Overview

This experiment determines the resistivity of a metallic wire by measuring its resistance using a voltage-current graph and combining it with precise measurements of the wire’s length and diameter.

What This Experiment Demonstrates

• Relationship between resistance, length, and cross-sectional area
• Experimental determination of resistivity
• Use of V–I graphs to calculate resistance

Apparatus Required

• Uniform metallic wire (nichrome or constantan)
• DC power supply
• Ammeter
• Voltmeter
• Switch
• Connecting wires
• Meter ruler
• Micrometer screw gauge or vernier calipers

Theory

The resistance \( R \) of a uniform wire is given by:

\[ R = \rho \frac{L}{A} \]

where \( \rho \) is the resistivity of the material, \( L \) is the length of the wire, and \( A \) is its cross-sectional area.

The resistance can be determined experimentally from the slope of the voltage-current graph using Ohm’s Law:

\[ R = \frac{V}{I} \]

Once \( R \), \( L \), and \( A \) are known, the resistivity of the wire can be calculated.

Method

1. Stretch the wire tightly along a meter ruler and measure its effective length \( L \).
2. Measure the diameter of the wire at several points using a micrometer screw gauge and calculate the mean diameter.
3. Set up a circuit with the wire in series with an ammeter and switch.
4. Connect a voltmeter in parallel across the test wire.
5. Switch on the circuit and vary the voltage gradually.
6. For each voltage, record the corresponding current.
7. Take at least 5–6 readings over a suitable range.
8. Plot a graph of voltage \( V \) against current \( I \).

Observations

Record the following data:

• Length of the wire \( L \)
• Diameter readings and mean diameter
• Voltage and current readings

Calculations

• Calculate cross-sectional area using \( A = \pi r^2 \).
• Determine resistance from the slope of the V–I graph.
• Calculate resistivity using \( \rho = \frac{RA}{L} \).

For accurate graph plotting and slope calculation, refer to our Graph Guide.

Result

The resistivity of the given wire is calculated using experimental values of resistance, length, and cross-sectional area, and is consistent with the known resistivity of the material within experimental uncertainty.

Sources of Error & Precautions

• Ensure tight connections to avoid contact resistance.
• Avoid heating of the wire by keeping current low.
• Measure diameter at multiple points to reduce systematic error.
• Do not force the micrometer screw gauge.

Video Demonstration

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