Method

1. Measure Wire Diameter:

• Using the micrometer, measure the diameter $d$ of the constantan wire at several points along its length. Calculate the mean diameter to ensure accuracy, as this is used to determine the cross-sectional area $A$ of the wire.

2. Set Up Circuit:

• Connect the apparatus as shown in the diagram, with the power supply, ammeter, and voltmeter connected to the wire via crocodile clips.

3. Adjust Length:

• Set the length $l$ of the wire to 0.100 m, measured from one crocodile clip to the other using the metre ruler.

4. Measure Current and Voltage:

• Switch on the power supply and record the current $I$ from the ammeter and the voltage $V$ from the voltmeter.
• Calculate the resistance $R$ of the wire section using Ohm's law:

5. Repeat for Different Lengths:

• Increase $l$ by increments of 0.100 m, up to a maximum length of 0.800 m, and repeat the measurements of $I, V$, and $R$ for each length.
• Repeat the entire process twice more to obtain average values of $R$ for each length $l$.

Safety

• Heating of Wire: Disconnect the crocodile clips between measurements to prevent the wire from heating up, which can alter its resistance and cause burns if touched.
• High Currents: If the current is high, lower the voltage on the power supply to avoid overheating. Wear safety goggles in case of any wire snapping under tension.

Key Concepts

• Resistivity $\rho$: A material property that quantifies how strongly a material opposes the flow of electric current. It depends on the material and its temperature.
• Ohm's Law: For a uniform wire, $R = \frac{V}{I}$ defines the relationship between voltage, current, and resistance.
• Graphical Analysis: By plotting resistance vs. length, the linear relationship allows us to calculate resistivity from the gradient, linking macroscopic measurements (resistance and length) to a fundamental property of the material. This experiment provides hands-on experience with electrical resistance and demonstrates how resistivity can be determined practically, reinforcing both theoretical and practical understanding of electrical properties.