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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 on the resistance, length, and diameter of the nichrome wire, the following methods were employed:
- Resistance Measurement: The resistance was measured using an ohmmeter or multimeter, ensuring accurate readings were taken by calibrating the instrument beforehand.
- Length Measurement: The length of the wire was obtained using a metre stick, placed along the wire to ensure precision. Care was taken to avoid any slack in the wire, which could affect the length.
- Diameter Measurement: A micrometer was used to measure the diameter of the wire. This instrument allows for precise measurements, vital for calculating resistivity accurately.
- Uniform Diameter Assurance: To ensure uniformity, the diameter was measured at different positions along the wire, ensuring there were no kinks or irregularities.
Step 2
How did the student ensure that the wire was of uniform diameter?
Answer
The student measured the diameter at various points along the wire using a micrometer. By taking multiple readings and ensuring that there were no significant variations in diameter, the student ensured that the wire was of uniform diameter.
Step 3
Use the data to calculate the resistivity of nichrome.
Answer
The resistivity can be calculated using the formula:
ho = R imes rac{A}{L}$$ where: - $R$ is the resistance (29.1 Ω) - $A$ is the cross-sectional area of the wire and can be calculated using $$A = rac{ ext{π} imes d^2}{4}$$ - $d$ is the diameter (0.21 mm = 0.00021 m) and - $L$ is the length of the wire (95.1 cm = 0.951 m). Calculating the area: $$A = rac{ ext{π} imes (0.00021)^2}{4} ext{ m}^2$$ determining $L$: $L = 0.951 ext{ m}$ Substituting the values:ho = 29.1 imes rac{A}{0.951}$$
ho = 1.06 imes 10^{-6} ext{Ω m}$$
Step 4
Draw a labelled diagram of the arrangement of the apparatus used in this experiment.
Answer
The diagram should include:
- Thermometer: to measure the temperature of the liquid.
- Source of Heat: used to heat the wire and liquid.
- Wire in Container of Liquid: the nichrome wire placed in a suitable liquid to measure the resistance.
- Ohmmeter/Multimeter: connected across the wire to measure the resistance as the temperature changes.
Label all the components clearly.
Step 5
Draw a sketch of the graph. Describe this relationship.
Answer
The sketch should illustrate a graph with:
- X-axis: Temperature (T)
- Y-axis: Resistance (R)
Description of the Relationship: The graph shows a straight line with a positive slope, indicating a direct linear relationship between resistance and temperature. As the temperature increases, the resistance of the nichrome wire also increases. This proportional relationship is characteristic of conductive materials, confirming that nichrome’s resistance is temperature-dependent.