Wheatstone Bridge Circuit Diagram
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A Wheatstone bridge circuit diagram shows four resistors arranged in a diamond (bridge) configuration with a voltage source and a galvanometer across the midpoints. When the bridge is balanced, no current flows through the galvanometer, and the unknown resistance can be calculated precisely. This null-deflection method makes the Wheatstone bridge one of the most accurate passive measurement techniques in electronics.
The Wheatstone bridge was proposed by Samuel Hunter Christie in 1833 and popularised by Sir Charles Wheatstone in 1843. Despite its age, the circuit remains the standard approach for precision resistance measurement in laboratory and industrial settings.
The topology consists of four resistors — R1, R2, R3, and Rx — arranged in a diamond. A DC voltage source (V) is connected across the top and bottom vertices. A galvanometer (G) bridges the two middle vertices. R1 and R2 form the left branch; R3 and Rx form the right branch.
Bridge balance condition: The bridge is balanced when the ratio of the two resistors in the left branch equals the ratio in the right branch. Mathematically: R1/R2 = R3/Rx. Rearranging gives the unknown resistance: Rx = (R3 × R2) / R1. At balance the potential at both galvanometer nodes is identical, so zero current flows and the galvanometer reads null.
To measure Rx, three resistors must be known. R1 and R2 are usually precision fixed resistors (ratio arms), and R3 is an adjustable standard resistance (decade box or rheostat). R3 is varied until the galvanometer deflects to zero, then Rx is calculated from the balance equation.
Sensitivity and sources of error: Sensitivity is highest when all four arms have similar resistance values. The galvanometer must have appropriate sensitivity for the resistance range being measured. Thermal EMF at junctions, lead resistance in four-wire variants (Kelvin double bridge for very low values), and contact resistance at switches introduce error. For resistances below 1 Ω, the Kelvin bridge extension is preferred.
Derivation of the balance condition: When balanced, no current flows through the galvanometer, so nodes B and D are at the same potential. The current through R1 and R2 is I1 = V/(R1+R2). The current through R3 and Rx is I2 = V/(R3+Rx). At balance, the voltage across R2 equals the voltage across Rx: I1×R2 = I2×Rx. Substituting I1 and I2 and simplifying gives R1/R2 = R3/Rx.
Practical construction: Use a 6 V battery or regulated DC supply. Connect R1 (known, e.g. 1 kΩ) and R2 (known, e.g. 1 kΩ) in series across the supply — this is the left branch. Connect R3 (decade box, 0–10 kΩ) and Rx (unknown resistor) in series across the same supply — this is the right branch. Connect the galvanometer between the junction of R1/R2 and the junction of R3/Rx. A protective resistor (1 kΩ) in series with the galvanometer prevents damage during initial balance search.
Applications: Wheatstone bridge circuits are the foundation of strain-gauge load cells, platinum resistance thermometers (PRTs), resistance temperature detectors (RTDs), and many sensor conditioning circuits. In a load cell, all four arms are strain gauges bonded to an elastic member; applied force changes the gauge resistances and unbalances the bridge, producing an output voltage proportional to load.
Unbalanced bridge output: When the bridge is not at null, the output voltage Vout = V × (R3/(R3+Rx) − R2/(R1+R2)). This is the basis for transducer signal conditioning. The output is linear only when the imbalance is small; for large excursions a linearisation correction is needed.
You can draw and simulate a Wheatstone bridge in the free circuit diagram editor at circuitdiagrammaker.com — place four resistors in the diamond layout, add a voltage source, and connect a galvanometer to test the balance condition interactively.
How to wire wheatstone bridge circuit diagram
- Gather components Collect two known precision resistors (R1, R2 as ratio arms), a decade resistance box (R3), the unknown resistor (Rx), a 6 V DC supply, and a sensitive galvanometer.
- Wire the left branch Connect R1 and R2 in series between the positive supply terminal and ground to form the left voltage divider.
- Wire the right branch Connect R3 (decade box) and Rx in series between the positive supply terminal and ground to form the right voltage divider.
- Connect the galvanometer Wire the galvanometer (with a 1 kΩ protective series resistor) between the midpoint of R1/R2 and the midpoint of R3/Rx.
- Apply power and adjust R3 Switch on the supply and slowly adjust R3 until the galvanometer reads zero (null). Remove the protective resistor for the final fine balance if needed.
- Record R3 value Note the resistance value of the decade box at null balance.
- Calculate Rx Apply the formula Rx = (R3 × R2) / R1 to find the unknown resistance.
