A student investigated the variation of the resistance R of a metallic conductor with its temperature θ - Leaving Cert Physics - Question 4 - 2008

To illustrate the relationship, create a graph with:

• X-axis: Temperature (°C) ranging from 20 to 80 °C
• Y-axis: Resistance (Ω) ranging from 4.6 to 6.1 Ω
• Data Points: Plot the recorded values (θ, R) from the table. The points should show an increasing trend.
• Line of Best Fit: Draw a straight line connecting the points as they are nearly linear, showing the positive correlation between temperature and resistance.

To estimate the resistance at −20 °C, we can use the linear extrapolation method based on the graph:

1. Extend the line of best fit downwards to the temperature of −20 °C.
2. From the graph, it can be calculated that the resistance R at –20 °C will be approximately 4.0 Ω (confirming actual extrapolation from the plotted line).

Using the graph, find the resistance at the starting temperature and at the higher temperature:

1. At the base temperature of 20 °C, the resistance is approximately 4.6 Ω.
2. At 80 °C, the resistance is 6.1 Ω.
3. The change in resistance (ΔR) is given by: $ΔR = R_{final} - R_{initial} = 6.1 ext{ Ω} - 4.6 ext{ Ω} = 1.5 ext{ Ω}$.

The relationship between the resistance of a metallic conductor and its temperature is not linear due to several factors:

1. Intrinsic Properties: As temperature increases, mobile charge carriers gain energy, leading to more collisions with lattice ions, which increases resistance.
2. Non-linear Behavior at Extremes: At very low temperatures or high temperatures, materials exhibit behaviors such as superconductivity or thermally-induced structural changes, leading to deviations from linearity.
3. Scatter in Data: External factors such as impurities and physical structure can also cause non-linear tendencies in the resistance observed.