The Carey Foster Bridge: Precision Resistance Measurement

A Wheatstone Bridge Variant for Low Resistances

The Carey Foster bridge (often called Carey Foster slide-wire bridge) is a modified Wheatstone bridge designed for measuring low resistances (milliohms to ohms) or comparing nearly equal resistances with high precision. It's a staple of physics labs and precision metrology.

Circuit Principle

Like a Wheatstone bridge, it balances two voltage dividers. The innovation: ratio arms P and Q are a uniform slide wire (typically 1–2 m of manganin or constantan), allowing continuously adjustable, precisely measurable ratios.

Balance Condition (Galvanometer G reads zero):

R / P = S / Q  →  R = S × (P / Q)

Where:

• R = unknown resistance
• S = standard known resistance
• P, Q = resistances of slide wire segments (proportional to lengths)

Operating Procedure

1. Connect R and S in the two gaps; battery B and galvanometer G across the bridge.
2. Slide contact (jockey) along wire to find balance point C (G = 0).
3. Measure lengths: AC = l₁, CB = l₂ (total wire length L = l₁ + l₂).
4. Ratio P/Q = l₁/l₂ (since wire is uniform).
5. Calculate: R = S × (l₁ / l₂)

Eliminating End Resistance Errors

The true genius: swap R and S, re-balance at new point C' (lengths l₁', l₂'). Then:

R - S = ρ (l₁' - l₁)   where ρ = resistance per unit length of wire

This cancels unknown contact/lead resistances at the gaps—critical for milliohm accuracy.

Key Advantages

• High precision (0.01–0.1% achievable).
• No need for standard resistance boxes (just one S).
• Self-calibrating wire (ρ determined from known R, S).
• Temperature compensation (manganin/constantan low TCR).

Applications

• Lab measurement of wire resistivity, contact resistance, shunt calibration.
• Quality control for low-value resistors, shunts, busbars.
• Teaching: bridge principles, null methods, error analysis.

Limitations

• Only for low resistances (< ~10 Ω); high R requires different bridge (e.g., Kelvin double bridge for very low, Megger for high).
• Requires stable, uniform slide wire; sensitive to thermal EMFs (use AC or reverse battery).
• Manual balancing—slow vs. digital DMMs.

The Carey Foster bridge remains the gold standard for teaching and calibrating low-resistance measurements—where geometry meets precision.