Another variable that could be investigated with a solar cell is the distance between the solar cell and the light source, and the effect upon the energy transferred to the solar cell when varying distances between the solar cell and light source.
Distance direct affects the intensity of the light, and as distance increases, the light intensity decreases. We can see this in the below formula which shows us to what extent the distance between the light source and solar cell affects the energy supplied.
Light Intensity= Power/area
The value area will be replaced with the value ‘4∏r²’, because as light travels, it spreads in all directions in a spherical shape. This variable can easily be changed and controlled, therefore meaning it is easy to test. Therefore, I will test this variable in my investigation.
Variable 3: Power
The Solar Cell
This is the amount of energy supplied to the bulb. When increasing this, it would output more light, and when decreasing the power, less energy would be output in the light. You can vary this variable using a power pack, and it is also very easy to control with this equipment, therefore I will also measure this variable.
Lamps with white light were chosen, in case the colour of the light had any effect over the results of the experiment. To ensure that nothing like this would happen, the same bulb was used. The frequency (colour) of the light changes the energy and velocity of the light, as shown by the following formulae:
E = h f
Where E stands for Energy
Where h stands for a constant (“Planck’s Constant”)
Where f stands for frequency
This shows that if you decrease the frequency, you will decrease the energy of the wave, which means less energy to be transferred to electrical energy in the solar cell.
From this, we can deduce that different parts of visible light travel with more speed.
By using the formula:
v = f
Where v stands for velocity
Where f stands for frequency
Where stands for wavelength
We can find out which parts of light have more/ less energy.
Violet has the shortest wavelength of visible light, with around 400 x 10-9.
So, with all electromagnetic waves travelling at 300 000 000 (3 x 108) m/s:
3 x 108 = 400 x 10-9 f
(3 x 108) / (400 x 10-9) = f
3/400 x 1017 = f
3000/400 x 1014 = f
7.5 x 1014 Hz = f
E = h f
h = 6.63 x 10-34 Js
E = 6.63 x 10-34 Js x 7.5 x 1014 s-1
E = 4.9725 x 10-19 J
Whereas with Red, it has the largest wavelength of visible light:
3 x 108 = 700 x 10-9 f
(3 x 108) / (700 x 10-9) = f
3/700 x 1017 = f
3000/700 x 1014 = f
4.29 x 1014 Hz = f
E = h f
h = 6.63 x 10-34 Js
E = 6.63 x 10-34 Js x 4.29 x 1014 s-1
E = 2.8414 x 10-19 J
As you can see, the amount of energy is nearly double in Violet, than that in Red, due to their different wavelengths.
I will investigate into the effects of distance, as it is easy to measure, and does not require sophisticated machinery and the knowledge of them to perform, as changing the colour would. As an object becomes further away, light intensity decreases.
The diagram illustrates how the further away an object is, the lesser the degree of the light emitted by the bulb. This means that the further away from the bulb the same object is, the less intensity of light it receives due to attenuation and using up a smaller angle of the light emitted.
I will also investigate into the effects of power to the bulb. This will be changed by a Rheostat and the power pack; however the power input type will always remain D.C. (Direct Current). With a higher power, more energy is ‘sent’ to the bulb per second (a formula for power is Joules per second), therefore more energy is expelled from the bulb, and more energy is ‘absorbed’ by the solar cell.
The Solar Cell works by ionisation inside the solar cell. Photons of light hit the solar cell with such force, that they give their energy to an electron, which can then leave the atom. This is why having different colour lights affect results, as red does not delocalise as many electrons as violet would, for example, as they have different energies. Due to such a great amount of energy required to delocalise electrons, solar cells are only about 20-30% efficient.
In order to ensure a fair test, the distance will be read off and checked by the same person (me). In addition, I will have to keep the constant factors throughout this experiment constant, whilst effectively keeping the variables varying. When taking readings, I will ensure that no extra light is reflected onto the solar cell by my white shirt, by positioning the meters away from the solar cell, so that I only need go near it to change it, thereby not affecting results. I will also take care not to rearrange the bulb, but this may be a difficulty in itself to break, as the bulb will become very hot very quickly (that’s why bulbs are less than 5% efficient) which is a safety risk or burning.
Hypothesis 1: As the distance between the lamp and the solar cell increases, the current output will decrease.