Specifications
| Balance condition | R1/R2 = R3/Rx |
|---|---|
| Unknown resistance formula | Rx = (R3 × R2) / R1 |
| Output voltage (unbalanced) | Vout = V × [R3/(R3+Rx) − R2/(R1+R2)] |
| Galvanometer current at balance | 0 A (null deflection) |
| Typical supply voltage | 1.5 V – 12 V DC |
| Measurable resistance range | 1 Ω – 1 MΩ (standard bridge) |
| Accuracy (lab grade) | ±0.01% – ±0.1% |
| Ratio arms R1:R2 common values | 1:1, 1:10, 1:100, 10:1 |
| Standard arm R3 (decade box range) | 1 Ω – 10 kΩ adjustable |
| Galvanometer sensitivity required | 1 μA / division (typical) |
Safety warnings
- Do not exceed the power rating of any resistor in the bridge arms — calculate P = V²/(R1+R2) and ensure it is below the component's rated wattage.
- Always insert a protective series resistor (at least 1 kΩ) in series with the galvanometer before the first balance attempt to prevent overload damage.
Tools needed
- DC regulated power supply (1.5 V – 12 V)
- Sensitive galvanometer or microammeter
- Decade resistance box (1 Ω – 10 kΩ)
- Precision resistors for ratio arms (0.1% tolerance)
- Digital multimeter (for verification)
- Breadboard and connecting wires
Common mistakes
- Using resistors with insufficient precision for ratio arms (R1, R2) — always use 0.1% or better tolerance metal-film resistors.
- Omitting the protective series resistor on the galvanometer during initial balance search, risking burning out the sensitive movement.
- Neglecting lead resistance when measuring low-value resistors — use short, thick leads or upgrade to a Kelvin bridge.
- Leaving the power supply on continuously — prolonged current causes resistor self-heating, which drifts Rx and introduces error.
- Misidentifying which node is B and which is D, causing a crossed galvanometer connection and inverted deflection.
Troubleshooting
- Galvanometer never reaches null regardless of R3 adjustment
- Cause: One of the resistors in the bridge may be open-circuit, or the galvanometer is not connected to the correct midpoint nodes. Fix: Check continuity of all four arms with a multimeter and verify the galvanometer is wired across the two midpoint junctions, not across the supply.
- Galvanometer deflects strongly in one direction only
- Cause: The range of R3 (decade box) does not cover the value of Rx, so balance cannot be reached. Fix: Adjust the ratio R1/R2 — for example, switch to a 1:10 ratio if Rx is ten times larger than the current R3 range.
- Measurement results vary each time
- Cause: Thermal EMF or unstable supply voltage causing drift. Fix: Use a stable regulated DC supply, allow components to reach thermal equilibrium before reading, and use a reversing switch to cancel thermal EMF effects.
Frequently asked questions
What is the balance condition for a wheatstone bridge circuit diagram?
The bridge is balanced when R1/R2 = R3/Rx, meaning the product of opposite arm resistances are equal (R1×Rx = R2×R3). At this point, the galvanometer reads zero current.
Why is the Wheatstone bridge more accurate than a simple ohmmeter?
The null-deflection method eliminates the effect of battery voltage variation and galvanometer internal resistance because the measurement only depends on the ratio of known resistors, not on absolute voltage or current.
What happens if the bridge is not balanced?
A current flows through the galvanometer. The output voltage is Vout = V × [R3/(R3+Rx) − R2/(R1+R2)], which can be used in sensor applications to produce a signal proportional to the imbalance.
Can a Wheatstone bridge measure very low resistances?
For resistances below about 1 Ω, lead and contact resistances introduce significant error. The Kelvin double bridge (Thomson bridge) uses additional ratio arms to eliminate lead resistance, extending accuracy to milliohm values.
What is a strain gauge Wheatstone bridge?
In a strain-gauge bridge, all four resistors are strain gauges bonded to a structural member. Applied force changes gauge resistance and unbalances the bridge, producing an output voltage proportional to strain or load. This is the principle used in load cells and pressure sensors.
What supply voltage should I use for a Wheatstone bridge?
A 1.5 V to 12 V DC regulated supply is typical. Higher voltages increase sensitivity but also cause self-heating of the resistors, which changes their values. For precision work, keep power dissipation in each arm below 100 mW.
What is the sensitivity of a Wheatstone bridge?
Sensitivity is the galvanometer deflection per unit change in the unknown resistance. It is maximised when all four arms have equal resistance values and the galvanometer has a low internal resistance relative to the bridge arms.