Our aim for this investigation is to find out how the electrical resistance of a wire changes in relation to the size of the wire:~

• Length of the wire: The longer the wire, the more atoms there are for the electrons to collide with (this raises the resistance).
• Width of the wire: It causes resistance to decrease because of the increase of space inside of the wire. The increase of space means that there is more space for the electrons to flow freely because there would be fewer collisions with any atoms.
• Material the wire is made from: This is mentioned in the first paragraph of the theory section; if the material being used contains atoms with a large number of electrons on the outer shells, then there are more electrons available. So if the material has a large number of atoms, there should be less resistance, because of the higher number of electrons. If the atoms in the wire are closely packed, then this will cause an increase in resistance, due to frequent collisions.
• Temperature: Temperature is the final variable. At high temperatures, atoms vibrate more, therefore increasing the resistance of the wire and making it harder for the electrons to pass through.

Circuit:~

                                 

     Above is the circuit that I will use to carry out our investigation. After concerning each of the factors that could affect the resistance, I have chosen to record the results depending on the width of the wire. I will use several 10cm wires made of constantan, with each wire 0.375 mm thicker then the last, begging my experiment using a wire 0.375 mm thick and ending after the use of a wire that is 3.0 mm thick. This is because constantan has a high resistance; making it easier to record my results. I will also be keeping the experiment at room temperature constantly through the investigation; this will make it a fair test.

Apparatus:~

Constantan wire
Power supply
Two crocodile clips
Voltmeter
Ammeter

Safety:~

     This experiment is not particularly dangerous, although we are going to avoid using a wire that is less then 0.375 mm in diameter to avoid over-heating. Also handling the equipment with wet hands or near water is to be avoided entirely.

Fair test:~

     In order to make this a fair test, the lengths of constantan must be exact and should not differ when the experiment is carried out for a second time.

Prediction:~

      I think that the thicker the wire, the less resistance there will be. This is because there is more space for the atoms to move freely, reducing the number of collisions.

Results:~

First attempt:

Second attempt:

Average results:

Presented are graphs to show my results:~

Analysis:~

     From looking at my results it is evident that there is a relationship between the cross-sectional area of a wire and its resistance.

As the cross-sectional area of the wire increases the wires resistance decreases. This is because there is more space for the atoms to move freely, reducing the number of collisions, and so proves that my prediction was correct. However, there is an anomaly that can be seen within the graphs due to the second experiment. There are various reasons why this could have happened, of which are explored in the evaluation, but because it is so irregular when compared to the other results that it can be safely assumed that an error in the experimentation may have occurred. Further experiments would be able to prove this point. Each of the graphs roughly fit their own line of best fit which shows that the experiments held were presumably quite successful – although the anomaly has shown that certain aspects of the tests were neglected and that the results could be improved.  

Conclusion:~

I have concluded that, as the cross sectional area of a wire increases the resistance that it has will decrease. This is because as the width of the wire decreased, the electrons that made up the current had to travel through more of the fixed particles in the wire causing more collisions and therefore a higher resistance. This complies with my prediction. This conclusion is shown clearly in my results and in my analysis. I believe that the results obtained from my experiment support my conclusion

Evaluation:~                                                                                                                                                                                                I                .    I believe that this experiment was an overall success. My results fulfilled my aim and complied with the prediction I made and the background theory that I had assembled. The results supported my prediction because the background reasoning I used to produce the prediction specifically explained the behaviour of the flow of electrons which would be affected by resistance. Unfortunately, an inaccurate result occurred during the second attempt, and this can be seen clearly on the graph. This inaccurate result could have been due to faulty equipment, improper use of the equipment, or even that the wrong sized wire was used during the experiment.  We assume that the results probably would have been more accurate if further experiments had taken place. This would give a better example of what the results for this experiment should be like. Also a wider range of various sized wires would have given a larger view of how resistance is affected by certain aspects of a wire. All the equipment should have been checked for faults before each experiment to show if they gave the correct readings. These readings should have been viewed by each person participating in the experiment in order to abolish incorrect readings that would obviously lead to inaccurate results. Though the graph and the tables do show a decrease in resistance due to an increase in the wires width, so my experiment was still successful.