Wheatstone Bridge: circuit, details

The Wheatstone bridge is a circuit that is often encounter during physics school lessons and then forgotten about, but it is widely used for test and measurement systems, sensors and in many more areas.

Bridge Circuits Includes:
Bridge circuits: the basics Wheatstone bridge

The Wheatstone bridge is the most widely known of the large variety of bridge circuits that are used.

The Wheatstone bridge circuit consists of four resistors, two in each arm, with meter bridging the centres of the two arms.

Wheatstone bridge - showing the two main arms: R1 + R4, and then R2 + R3 with a meter bridging the two arms — The Wheatstone bridge is one of the more widely known bridge circuits

This bridge circuit is an essential element used in the making many types of accurate measurement.

It is often used in various forms of electronic measuring instrumentation to this day, in fact in many more measuring instruments, sensors and other applications than we might imagine.

Wheatstone bridge basics

One of the key applications for the Wheatstone bridge is in proving a platform for making very accurate measurements of resistance.

The bridge can be used to measure an unknown electrical resistance by balancing two legs of a bridge circuit. This can be done by having known components elsewhere int he circuit and the unknown one in one leg.

The Wheatstone bridge used for measuring unknown resistance

When using the bridge, the unknown resistance is placed into the circuit as in the example circuit shown above. The valuable resistor is then adjusted until the bridge balances and no current flows through the galvanometer.

The unknown resistance can then be calculated using the formula below:

R_{3} = \frac{R_{2} R_{4}}{R_{1}}

Where:
Rx is the unknown resistance
R1, R2, and R3 are the values of the known resistors

To enable the value of the variable resistor to be known, a potentiometer used to be used. These older potentiometers had a length of resistance wire and a sliding contact. The distance where the slider was at any given point could be accurately determined and the resistance could be determined by the length along the track. This was normally calibrated so that the distance and hence the resistance could be easily measured and determined.

Today, there are electronic variable resistors for which the value can be accurately determined - these can consist of series resistors which can be electronically switched, etc.

It is worth noting that if accurate measurements are required, then the known resistors should be accurate high stability types with low temperature coefficients of resistance.

Understanding the Wheatstone bridge

In the diagram shown in the previous section, R3 is the resistor with an unknown value, and the other three resistors are known.

In operation, the bridge circuit is adjusted until the bridge is "balanced" i.e. no current flowing through the meter.

At this point, the potential difference between the two midpoints (B and D) is zero.

This means that the ratio of the two resistances in the known leg (R4 / R1) is equal to the ratio of the two resistances in the unknown leg (R3 / R2).

If the bridge is unbalanced, the direction of the current indicates whether R2 is too high or too low.

At the balance point the ratios of the resistances in the two arms are equal, hence:

\frac{R_{4}}{R_{1}} = \frac{R_{3}}{R_{2}}

Hence it is possible to deduce that:

R_{3} = \frac{R_{2} R_{4}}{R_{1}}

Advantage of using a Wheatstone bridge

Although the Wheatstone bridge might seem like a rather archaic system, it is actually very useful where high accuracy measurements are needed.

It is possible to use high accuracy fixed resistors and also a high accuracy variable resistor.

The measurement then simply requires a balance point to be found, and detecting a zero point does not rely on any calibrated meter and therefore it is very accurate.

As a result of this, bridge circuits, including the Wheatstone bridge find uses in many high accuracy measurement systems.

Current Wheatstone bridge applications

The Wheatstone bridge is widely used in a number of applications to this day.

Calibration: The bridge circuit plays a vital role in calibrating other electrical instruments, ensuring their accuracy. Its high accuracy resulting from its "null" type measurements means that it is very accurate and reliable.
Strain Gauge Measurements: Wheatstone bridges are used in conjunction with strain gauges to measure tiny changes in physical dimensions, which have applications in various fields like structural engineering and robotics. The bridge circuit lends itself to these measurements, especially with regard to the accuracy needed. Often the strain gauge assembly incorporates the Wheatstone bridge.
Sensor Interfacing: Variations of the Wheatstone bridge can be used to interface various sensors with electronic circuits. Again, like strain gauges, other forms of sensor may have small changes in resistance, for which the Wheatstone bridge is an ideal option.

Although the basic Wheatstone bridge is used for resistance measurements and for applications like strain gauges, and various forms of sensor, resistance is by far the most widely needed measurement to be made. However, other variations on the basic bridge theme can be used for other types of measurement.

The Wheatstone bridge has been established as an accurate method for making resistance measurements for very very many years. It was used at the very earliest days of electrical science, and it is very widely used today where high accuracy measurements are needed.