Overview

This experiment uses a Wheatstone bridge to determine the value of an unknown resistance by balancing two arms of a bridge circuit, eliminating the need for current measurement.

What This Experiment Demonstrates

• Precise measurement of resistance
• Concept of bridge balance (null deflection)
• Reduction of systematic errors

Apparatus Required

• DC power supply or cell
• Galvanometer
• Known resistors \( R_1 \) and \( R_2 \)
• Unknown resistor \( R_x \)
• Variable resistor (rheostat or resistance box)
• Switch
• Connecting wires

Theory

A Wheatstone bridge consists of four resistances arranged in a diamond shape. When the bridge is balanced, no current flows through the galvanometer.

At balance condition:

\[ \frac{R_1}{R_2} = \frac{R_x}{R_3} \]

where \( R_3 \) is the variable resistance adjusted to achieve null deflection.

The unknown resistance is given by:

\[ R_x = \frac{R_1}{R_2} \times R_3 \]

Method

1. Set up the Wheatstone bridge circuit using known resistors \( R_1 \) and \( R_2 \).
2. Connect the unknown resistance \( R_x \) in one arm of the bridge.
3. Insert the galvanometer between the two junctions.
4. Close the switch and adjust the variable resistor \( R_3 \).
5. Observe the galvanometer and adjust until null deflection is obtained.
6. Record the balanced value of \( R_3 \).
7. Repeat the procedure with different ratios of \( R_1 \) and \( R_2 \).

Observations

• Values of \( R_1 \) and \( R_2 \)
• Balanced value of \( R_3 \)
• Consistency of null deflection

Calculations

Calculate the unknown resistance using:

\[ R_x = \frac{R_1}{R_2} \times R_3 \]

Take the mean value if multiple trials are performed.

Result

The unknown resistance is determined using the Wheatstone bridge method and is accurate due to the null measurement technique.

Sources of Error & Precautions

• Ensure all connections are tight and clean.
• Use low current to prevent heating of resistors.
• Always check for true null deflection.
• Do not keep the circuit closed for long durations.

Video Demonstration

Video courtesy of Electronoobs (YouTube). Used for educational purposes under YouTube’s embedding policy.