How would the power input to a solar cell change if it was not square onto incoming radiation?

Introduction

Finding the power input to a photovoltaic cell under varying angular positions would prove to be a useful fact in life. Obviously a photovoltaic cell used in real life situations is best used at maximum efficiency. The closer to the equator a photovoltaic cell is the flatter it will need to be to the ground, as on the equator the sun is directly above level ground and as you move longitudinally away from the equator to each direction the larger the angle the solar cell will have to be at to face the sun directly. This is not taking into account various times of day, only noon, as at other points in the day latitude would also have to be taken into account and I am not going to be changing the angle of my solar cell in both of these ways.

This experiment would also of course be very useful in application to satellites, as solar energy is there main source of power, so they can make the most of the radiation from the sun if they know at which angle to incoming radiation a solar cell functions best at.

Hypothesis

I predict that the findings of this experiment will show;

The closer the light source is to the photovoltaic cell, the higher the amount of energy that will be transferred in the cell.
The closer the angle the photovoltaic cell is facing to 90° (90° being when the solar cell is exactly facing the light source) the higher the amount of energy transferred will be. 90° being the maximum.
The load will not affect the power output as uniformly as the angle and distance will. This is due to the fact that current and voltage do not rise or drop by relative amounts to each other. This means that the graph showing the relationship between load and power output would not be a linear graph or even a simple curve graph. It will reach a very clear peak and then clearly drop after that. However with my current background knowledge I cannot predict the exact number of ohm’s that the graph will peak at, only that it will.

Risk Assessment

Upon planning this experiment I obviously had to take into account safety, not only of myself, but others around me also. Although at first thought there appears to be little safety precautions to think of it does not take long to realise that there are a few almost obvious things to take into account.

These are as follows;

The bulb must not be touched at all after prolonged periods of use for at least 5-10 minutes after the bulb has been turned off, as it could easily burn naked skin. This will not only burn skin, but also anything that it touches, such as paper, plastic and other such materials, this is obviously a fire hazard.
The emitted light from the bulb must not be pointed at anyone’s eyes, as it is relatively powerful and can burn the retina. This can be helped by keeping the light pointing no higher than horizontal, as the desk is only roughly waist high no one in the laboratory will be able to see the naked bulb. The lamp also has a sheathe covering the whole length of the bulb and a little more, this is made from metal and lets no light through. Consequently no light escapes this way either and light is only emitted horizontally.
I am going to have to use an extension lead to plug in my lamp, this is obviously a hazard. Anyone could trip or fall on the extension cable. To try and combat this problem I am going to do the following; make sure the extension lead is not taught, so if for some reason someone was to walk into the cable it would have a bit of give in it and possibly not trip them. I would also put a barrier of readily available stools to put around the cable, so it would be clearly visible that the cable was there and people would not physically be able to trip over it without before hand moving the barrier.
I would make sure that people in the laboratory knew where first aid materials were and how to use them in the event of any burns or eye injuries. Ideally also it would be good to have access to a qualified first aider in the room or even the building.

Method

I have chosen to perform 2 preliminary tests to find the best conditions to run my penultimate test in. This will involve testing the maximum output of the solar cell under varying loads and testing the distance at which the output of the solar cell is at an absolute maximum. These tests will be very useful, as when it comes to doing the penultimate experiment the solar cell will be in a position where the output is at an absolute maximum.

At this point the output will be a fairly large number (in watts), this means it will be very easy to read the measurements and due to the fact the ammeter’s and voltmeter’s are only accurate to a fixed number of decimal places it will be of higher volubility.

The circuit setup used in the preliminary tests and the final test is shown below;

This setup contains a photovoltaic cell in series, an ammeter in series, a resistor in series and a voltmeter in parallel. The full list of apparatus and details of each are as follows;

Voltmeter - I will decide which setting to put the voltmeter on when I start my preliminary tests, as to ensure that it is the setting that can display the whole number with the most decimal places, to ensure accuracy.
Ammeter - I will decide which setting to put the voltmeter on when I start my preliminary tests, as to ensure that it is the setting that can display the whole number with the most decimal places, to ensure accuracy.
Photovoltaic cell – The area of my solar was 0.001925m², this is made up of crystalline silicon, as a solar cell has to be a very good semi-conductor, of which silicon is. Highly pure silicon however is not so efficient to use, impurities are added such as boron to create an internal electric field, which allows electrons to move down the surface of the cell. At 0°C the average efficiency of a solar cell is 24%, however at standard room temperature (12°C) the efficiency is only 12%. Something contributing to this relatively low efficiency is the fact that there is some internal resistance in the silicon crystals that inhibits the free flow of electrons, this resistance increases as the temperature of the crystals increases, the electrical conductivity also decreases as it heats up. 43% of photon energy is still transferred into heat energy, warming the cell. Light in this case is measured in photons; these are a unit of electromagnetic energy, although they have no electrical charge or mass. They also cannot be used up, like any energy, they can only be transferred. The photon energy in my experiment will be oppositely proportional to the wavelength of the light from my light source. Visible light photons are measured in electron volts (eV), of which it is between 1.5 and 3eV. An electron volt is the amount of energy required to move one electron through a potential difference of 1 volt.
Lamp – I used a 240 volt and 40 watt desk lamp. This was kept 0.043 metres above the surface of the solar cell. This lamp is not perfect, it has impurities in the glass from when it was blown, and these cast shadows if you hold it above a white surface. This could be a problem in my experiment, as when varying the angle a shadow from the glass may fall on part of the cell and cause an anomalous result. I used the lamp for only 2 minutes maximum at a time, to avoid the heat affecting the results, for the reasons as described above. As well as the fact that the wires will heat up also, making the electrons vibrate in the wire and electrons that want to pass through the wire have to zigzag in and out of the vibrating electrons, this slows them down and of course this flow of electrons is called the current meaning that the higher the heat, the lower the current. Ideally I would have liked to have used a fluorescent light source, as this gives out very little heat energy; however I did not have access to one of these.
Decade resistance box – A variable resistor that is accurate at 18˚C. Resistance can range from 1Ω to 99Ω; this is accurate to 0.1%.
Copper wires – 5 of these were used to connect together the varying components used in the experiment. The effect heat has on these wires is a very important principle in this experiment and is described above.

I have selected and prepared this apparatus carefully, making sure that all apparatus I am going to use will be the same by putting my name on all apparatus, as there could be slight difference between pieces of the same type of equipment (especially in the case of solar cells, as each has a different number of scraps).

Preliminary Tests

Experiment to find the maximum output of a solar cell under varying loads

I am going to start this experiment by finding the maximum output of my solar cell under different levels ...