## What is a Wheatstone bridge method?

A Wheatstone bridge is a circuit used to measure unknown resistance by measuring the ratios of the two branches of the circuit such that each branch has two resistance and out of four resistance one is unknown. The two branches are joined in between with the help of galvanometer which is used to determine the direction of the current. The main advantage of this circuit is that it can provide the most accurate measurement (different from a simple voltage separator).

## Principle of Wheatstone bridge

The Wheatstone bridge operates on a principle of zero deviation of the galvanometer. As the ratio of the resistances in the two branches are equal there is no current that flows through the galvanometer and hence the deflection is zero, this condition is called the normal conditions. The bridge is considered to be working in the stable state when there is current flowing through the galvanometer. The stable condition of the circuit is obtained by varying the resistance of the variable resistance present in the circuit until there is no current flowing through the galvanometer.

## Construction of the Wheatstone bridge method

The Wheatstone bridge circuit is nothing more than two simple series resistance systems connected between the power supply terminal and the ground, which produces a zero voltage difference between the two corresponding branches during the measurement. The Wheatstone bridge circuit has an input terminal and an output terminal, including 4 resistances, arranged in a standard diamond structure.

The Wheatstone bridge circuit consists of four arms, of which two arms include resistors with known resistances. while the other arms includes unknown resistors and a variable resistors. The circuit also contains a galvanometer and an electric power supply. The source of electromotive force is connected between points A and B and the variable resistance is connected between points C and D. The current flowing in the circuit depend upon the effective resistance of the circuit and the emf across the circuit.

For the diagram, the known resistances are  the unknown resistance is ${R}_{x}$.

Then, under balanced conditions the ratios are,

$\frac{{R}_{1}}{{R}_{2}}=\frac{{R}_{3}}{{R}_{x}}$

Then, the value of the unknown resistance is calculated by the below formula.

${R}_{x}=\frac{{R}_{2}{R}_{3}}{{R}_{1}}$

## Galvanometer

The principle behind the moving coil galvanometer is based on the discovery by Hans Christian Oersted that there is a magnetic field around a current-carrying wire and thus the magnetic force is exerted. Oersted found that the larger the current in the conductor, the greater the magnetic force.

The force can be made stronger by wrapping the wire in a magnetic core such as iron. Then the motor effect of electric current was discovered. The moving coil galvanometer is experiences the motor effect of electric current. Hence galvanometer can be used to measure if the wheatstone bridge is in balanced condition or not. If no current flows in the galvanometer, the bridge is said to be balanced.

## Sensitivity of the Wheatstone bridge

The Wheatstone bridge reflects the concept of the differential measurement and it is very accurate. The Wheatstone bridge, can be used to measure inductance, impedance, and other quantities like the amount of gases that are present in a sample the help of exlosimeter meter. Kelvin bridges are designed from the principle of the Wheatstone bridges and are used to measure the resistances of very small range.

The Wheatstone bridge is very sensitive when the values of the ratio of all the resistances are of equal range and the ratio is unity. When the value of the ratio is lower than unity, their sensitivity will decrease. Decreasing the sensitivity will reduce the accuracy of the bridge.

It is often desirable to know the galvanometer response that should be expected on an unbalanced bridge to the flow current within the galvanometer in the bridge network. The following conditions are often used.

• Selecting a galvanometer where a given imbalance can be found in the construction of a particular bridge,
• Determine the apparent minimum inequality with the galvanometer provided within the design of the bridge,
• Determine the expected deviation of certain inequalities.
• Sensitivity to balancing can be done electronically by adjusting the bridge cycle to get a smaller balance.

## Error of the Wheatstone bridge method

The following are the errors in the Wheatstone bridge.

• The difference between the true value and the marked value of the resistors that are connected in the bridge can result in error in the measurments.
• There can be error in the measured value of the balanced bridge as Wheatstone bridge are not very sensitive.
• The resistance of the bridge changes due to self-heating, causing errors.
• The values of the emf source connected can also lead to inaccuracy of the measured resistance.

To reduced the above mentioned error one can make use of quality resistance with a galvanometer. Using resistance for the short term can reduce the errors that are caused by resistance heating. The thermal effect is reduced by connecting a reversing switch between just after the battery in the circuit.

## Limitation of the Wheatstone bridge method

The following are the limitation of the Wheatstone bridge.

• If it is not balanced, the Wheatstone bridge will provide incorrect readings.
• The Wheatstone bridge cannot measure the resistances of very low value.
• With a low level of resistance, resistance to tracking will be critical and introduce errors.
• The measuring of very large resistance will lead to non linearity of results.

## Uses of the Wheatstone Bridge method

The following are the application in the Wheatstone bridge.

• Wheatstone bridges are used for complete measurements of resistances.
• Wheatstone bridges and operational amplifiers are used together to interface the circuit such as transducer and sensors.

## Common Mistakes

Remember that, the Wheatstone bridge is less accurate when used to measure maximum resistance. When high resistance is measured, the results are usually not linear. Sometimes the resistance level will decrease depending on the temperature and the EMF used.

## Context and Applications

In each of the expert exams for undergraduate and graduate publications, this topic is huge and is mainly used for,

• Bachelor of Technology in Electrical and Electronics Department
• Bachelor of Science in Physics
• Master of Science in Physics
• Kelvin bridge
• Difference between AC & DC bridge
• Carey-Foster Slide-Wire bridge
• Maxwell’s bridge
• Anderson’s bridge

## Practice Problems

Q1. Wheatstone bridge is a __________.

a) AC bridge

b) DC bridge

c) high voltage bridge

d) power dissipation bridge

Correct option: (b)

Explanation: Wheatstone Bridge is a DC bridge used to measure the internal resistance. Schering bridges are used to measure high voltages. AC bridges include Anderson bridges, Maxwell bridges, etc.

Q2. How can the Wheatstone bridge be used to measure portable parameters?

a) In conjunction with a rectifier

b) Along with an op-amp

c) By connecting it to a thermistor

d) By making use of a transducer

Correct option: (b)

Explanation: Wheatstone bridges can be used to measure portable parameters such as temperature, weight, light, etc, using a operational amplifier.

Q3. The Wheatstone bridge can be compensated for sensitivity by which of the following method.

a) Using more than one resistive sensor

b) Making use of a heat sink

c) Using cooling fans

d) Immersing the circuit into a liquid

Correct option: (a)

Explanation: Using more than one pressure-resistant sensor between the four arms of the Wheatstone bridge, we obtain a full-bridge, a half-bridge, or a quarter bridge set up with an automatic measurement effect.

Q4. Which of the following is the application of the Wheatstone bridge.

a) Voltage measurement

b) Vurrent measurement

c) Light measurement

d) Power measurement

Correct option: (c)

Explanation: The Wheatstone bridge contains simple resistance in the standard arm. One of the simplest uses of the Wheatstone bridge is to measure light through a photo-blocking device.

Q5. Why Wheatstone bridge is used in the Telephone companies.

a) Measuring the telephone resistance

b) Computing the line strength

c) Maintaining dial tone

d) Locating the cable faults

Correct option: (c)

Explanation: Phone cable faults can be detected by telephone companies using the Wheatstone bridge. The dial tone is stored using optical fiber technology.

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### Wheatstone bridge method

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