Wheatstone Bridge: Principle, Circuit, and Applications Explained

Wheatstone bridge is an electrical circuit designed for the precise measurement of resistance and detection of its small variations. The circuit consists of four resistive elements connected in such a way that it allows comparison of voltages across two parallel branches.

The main feature of the Wheatstone bridge is its ability to detect very small changes in resistance by measuring the resulting voltage difference. This makes the circuit widely used in electronic scales, pressure sensors, measuring instruments, and industrial automation systems.

What Is a Wheatstone Bridge and How Is It Constructed?

The Wheatstone bridge is an electrical network made up of four resistors forming two parallel branches. Each branch contains two resistors connected in series, with measurement points located between them to capture the voltage difference.

The classic Wheatstone bridge circuit includes the following elements:

• R1 and R2 - resistors of the first branch.
• R3 and R4 - resistors of the second branch.
• Power supply - creates voltage between the top and bottom nodes of the circuit.
• Measuring device - connected between the midpoints of each branch to detect the potential difference.

One resistor can be of unknown resistance to be determined. In sensors, a sensitive element often replaces a standard resistor, changing its resistance under pressure, load, or deformation.

This bridge circuit for resistance measurement allows comparison of the electrical properties of both branches, detecting even minute resistance changes that cannot be measured directly with a standard ohmmeter.

When the ratio of resistances in both branches is equal, the voltages at the midpoints match. If one resistor changes, balance is lost, and a potential difference appears between the measuring points. This is the fundamental operating principle of the Wheatstone bridge.

How the Wheatstone Bridge Works

The Wheatstone bridge operates by comparing voltages across two parallel branches of an electrical circuit. Each branch acts as a voltage divider, and the measuring device detects the potential difference between their midpoints.

The functioning of the bridge depends on the ratio of its four resistances:

• Balanced condition: Voltages at the midpoints are equal, so the measuring device reads zero.
• Unbalanced condition: When one resistance changes, the corresponding midpoint voltage shifts, creating a potential difference between the branches.
• Restoring balance: Adjusting a known resistor restores zero voltage, revealing the unknown value.

The Wheatstone bridge balance condition for a circuit where R1 and R2 form the first branch, and R3 and R4 the second, is expressed as:

R₁/R₂ = R₃/R₄

This means the ratio of resistances in both branches must be identical. If this condition is met, the voltage difference between the midpoints is zero.

For example, with all four resistors at 100 Ω, the bridge is balanced. If R1 increases to 101 Ω, the balance is disturbed, and a small output voltage emerges.

The greater the change in the resistance ratio, the larger the output signal. Its magnitude also depends on the power supply voltage and resistor values.

Such dependence allows the Wheatstone bridge not only to determine unknown resistance but also to register small physical changes that sensors convert into resistance variations.

Wheatstone Bridge Circuit and Formulas

Calculating a Wheatstone bridge involves the resistance ratios of its two branches. If the bridge is balanced, the unknown resistance can be found using the three known resistors.

The balance condition is given by:

R₁ × R₄ = R₂ × R₃

If R4 is the unknown resistance, the equation becomes:

R₄ = (R₂ × R₃) / R₁

Simply determine the other three resistances and adjust for zero voltage across the measuring diagonal.

Example Calculation of a Wheatstone Bridge

Suppose the following resistances are used in the circuit:

• R1 = 100 Ω
• R2 = 200 Ω
• R3 = 150 Ω
• R4 = unknown

Substituting into the formula:

R₄ = (200 × 150) / 100 = 300 Ω

With R4 at 300 Ω, the bridge is balanced, and the voltage between the branch midpoints is zero.

For measuring resistance changes, the output voltage formula is also important:

U_out = U_supply × (R₂/(R₁+R₂) - R₄/(R₃+R₄))

Here, U_supply is the power supply voltage, and U_out is the potential difference between the branch midpoints.

The formula shows that the output voltage depends on the ratios of all four resistances. Any imbalance produces a nonzero output, allowing detection of even minor sensor parameter changes.

How the Wheatstone Bridge Measures Small Resistance Changes

The Wheatstone bridge enables detection of resistance changes too small for conventional ohmmeters. Instead of measuring absolute values, the circuit converts resistance changes into a voltage difference between its two branches.

For example, if a sensor's resistance rises from 100 to 100.1 Ω-a change of just 0.1%-this slight deviation unbalances the bridge and generates a measurable electrical signal.

With a 5 V supply and the other resistors at 100 Ω, the output voltage is approximately 1.25 mV. This signal can then be amplified and processed by electronic circuits.

The sensitivity of the Wheatstone bridge depends on several factors:

• Supply voltage: Higher voltage increases the output signal.
• Resistance change: Greater deviation in the sensitive element causes a larger imbalance.
• Resistor accuracy: Value variations introduce initial offset and can reduce measurement accuracy.
• Temperature stability: Heating alters element resistances and may introduce errors.

For particularly weak signals, instrumentation amplifiers and analog-to-digital converters (ADC) are used to boost and digitize the output voltage.

Measurement systems also employ temperature compensation and calibration to separate useful sensor signals from resistance changes due to environmental factors.

Applications of the Wheatstone Bridge

The Wheatstone bridge is widely used in measurement electronics, especially where physical effects cause small changes in electrical resistance. The circuit converts these changes into voltage, which is then processed by electronic devices.

Key areas of application include:

• Electronic scales: Strain gauges change resistance when deformed under load. The bridge circuit converts these changes into an electrical signal to determine weight.
• Pressure sensors: Sensitive elements deform under fluid or gas pressure, with resistance changes used to calculate pressure.
• Strain measurement: Strain resistors attached to structures help monitor tension, compression, and mechanical loads.
• Temperature sensors: Thermistors alter resistance with heating or cooling, and the bridge registers these changes.
• Industrial automation: Bridge circuits monitor equipment parameters and transmit measurement signals to control systems.

The Wheatstone bridge is especially common in electronic scales, where multiple strain gauges can form a full bridge. This configuration increases the output signal under load and helps compensate for some temperature effects.

For a detailed explanation of how mechanical loads are converted into electrical signals, see our article on how load cells work in electronic scales: principle and measurement accuracy.

Conclusion

The Wheatstone bridge is a simple electrical circuit that enables precise resistance measurement and the detection of small variations. Its operation is based on comparing voltages in two branches and recording deviations from balance.

To determine unknown resistance, the bridge is balanced; for sensor operation, the output voltage is measured. Thanks to these advantages, the Wheatstone bridge remains a popular solution in electronic scales, strain measurement, pressure sensors, and industrial measurement equipment.