﻿ Work task - V-A characteristics of the LED
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## V-A Charakteristics of LED(Determination of Planck's constant)

### Work Tasks and Measurement Procedures

1. Measure the point-to-point, volt-ampere characteristics of LEDs of different colors (red, yellow, green, blue, and white).

2. Plot the obtained values and qualitatively compare the shape of the obtained dependencies. Explain the similarities in the V-A characteristics of white and blue LEDs.

3. Fit the linear part of the V-A characteristics to determine the threshold voltage U* of each LED.

4. Obtain the value of the slope of the linear part of the V-A characteristics using linear regression (e.g. using a spreadsheet) and determine the dynamic (differential) resistance of the LED.

5. Determine the wavelength of light emitted by the LEDs (except white) from the threshold voltage values and compare it with the value specified by the manufacturer.

or

1. Determine the value of Planck's constant (at least to the order of magnitude) from the value of the threshold voltage of each LED and knowledge of the emitted wavelengths.

#### Measurement Procedure

1. Start the CEcIL remote experiment.

2. Select a measured LED (see description of controls).

3. Using the slider (PC) or the + & buttons (tablet), gradually set different values of electric voltage on the LED.

4. Read the voltage and current values and write them in the table.

5. Monitor the measured values in the table continuously and in case of larger gaps between the points of dependence measure the missing parts.

6. Repeat the same procedure for each LED. After measuring each LED, you can save the obtained experimental data on the disk of your PC.

7. Exit the remote task after measuring the required number of data (and save all files of experimental values!).

8. Open the selected experimental data file in a spreadsheet.

9. Plot the dependence of the electric current through the LED connected to an electric voltage on the graph. Check that the shape of the obtained dependence corresponds to the expected shape.

10. Select the points of the linear part of the dependence and interleave by a linear regression including display of its equation. Obtain the threshold voltage U* by determining the intersection with the horizontal axis (graphically and numerically).

11. The slope of the regression line corresponds to the dynamic (differential) resistance of the LED.

12. All V-A characteristics can be compared by plotting on a common graph.

##### Determine the wavelength of the emitted light
1. Using the values of the threshold voltage of a formula (4)

2. You will get the following expression (through formula (4)), which you can use to calculate the wavelength:

$λ = h · c e · U *$
1. Compare the wavelength values with the wavelength table below for the LED used in this experiment. Note the deviation measurement!

Color  λ / nm
red  640
yellow  590
green  568
blue  470

or

##### Approximation of Planck's constant
1. Also here you will know the value of the threshold voltage U* and the formula (4), which you can edit in the this form, from which we determine the value of Planck's constant:

$h = e · U * · λ c$
1. Calculate the value of Planck's constant for all monochrome LEDs and average the values obtained.

2. Compare the determined value of Planck's constant with a theoretical value. It is more of an order of magnitude estimate (with respect to the configuration of the experiment), but it should match.