The Metre Bridge Application 3: How to Calculate Unknown Resistance Ry

Discover the working principle, applications, and setup of a metre bridge. Learn how to measure resistance using a metre bridge, also known as a Wheatstone bridge, with detailed diagrams and calculations
The Wheatstone Bridge is a fundamental electrical circuit that measures unknown electrical resistances by balancing two legs of a bridge circuit. It was invented by Samuel Hunter Christie in 1833 and later popularized by Sir Charles Wheatstone in 1843. The working principle of the Wheatstone Bridge is based on the concept of null deflection, where the bridge is balanced and no current flows through the galvanometer.
Components of the Wheatstone Bridge
1. **Four Resistors**: The bridge consists of four resistors arranged in a diamond shape. These are:
- Two known resistors \( R_1 \) and \( R_2 \)
- One variable resistor \( R_3 \) (or a standard known resistor)
- One unknown resistor \( R_x \)
2. **Galvanometer**: A sensitive device placed between the two legs of the bridge to detect the presence of current.
3. **Power Source**: A voltage source is connected across the bridge to provide the necessary potential difference.
Working Principle
The Wheatstone Bridge operates on the principle of null deflection, which occurs when the bridge is balanced. This balance is achieved when the ratio of the two known resistors equals the ratio of the unknown resistor and the variable resistor.
1. **Initial Setup**: Connect the known resistors \( R_1 \) and \( R_2 \), the variable resistor \( R_3 \), and the unknown resistor \( R_x \) in a diamond shape. The galvanometer is connected between the two midpoints of the bridge, and a voltage source is connected across the bridge.
2. **Balancing the Bridge**: Adjust the variable resistor \( R_3 \) until the galvanometer shows zero deflection. At this point, no current flows through the galvanometer, indicating that the bridge is balanced.
3. **Mathematical Balance Condition**: When the bridge is balanced, the following condition holds true:
\[ \frac{R_1}{R_2} = \frac{R_x}{R_3} \]
From this, the unknown resistance \( R_x \) can be calculated as:
\[ R_x = R_3 \left(\frac{R_1}{R_2}
ight) \]
Applications of the Wheatstone Bridge
1. **Resistance Measurement**: The primary application is to measure an unknown resistance accurately.
2. **Strain Gauge Measurements**: In mechanical engineering, Wheatstone bridges are used with strain gauges to measure small deformations in structures.
3. **Temperature Sensing**: The bridge can be used with thermistors or resistance temperature detectors (RTDs) for precise temperature measurements.
4. **Sensor Calibration**: Wheatstone bridges calibrate and measure various sensor outputs, ensuring accurate readings.
5. **Low Resistance Measurement**: By using precise standard resistors and careful balancing, very low resistances can be measured with high accuracy.
Advantages of the Wheatstone Bridge
1. **High Accuracy**: It precisely measures unknown resistances.
2. **Sensitivity**: The null method using a galvanometer allows for the detection of very small changes in resistance.
3. **Versatility**: Can be adapted for various types of sensors and measurement scenarios.
Limitations of the Wheatstone Bridge
1. **Temperature Sensitivity**: Resistance values can change with temperature, affecting accuracy.
2. **Complex Setup**: Requires careful balancing and adjustment of the variable resistor.
3. **Limited Range**: Best suited for measuring moderate resistances; very high or very low resistances may require specialized setups.
The Wheatstone Bridge remains a crucial tool in electrical and electronic measurements, providing a reliable and precise method for determining unknown resistances and calibrating sensors.