Short Answer:

The Wheatstone bridge works on the principle of null deflection, where the bridge is said to be balanced when the voltage between the two midpoints is zero. This happens when the ratio of resistances in one branch is equal to the ratio in the other branch, and no current flows through the galvanometer.

It is mainly used to measure unknown resistance with high accuracy by comparing it with known resistances. When the bridge is balanced, calculations become simple and very precise using Ohm’s law.

Detailed Explanation:

Principle of Wheatstone bridge

The Wheatstone bridge is a very useful and accurate electrical circuit used to measure an unknown resistance by comparing it with known resistances. It was invented by Samuel Hunter Christie and later popularized by Sir Charles Wheatstone. The circuit works on a simple principle based on Kirchhoff’s laws and Ohm’s law.

It is mostly used in laboratories, instrumentation systems, and in strain gauge measurements because of its precision and sensitivity.

Basic Structure:

A Wheatstone bridge has four resistors arranged in a diamond shape:

• Resistors R1 and R2 are in one branch.
• Resistors R3 and R4 are in the other branch.
• A voltage source is connected across one diagonal.
• A galvanometer or voltmeter is connected across the other diagonal.

Working Principle:

The principle of the Wheatstone bridge is that:

When the ratio of resistances in one branch is equal to the ratio in the other branch, the potential difference across the galvanometer becomes zero, and no current flows through it.

This condition is known as bridge balance and can be written mathematically as:

R1R2=R3R4\frac{R1}{R2} = \frac{R3}{R4}R2R1​=R4R3​

In this state, the bridge is balanced, and the unknown resistance can be calculated easily.

Steps of Operation:

1. Power Supply:
   • A constant voltage is applied across the opposite corners of the bridge.
2. Balancing the Bridge:
   • The values of three resistors are known, and one resistor is unknown (typically R4).
   • The bridge is adjusted (using variable resistors) until the voltmeter shows zero voltage (null condition).
3. Calculation:
   • At null condition, the formula becomes:

R4=R3⋅R2R1R4 = \frac{R3 \cdot R2}{R1}R4=R1R3⋅R2​

1. • This allows for the accurate calculation of the unknown resistance R4.

Applications:

• Measurement of unknown resistance
• Strain gauge circuits for pressure, force, or stress measurement
• Temperature sensors (using RTDs)
• Precision measurement and calibration systems
• Detection of small changes in resistance

Advantages:

• Very high accuracy in resistance measurement
• Simple and easy to use
• Can detect very small changes in resistance
• No current through galvanometer during balance condition, reducing error

Conclusion:

The Wheatstone bridge works on the principle of balancing two resistor networks so that no current flows through the middle branch when the bridge is balanced. This condition makes it possible to measure unknown resistances with high precision. Its simplicity, accuracy, and reliability make it a popular choice in both academic and industrial applications, especially where sensitivity and precision are important.