Introduction
In the advanced world of electrical circuits, accuracy is everything. Whether working in a physics laboratory or working in industrial measurement enterprises, a precise determination of an unknown resistance can have significant benefits. Of the contrivances that have been designed with this object in view, the Wheatstone Bridge is both ingeniously simple and very effective.
The Wheatstone Bridge was first proposed in 1833 by Samuel Hunter Christie and popularised by Sir Charles Wheatstone in 1843. It remains one of the most significant electrical engineering devices of modern times. Its effectiveness is due to the possibility of determining the resistance values with a high degree of accuracy by using the principle of balance.
In this discussion, we will discuss how the Wheatstone Bridge was constructed, the principle behind its construction, the derivation of the answers analytically, the practical uses and examples that can be given, referring to Fig. 1 and Fig. 2 in the reference text.
What is a Wheatstone Bridge?
The Wheatstone Bridge is a network of four resistors, which are organized in the form of a quadrilateral topology. A galvanometer, which is a very sensitive current detector device, is connected to the midpoint of the two adjacent legs, and a voltage source is connected to the rest of the opposing nodes.
Structure of the Wheatstone Bridge
As shown in Fig. 1, the bridge consists of:
- Four resistors, R1, R2, R3, and R4, form the arms of the bridge.
- A battery arm across points A and C.
- A galvanometer arm across points B and D.
This arrangement makes the Wheatstone Bridge look like a diamond with a cross-connection (the galvanometer).
Battery Arm and Galvanometer Arm
- The line connecting A and C is the battery arm, where the external voltage source is connected.
- The line between B and D is the galvanometer arm, which detects current.
If the galvanometer shows no deflection, it means the bridge is balanced.
Principle of Wheatstone Bridge
The Wheatstone Bridge works on the principle of null deflection. This means that when the bridge is balanced, no current flows through the galvanometer. At this balance point, the ratio of two known resistors is equal to the ratio of the other two resistors.
Balanced Condition of Wheatstone Bridge
When the bridge is balanced, the following relationship holds:
R2/R1 = R4/R3
This is called the balance condition of the Wheatstone Bridge. It allows us to calculate an unknown resistance if the other three resistances are known.
For example, if R1, R2, R3 are known and R4 is unknown, we can determine it as:
R4 = (R3R2)/R1
This simple formula forms the heart of the Wheatstone Bridge.
Mathematical Derivation of Balance Condition
To understand this mathematically, let us apply Kirchhoff’s Laws to the Wheatstone Bridge.
From Fig. 1:
- The first loop (ABDA) gives:
–I1R1 + I2R2 = 0
- The second loop (CBDC) gives:
I2R3 – I1R4 = 0
For a balanced bridge, Ig = 0, which means the current through the galvanometer is zero. Solving the above two equations, we arrive at the balance condition:
R2/R1 = R4/R3
Thus, the Wheatstone Bridge’s power lies in its ability to equate ratios and find the unknown resistance.
Applications of the Wheatstone Bridge
The Wheatstone Bridge is not just a theoretical tool; it has immense practical applications.
1. Measurement of Unknown Resistance
The most common use is to measure an unknown resistance by balancing the bridge. With the balance condition, an unknown resistor inserted in one arm can be calculated with precision.
2. The Meter Bridge
A Meter Bridge is a practical device based on the Wheatstone Bridge principle. Instead of using four separate resistors, a uniform wire of one meter is used. The unknown resistance is determined by balancing the lengths of the wire. This method is frequently used in school and college laboratories.
3. Strain Gauge Applications
The strain gauges used in engineering make heavy use of the Wheatstone Bridge. The electric resistance of a material in the case of extension or compression. Such small changes in resistance can be measured by a Wheatstone Bridge, thus allowing a strain to be measured accurately.
4. Temperature Measurement
Thermistors (temperature-sensitive resistors) can be placed in a Wheatstone Bridge circuit to measure temperature variations with high accuracy.
5. Detection of Small Resistance Changes
The Wheatstone Bridge is especially effective in measuring slight changes in resistance and so can be useful in sensor applications such as pressure transducers and displacement transducers.
Example Problem on Wheatstone Bridge
Let’s solve a practical problem to see the Wheatstone Bridge in action.
Problem Statement
As shown in Fig. 2, the resistances are:
- AB = 100Ω,
- BC = 10Ω,
- CD = 5Ω,
- DA = 60Ω.
A galvanometer of resistance 15Ω is connected across BD. A potential difference of 10V is applied across AC. Find the current through the galvanometer.
Step-by-Step Solution
We apply Kirchhoff’s Loop Rule to different meshes.
Mesh BADB:
100I1 + 15Ig – 60I2 = 0
Mesh BCDB:
10(I1 – Ig) – 15Ig – 5(I2 + Ig) = 0
Mesh ADCEA:
60I2 + 5(I2 + Ig) = 10
Simplifying and solving these equations step by step:
- From the third equation:
65I2 + 5Ig = 10
13I2 + Ig = 2
- Solving for I2:
I2 = 31.5Ig
- Substituting back, we get:
410.5Ig = 2
Ig = 4.87 mA
Final Answer
The current through the galvanometer is:
Ig = 4.87 mA
This demonstrates how the Wheatstone Bridge can be applied in real-world resistance measurements.
Advantages of the Wheatstone Bridge
- High Accuracy: Assures accurate determination of unknown resistors.
- Simplicity: This gives ease of construction and use.
- Sensitivity: Able to sense slight variations of resistance.
- Versatility: Flexible in measuring physical quantities like strain, temperature, and pressure.
Limitations of the Wheatstone Bridge
- Temperature Sensitivity: The change in temperature causes an observable change in the value of resistance.
- Stable Power Supply Needed: The accuracy of the measurement is directly dependent on the supply of a constant volume source.
- Limited Range: The instrument is not very suitable for making direct measurements of very high or very low resistances.
- Contact Resistance: Measurement errors can occur when the circuit has loose and intermittent connections.
Conclusion
The Wheatstone Bridge is an old electrical device that is a combination of analytical simplicity and operational accuracy. It allows calculating an unknown resistance with a very high level of accuracy by balancing a circuit in the form of four resistors. It is useful not only in educational environments but also in industrial, engineering, and research applications, in particular, sensor technology and strain measurement.
The Wheatstone Bridge is a beautiful and powerful tool in the electrical engineering profession, as shown in Fig. 1, which shows the basic structure, and Fig. 2, which shows a practical calculation. Despite the modern era of the wide use of digital multimeters, the general principle represented by the Wheatstone Bridge still remains to guide and influence other modern measurement systems.