Wheatstone Bridge

  • Description of the Wheatstone bridge and explanation of its applications
  • Methods and calculations used in Wheatstone bridge operation
  • List of the limitations of the Wheatstone bridge
  • Variations on the Wheatstone bridge and their applications

A Wheatstone bridge is a special type of electrical circuit that is used to accurately measure the unknown resistance of a component. It was also originally used to calibrate measurement instruments such as ammeters and voltmeters using a resistive slide wire.

The Wheatstone bridge was originally invented by Samuel Hunter Christie in 1823. In 1843, Sir Charles Wheatstone saw its potential for use in soils analysis, so he improved the design and in doing so, popularised its use.

Today the Wheatstone bridge is still used to measure very small resistances (on the order of milliohms) as it provides more accuracy than modern multimeters.

It can also be seen today in modern operational amplifiers, where it’s used to integrate transducers and sensors into the main circuit.

How does the Wheatstone bridge work?

The layout of the Wheatstone bridge consists of two simple series resistance arrangements that run in parallel, and which produce a zero voltage difference between the branches when the resistances are balanced. Each leg contains two resistors, making a total of four in a diamond formation. One of the resistors is the component of unknown resistance and another is a variable resistor.

Referring to the diagram above, R1 and R3 are resistors with known resistance, R2 is a variable resistor, and Rx is the component with unknown resistance. A voltmeter or galvanometer is connected between points B and D. To ascertain the unknown resistance, we simply vary the resistance at R2 until the meter reads zero, i.e. both legs are balanced. We can then work out Rx using the following method:

Wheatstone bridge formula

Other applications of the Wheatstone bridge

Apart from finding the unknown electrical resistance of components, the Wheatstone bridge has a variety of other uses, especially in the measurement of mechanical and electrical quantities.

One of the most common applications of a Wheatstone bridge circuit is the use of a photoresistive device to measure light. To do this, simply replace one of the bridge circuit resistors with a light-dependent resistor or LDR. LDRs can be used to indicate whether a light source is on or off or to measure the intensity of light.

The bridge circuit can be applied to measure the change in resistance of other variable quantities. For example, the photoresistive LDR can be replaced with a strain gauge, thermistor, pressure sensor, or any similar transducer. High-accuracy thermometers can be made using Wheatstone bridge circuits.

With a little modification of the Wheatstone bridge circuit, other values such as inductance, capacitance, and impedance can also be measured.

Wheatstone bridge limitations and errors

The following problems may reduce the accuracy of the Wheatstone bridge:

  1. Inaccuracies can occur within the galvanometer as it is less sensitive than the resistors
  2. The marked resistance value of any, or all, of the three resistors may be different than the true resistance value
  3. Self-heating of the circuit can generate an error within the bridge
  4. Thermal EMF may cause an error when measuring lower resistance values
  5. If the legs are unbalanced in any way, the readings will be inaccurate

Also, the Wheatstone bridge measures resistances from the two-to-three-ohm range up to mega-ohm values. The upper range can be extended by applying extra EMF to the bridge.

Any reduction in sensitivity reduces the accuracy of the bridge. The sensitivity of the Wheatstone bridge is higher when all the resistance values are equal or have a ratio in unity. The sensitivity is lower when the ratio of resistance is less than one.

Bridge modifications

The Wheatstone bridge can be considered the fundamental circuitry bridge. However, other modifications can be made, allowing the measurement of various types of resistance. Examples of these variations include:

Kelvin bridge – measures small four-terminal resistances

Carey Foster bridge – measures low resistance (below three ohms)

Maxwell bridge – measures reactive components.


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