In an experiment to measure the resistivity of nichrome, the resistance, the diameter and appropriate length of a sample of nichrome wire were measured - Leaving Cert Physics - Question 4 - 2009

To determine the average diameter of the nichrome wire, you should follow these steps:

1. Use Appropriate Equipment: Utilize a micrometer or digital calipers for accurate measurement.

2. Initial Placement: Position the wire between the jaws of the caliper. (Indicate if using a digital device.)

3. Tightening: Carefully tighten the jaws around the wire to keep it in place.

4. Take Readings: Read the initial measurement and note it down.

5. Repeat Measurements: Measure at different points along the wire to account for any irregularities in thickness.

6. Calculate Average: Sum all the diameter readings and divide by the number of measurements to find the average diameter.

To calculate the resistivity of the nichrome wire, use the formula:

$\rho = \frac{R A}{l}$

where:

• $\rho$ is the resistivity,
• $R$ is the resistance (7.9 Ω),
• $A$ is the cross-sectional area,
• $l$ is the length of the wire (in meters).

1. Calculate the Area: The diameter is 0.31 mm, hence the radius is: $r = \frac{0.31}{2} \times 10^{-3} \text{ m} = 0.155 \times 10^{-3} \text{ m}$

   The area is: $A = \pi r^2 = \pi (0.155 \times 10^{-3})^2 \approx 7.55 \times 10^{-8} \text{ m}^2$

2. Substitute Values: Using the length of wire (54.6 cm = 0.546 m):

   $\rho = \frac{7.9 \times 7.55 \times 10^{-8}}{0.546}$

3. Calculate: $\rho \approx 1.09 \times 10^{-6} \Omega m$

On a warmer day, the following effects can be observed:

• Resistance Increased: The increase in temperature generally leads to an increase in resistance in metallic conductors.
• Wire Expansion: The effective length of the wire may expand, leading to an increase in overall diameter.
• Diameter Measurements: As the wire expands, the diameter may increase, affecting calculations based on measurements taken at lower temperatures.