﻿ Work task - Temp. dependence of the resistance of metal and semiconductor
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## Temperature Dependence of Resistance of Metals and Semiconductors

### Work task and measurement procedure

1. ##### METAL
1. Measure the dependence of the resistance of metal wires on temperature for at least 12 different temperatures ranging from -5 °C to 65 °C.

2. Plot the values obtained on a graph and qualitatively compare the shape obtained as a function of Rk(t) with the theory.

3. Calculate the average resistivity of the metal under study.

4. Fits in a spreadsheet dependence Rk(t) of linear regression equation. From coefficients of the equation (y = a·x + b determine the temperature coefficient of resistance, or resistivity at 0 °C.

5. Compare the two values of the temperature coefficient of resistance (Sections 3 and 4) with each other and you will know if the metal examined was platinum, and compare with the tabulated value.

2. ##### SEMICONDUCTOR
1. Measure the temperature dependence of the resistance of a semiconductor thermistor for at least 12 different temperatures in the range of -5 °C to 65 °C.

2. Plot the values obtained on a graph and qualitatively compare the shape of the obtained dependence of Rk(t) with theory.

3. Calculate the average thermistor temperature constant β for the semiconductor under consideration.

4. Construct the graph of ln[Rp(T)] versus 1/T in a spreadsheet. From the coefficients of the equation (y = a·x + b), determine the temperature coefficient β of the semiconductor or the resistivity at 0 °C.

5. Compare the two values of the thermistor temperature constant β (sections 3 and 4). From the average value of β, determine the activation energy ΔE of the semiconductors used – convert it to eV.

You can download (for processing of experimental data) (Czech only) worksheet for experiment VILI.

#### Measurement Procedure

1. Run the remote experiment.

2. Use the controls (see below) to gradually adjust the temperature of different elements.

3. Read the temperature and save the measured resistance values at the selected moments.

4. After measuring the required data, save the experimental values to the hard disk of your PC and quit the remote experiment.

5. Open the obtained CSV file in a spreadsheet program.

6. METAL: Using formula (2) determine the values of the coefficient of metal resistance and average them.

7. Plot the dependence of the metal resistance in the above graph and fit the data with the linear regression equation (y = ak·x + bk) with the displayed regression coefficients.

8. Regression coefficient bk has direct relevance to the value of R0 resistance element of used at 0 °C.

9. The temperature coefficient of electric resistance α is obtained by dividing the coefficients of linear regression:

$α = a k b k$
10. SEMICONDUCTOR: The spreadsheet can construct the graph of Rp(t) versus t and compare the quality of its temperature dependent electrical resistance of the metal.

11. Construct the graph of ln[Rp(T)] versus 1/T01/T in a spreadsheet. We choose T0 as 273,15 K (ATTENTION: we are moving from °C to K!).

12. We use the data for the graph of and according to formula (4) we obtain a series of β values that are averaged.

13. We return to the graph and we obtain the linear regression equation (y = ap·x + bp) with the regression coefficients displayed.

14. The regression coefficient bp has the meaning of ln(R0). From it we determine the value of R0 – we can observe with the experimentally determined value at 0 °C.

15. The regression coefficient ap has the meaning of finding the value of the thermistor temperature constant and we get the value of the activation energy ΔE by the relation ΔE = β·k (k – Boltzmann's constant).

16. We can interspace the experimental values of electrical resistance of the two elements obtained dependencies with completed parameters: R0, α, β: