formatted to mV/µV when small, and galvanometer resolution in amperes (e.g. 100 nA = 1e-7 A).