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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 | ... 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 setup is used:
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Materials Needed: A metallic conductor, a power supply, a thermometer, and a multimeter.
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Setup:
- Connect the metallic conductor to the power supply in series.
- Incorporate the thermometer to monitor the temperature of the metallic conductor in real time.
- Use a multimeter to measure the resistance of the conductor as the temperature changes.
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Procedure:
- Gradually heat the conductor and record the resistance at various temperatures (as noted in the tabulated data).
- Ensure consistent heating and use the thermometer to track temperature changes precisely.
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Labelled Diagram: The diagram should illustrate the circuit connection, along with the positioning of the thermometer and multimeter, indicating their respective functions.
Step 2
Draw a suitable graph to show the relationship between the resistance of the metal conductor and its temperature.
Answer
To draw the graph:
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X-axis: Temperature (θ) in °C, ranging from 20 to 80.
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Y-axis: Resistance (R) in Ω, ranging from 4.6 to 6.1.
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Plot the points based on the provided data in the table:
- (20, 4.6)
- (30, 4.9)
- (40, 5.1)
- (50, 5.4)
- (60, 5.6)
- (70, 5.9)
- (80, 6.1)
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Draw a line of best fit through the points to indicate the trend in the data, showing an upward slope.
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Labeling: Include a title for the graph, axes labels, and ensure data points are clearly marked.
Step 3
(i) estimate the resistance of the metal conductor at a temperature of -20 °C;
Answer
Using the graph, extrapolate to estimate the resistance at -20 °C. Observing the trend, you may find that the resistance at this temperature is approximately 4.0 Ω (this value is to be noted as an approximation).
Step 4
(ii) estimate the change in resistance for a temperature increase of 80 °C;
Answer
From the table, the resistance at 80 °C is 6.1 Ω and at the starting reference point (assumed at 20 °C), it is 4.6 Ω.
The change in resistance (∆R) is calculated as:
Thus, the change in resistance for an increase of 80 °C is approximately 1.5 Ω.
Step 5
(iii) explain why the relationship between the resistance of a metallic conductor and its temperature is not linear.
Answer
The relationship is not linear due to the material properties of metals. While initial increases in temperature can create a linear response, as temperature increases further, factors like thermal agitation of the lattice structure increase significantly. This results in non-linear resistance increases as temperature rises. Additionally, at very high temperatures, metals may exhibit changes in electron mobility and availability, altering the linearity of the resistance characteristics further.