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In an experiment to measure the resistivity of nichrome, a student measured the length, resistance and diameter of a sample of nichrome wire of uniform diameter - Leaving Cert Physics - Question 4 - 2016
Question 4
In an experiment to measure the resistivity of nichrome, a student measured the length, resistance and diameter of a sample of nichrome wire of uniform diameter. Th... show full transcript
Worked Solution & Example Answer:In an experiment to measure the resistivity of nichrome, a student measured the length, resistance and diameter of a sample of nichrome wire of uniform diameter - Leaving Cert Physics - Question 4 - 2016
Step 1
Describe how the data were collected.
Answer
To collect the data regarding the resistance, length, and diameter of the nichrome wire, the student used specific instruments:
- For measuring resistance, the student utilized an ohmmeter or multimeter. This device allowed for an accurate measurement of the electrical resistance of the wire.
- The length of the wire was measured using a metre stick, ensuring precise measurement, especially over a longer length.
- To measure the diameter of the wire, the student employed a micrometer, which provides a high level of accuracy for small diametric measurements.
To ensure that the wire was of uniform diameter, the student took care to measure the diameter at different positions along the wire and verified that there were no kinks or other deformations that could affect the consistency.
Step 2
Use the data to calculate the resistivity of nichrome.
Answer
To find the resistivity of nichrome, we can use the formulas for the area of the wire's cross-section and the relationships among resistance, resistivity, length, and area:
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Calculate the area of the wire's cross-section: A = rac{ imes ext{diameter}^2}{4} Given diameter = 0.21 mm = 0.21 × 10^{-3} m,
A = rac{ imes (0.21 imes 10^{-3})^2}{4} ext{m}^2
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Use the relationship between resistance, resistivity, length, and area:
ho l}{A}$$ where:
Rearranging gives:
ho = rac{R imes A}{l}$$ 3. Substitute in the values to calculate resistivity:ho = rac{29.1 imes A}{0.951} ext{Ω m}$$ After computing the area, the final value of resistivity is:
ho ext{ } ext{is found to be approximately } 1.06 imes 10^{-6} ext{Ω m}.$$Step 3
Draw a labelled diagram of the arrangement of the apparatus used in this experiment.
Answer
In this experiment, the apparatus typically consists of:
- Thermometer and source of heat to monitor temperature changes in the wire.
- Wire in a container of liquid (for thermal stability) immersed in the liquid that can transfer heat to the wire.
- An ohmmeter/multimeter connected across the wire for real-time measurement of resistance as temperature is varied.
Please note that a diagram should be drawn illustrating these components and their connections clearly.
Step 4
Draw a sketch of the graph. Describe this relationship.
Answer
The graph should have:
- Labelled axes: The x-axis represents Temperature (°C) and the y-axis represents Resistance (Ω).
- A straight line with positive slope and correct intercept, showing an upward trend: as the temperature increases, resistance increases, indicating a linear relationship between the two variables.
- The relationship is described as a linear/proportional relationship: this means that the resistance of nichrome wire increases in direct proportion to temperature; therefore, if the temperature is doubled, the resistance will also increase proportionally.