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A student investigated the variation of the resistance R of a metallic conductor with its temperature θ - Leaving Cert Physics - Question 4 - 2008
Question 4
A student investigated the variation of the resistance R of a metallic conductor with its temperature θ. The student recorded the following data. | θ / °C | 20 | 3... show full transcript
Worked Solution & Example Answer:A student investigated the variation of the resistance R of a metallic conductor with its temperature θ - Leaving Cert Physics - Question 4 - 2008
Step 1
Describe, with the aid of a labelled diagram, how the data was obtained.
Answer
To investigate the variation of resistance with temperature, the following method can be employed:
- Setup: Connect the metallic conductor in a circuit with a constant current source.
- Temperature Control: Use a heating or cooling bath to control the temperature of the conductor.
- Measurement: As the temperature is altered, the resistance is measured using an ohmmeter.
- Data Recording: Record the temperature (θ) and corresponding resistance (R) in a table.
- Diagram: The labelled diagram should illustrate the experiment setup, showing connections to the thermally controlled bath and the measuring instruments.
Step 2
Draw a suitable graph to show the relationship between the resistance of the metal conductor and its temperature.
Answer
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.
Step 3
(i) estimate the resistance of the metal conductor at a temperature of –20 °C;
Answer
To estimate the resistance at −20 °C, we can use the linear extrapolation method based on the graph:
- Extend the line of best fit downwards to the temperature of −20 °C.
- 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).
Step 4
(ii) estimate the change in resistance for a temperature increase of 80 °C;
Answer
Using the graph, find the resistance at the starting temperature and at the higher temperature:
- At the base temperature of 20 °C, the resistance is approximately 4.6 Ω.
- At 80 °C, the resistance is 6.1 Ω.
- The change in resistance (ΔR) is given by: .
Step 5
(iii) explain why the relationship between the resistance of a metallic conductor and its temperature is not linear.
Answer
The relationship between the resistance of a metallic conductor and its temperature is not linear due to several factors:
- Intrinsic Properties: As temperature increases, mobile charge carriers gain energy, leading to more collisions with lattice ions, which increases resistance.
- 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.
- Scatter in Data: External factors such as impurities and physical structure can also cause non-linear tendencies in the resistance observed.