Hypothesis 2: As the power to the bulb increases, the current output will too.
Equipment 1:
- Metre Rule
- Solar Cell
- Milli-ammeter
- 12V DC Power Supply
- W Lamp
- Leads
Equipment 2:
- Ammeter
- Voltmeter
- Solar Cell
- DC Power Supply
- Rheostat
- W Lamp and stand
- Leads
- Milli-ammeter
Method: The Experiment is to be set up as per the regulations listed above, and the previous diagram. For the first experiment, I took measurements every 5 cm and recorded the results. For the second, I took random settings of the rheostat and power supply.
Repeats will be made, and an average taken so that it won’t be greatly affected by faulty first experiments and such like.
Safety Precautions
When conducting these experiments, there are not many safety issues, because we will not be dealing with high currents/voltages. The heat of the wires and the lamp may be hazardous to touch; therefore we will not touch these when they are on.
Results: Distance Experiment
On this table are the results of the first experiment. In this experiment, I varied the power supplied to the lamp to see the output to the solar cell.
Power Experiment
Here are the results for the second experiment, where the distance between the solar cell and light source was varied to see the power output on the solar cell.
Analysis
From the results I collected of the first experiment, I plotted one start graph, Graph 1, from raw data. This graph is not proportional, or linear, but shows a very strong negative correlation between Current Output of the Bulb and Distance from the Bulb. This graph has a dramatic drop, which makes it harder to draw conclusions due to the bunched-up quality of the data.
As this graph is not very useful on its own, as it shows no relationship between the two, I decided to make a further graph, which was the same, except of inverse distance from the bulb. This graph shows a better correlation, not so strong, but nearly linear, however this time it has a positive correlation. However, I could square the distances to try to find a straight line.
Graph 3 shows a straight line, however the results are very concentrated at the lower end of the x-axis. At this scale it is almost impossible to see whether it goes through the origin (0,0) or not, so we have a straight, potentially proportional, line. This shows us that Current Output of the Bulb is proportional to inverse distance squared. Like gravity, it is an inverse square rule.
I α 1
d2
This is because as the object gets further away, the spheres of light that emanate from the bulb, every time they double in distance, they cover 4 times as much area, instead of just double, as hey operate in spheres. On paper, circles would have double the area, but as this is three-dimensional, you have to square it from x1 (paper) to x2 (real life).
Now onto the second experiment that investigated Power’s relationship with solar cell’s current output. The fourth graph shows a steady upwards-positive curve, resembling a squared curve’s beginnings. This graph’s line of best fit has a fairly good positive correlation to it.
As this graph resembled an x2 type graph, I decided to try square rooting the answers. After square rooting the answers, I found that they followed an almost perfect straight lie, which goes through the origin, showing that these two factors are directly proportional.
___
I α √W
I2 α W
This is because the formula W = I2 R, where R in this scenario is fixed (making them proportional) through fixed distance between the bulb and the solar cell, and no noticeable change in temperature once the experiment was under way.
Evaluation:
I feel that the experiment was a success, as I do not seem to have encountered any anomalies whilst doing my experiment. The values weren’t all precisely on the line, but it is rare for an experiment to go exactly correct, with slight errors being made, slightly off equipment, or faults of rounding.
The room I did my experiment in was not guarded against light from outside (this was performed next to an open window) or inside by any means, and in the greatly varying weather conditions of early February, some boys had their blazers off, reflecting even more light onto the solar panel due to their white shirts. To try to combat this, I took readings of the solar panel with no lamp on, and plotted this in the graphs, hoping that the amount of light reflected onto the solar panel, and the amount of shadow cast over it would be abut the same throughout the experiment.
On the last graph, the results curve up at the end. This is the closest thing to anomalous results I could find, but this may be a correct finding, or may be not, but if it is not correct, it could be the fault of bad result noting (only I did the experiment, so had to read 4 meters at once).
If I were to redo this experiment, I would do it in a completely dark room, and have results taken automatically, by a computer, and investigate the changes between different frequencies (colours) of light.
When looking at the graphs I made with my results that I took, I can see that generally there are very strong trends, but there are some anomalies in my data. Looking at the graph for my second experiment, the one where distance is plotted against √(1/output of current), we can see several anomalous points.
To expand this investigation, we could investigate light colour as a variable, to see if light colour actually does affect the current output in the solar panel.