A student measured the resistance R of a wire of length 30 cm at different values of temperature θ - Leaving Cert Physics - Question 4 - 2021

The student created a temperature of 0 °C for the wire by submerging it in an ice bath. This involves filling a container with a mixture of ice and water, ensuring that the wire reaches the freezing point of water.

To draw the graph:

1. Use θ (°C) as the x-axis and R (Ω) as the y-axis.
2. Label the axes correctly, ensuring both scales are uniform.
3. Plot the points (0, 5.35), (20, 5.60), (40, 5.85), (60, 6.04), (80, 6.28), (100, 6.51).
4. Draw a line of best fit to connect the points, showing the trend in the data.

Using the graph, locate the 6 Ω mark on the y-axis. Draw a horizontal line from this point until it intersects the drawn line of best fit, then drop a vertical line down to the x-axis. This will indicate the temperature corresponding to the resistance of 6 Ω, which is found to be approximately 55.5 °C.

The student measured the diameter of the wire using micrometers or digital calipers. These tools provide precise measurements of small diameters, ensuring accuracy in the data collected.

To calculate the resistivity, use the formula:

$\rho = \frac{R \cdot A}{L}$

Where:

• $R$ = Resistance (5.60 Ω at 20 °C)
• $A$ = Cross-sectional area, calculated using $A = \pi \left(\frac{d}{2}\right)^2$ (with $d = 2.4 \, \text{mm} = 0.0024 \, \text{m}$)
• $L$ = Length of the wire (0.3 m)

Calculating the area:

$A = \pi \left(\frac{0.0024}{2}\right)^2 = 4.52 \times 10^{-6} \, \text{m}^2$

Now substituting:

$\rho = \frac{5.60 \cdot 4.52 \times 10^{-6}}{0.3} = 8.84 \times 10^{-6} \Omega \, \text{m}$