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Physical Internet-controlled experiments

Grammar-school of J. Vrchlicky, Klatovy

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Temperature dependence of the resistance of metals and semiconductors

Work task and measurement procedure

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Work task:

  1. METAL
    1. Measure the dependence of the resistance of metal wires to a temperature of at least 12 different temperatures in the range of temperatures from –5 °C to 65 °C.

    2. Obtained values plotted on graph and qualitatively compare the shape obtained depending Rk(t) with the theory.

    3. Calculate the average resistance coefficient of metal under examination.

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

    5. Both the values of temperature coefficient of resistance (section 3 and 4) compare to each other and you know if that examined metal was platinum, and compare with the tabulated value.


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

    2. Obtained values plotted on graph and qualitatively compare the shape obtained depending Rk(t) with the theory.

    3. Calculate the average temperature coefficient β for the semiconductor under consideration.

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

    5. Both the values of temperature coefficient β (section 3 and 4) compare to each other. From average value of β determine the activation energy ΔE of used semiconductors - convert it to eV.

 



Measuring procedure

  1. Run the remote experiment.

  2. Use the controls (see below), gradually set the temperature of different elements.

  3. Read temperature and store the measured values of resistance in the selected moments.

  4. Save the experimental values to the HDD on your PC after measurement of the required data and exit remote experiment.

  5. Open the obtained CSV file in a spreadsheet.

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

  7. plot the dependence of metal resistance in the above chart and data proložíme of linear regression equation (y = ak.x + bk) with displayed regression coefficients.

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

  9. emperature coefficient of electrical resistance α is obtained by dividing the coefficients of of linear regression:

    α =  ak

    bk
  10. SEMICONDUCTOR: The spreadsheet can make the graph of Rp(t)] to t and compare the quality of its temperature-dependent electrical resistance of the metal.

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

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

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

  14. Regression coefficient bp has the meaning of ln(R0). We determine from it the value of R0 - we can observe with the experimentally determined value at 0 °C.

  15. Regression coefficient ap has the importance of finding value and we obtain the value of activation energy ΔE by relationship ΔE = β.k (k - Boltzmann constant).

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


 METAL: 

 R = R0.[1 + α.(t – t0)]

  SEMICONDUCTOR:
 

 R = R0.e
[β.(  1   –   1  )]  


T0 T
 

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