how to show with the help of a model that resistivity of a conductor increases with increase in temperature?
To demonstrate that the resistivity of a conductor increases with an increase in temperature, you can employ a simple experimental setup and use a resistor as a model conductor. Here's how to proceed:
Materials needed:
1. Resistor (preferably a metallic one, such as copper or aluminum)
2. Power supply (e.g., battery and wires)
3. Voltmeter and ammeter
4. Thermometer or temperature sensor
5. Heat source (e.g., Bunsen burner or hot plate)
6. Stopwatch or timer
Procedure:
1. Start by measuring and recording the initial resistance of the resistor at room temperature (T1) using the voltmeter and ammeter. Connect the resistor to the power supply so that it forms a closed circuit.
2. Measure the initial temperature of the resistor (T1) using a thermometer or temperature sensor. Note that this temperature should be the same as the room temperature.
3. Apply a constant current to the resistor by adjusting the power supply.
4. Heat the resistor using the heat source (e.g., position it over a Bunsen burner or on a hot plate).
5. Measure and record the final resistance of the resistor (R2) using the voltmeter and ammeter once the temperature has stabilized at the desired higher temperature (T2).
6. Measure and record the final temperature of the resistor (T2) using a thermometer or temperature sensor.
7. Calculate the change in resistance (∆R) by subtracting the initial resistance (R1) from the final resistance (R2): ∆R = R2 - R1.
8. Calculate the change in temperature (∆T) by subtracting the initial temperature (T1) from the final temperature (T2): ∆T = T2 - T1.
9. Calculate the fractional change in resistance (∆R/R1) by dividing ∆R by R1: ∆R/R1 = (∆R/R1) × 100%.
10. Calculate the fractional change in temperature (∆T/T1) by dividing ∆T by T1: ∆T/T1 = (∆T/T1) × 100%.
11. Plot a graph of ∆R/R1 on the y-axis against ∆T/T1 on the x-axis.
12. Analyze the graph and observe if there is a linear relationship between the fractional changes in resistance and temperature.
Conclusion:
If the graph shows an increasing trend, it confirms that the resistivity of the conductor (represented by the resistor) increases with an increase in temperature. The slope of the graph will give you the temperature coefficient of resistivity, which quantifies the change in resistivity per degree Celsius or Kelvin.
Remember, it's crucial to exercise caution while working with heat sources and electrical circuits.