Investigation into the Resistance in different lengths of wire

Introduction

In this investigation, I will be looking at how the resistance in a piece of wire changes when I change the length of the wire. The variable in the experiment will be the length, and the thing I am studying will be the resistance.

Equipment

For my experiment I will need:
Wires of set length - for connecting the circuit together
A Variable Power Pack - to give the experiment its power and so that I can adjust the current to a suitable level
Wire that I can cut and adjust - this is the wire I will be testing though, so it must be bare.
Crocodile clips, to secure the wire
Voltmeter - to measure the voltage
Ammeter - to measure the current

Diagram

Method

I will set up the experiment as shown above, and then connect the 100cm wire to the crocodile clips, and turn the power on. Then I will take a reading of the Ammeter and Voltmeter, and record them. Then I will remove this wire, and replace it with a 90cm long wire, take a reading, and remove it. I will do the same for the 80cm, 70cm and so on, until I have reached 0cm. I have decided to use wire at 10cm intervals because it gives a nice even spread over the 100cm range, and it is small enough for me to see where anomalies are. So this means that if anything goes wrong, I can easily see it.

I will repeat the experiment three times to make sure that none of my results are way off the mark. If I find that there is an anomaly somewhere in my results I can identify it easily and redo that part of the experiment. This will also help in keeping my investigation fair.

Fair Test

To keep my experiment a fair test, I can do many things. I will repeat my experiment three times, so that I know that my results are not ‘dud’ ones. I will use the same type of wire all the way through the experiment, as different types of wire will have different amounts of potential for resistance depending on their makeup - i.e. what metals are used, the amount of impurities in the wire, etc. I will also keep all the settings on the power pack the same as well, because this would seriously affect my results if I changed the power going into the circuit in any way. I will also keep all the other equipment the same, seeing as there is nothing that needs to be washed such as there might be in a chemistry experiment or similar.

There are variables that I cannot control, such as the temperature in the room. The only thing I can do to combat this is to do my experiment all at once on one day, and hope that the temperature does not fluctuate too much. Human error is another unavoidable variable seeing as we cannot get a robot to cut the wire! To minimise this, one person will cut the wire, and use the same ruler to do it on throughout the experiment.

If I stick to these rules, there should be no need to repeat any parts of the investigation, ...

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If I stick to these rules, there should be no need to repeat any parts of the investigation, because the results I get should be fair and true.

Prediction

I predict that the shorter the wire becomes, the less resistance there will be in the wire, and that there will be some kind of proportional relationship between the resistance and the length of the wre, possibly that when the length of wire is doubles, the resistance will also double. I think this will happen because the formula for resistance is:

resistance = voltage OR R=V/I

current

because it is a set equation, I think there will have to be some kind of set proportional relationship between the length of wire and the resistance.

Electricity is made by polarising a wire so that electrons will all flow one way around a circuit. This flow is then used to power things. In the case of a simple light bulb, the electrons are made to flow through a piece of wire that resists them, and so heats up and gives out heat and light energy. However, in any conductor, apart from extremely high level cables and chips and other high quality or fidelity equipment you will get resistance in any wire. Sometimes it can be useful, as in the case of the light bulb, and sometimes it can be a hindrance, such as when transmitting long distance land-line phone calls.

Resistance is caused by the electrons in the wire, that are trying to flow through, hitting ions which are also present in most wires. Ions can be caused by impurities in the metal, or extreme heat in one part of the wire, or any number of reasons. Although the number of ions in any one point in the wire is random, it is usually fairly equally spread out, so if the length of wire is doubled, and the thickness stays the same, there will be roughly twice as many ions for the electrons to it as they go down the wire trying to get to the other end. This is why I think that the relationship will be directly proportional. In the end it could be written as R ∝ L, where R is the resistance, and L is the length of wire. If my prediction is correct, I should see a straight line on my graph.

Results

Here are the results for my experiment...

the first time:

the second time:

and the third time:

these are my results for the three times I did the experiment. I will now take the averages and condense these three tables down into one table, from which I can draw my graph.

Averages

Graph

From this table of averages of my results, I can now draw my graph, with a line of best fit. The graph should be paper clipped to this page.

Anomalies

In my graph, there were three results that fell just off the line that all the others sat on perfectly. I think that this was probably just natural variation, possibly in the temperature of the experiments surroundings, that created more or less ions in the wire for the electrons to hit. It could also have been due to the measuring equipment (i.e. the ruler) not being accurate enough. In any case, the variation on the graph is tiny, so the cause is negligible. I think it was probably a combination of temperature fluctuation and human error.

Conclusion

From my graph and results, I conclude that as the length of a piece of wire increases, so does the resistance in that piece of wire. In fact, the relationship is directly proportional to each other, when the length of the wire doubles, the resistance doubles as well.

So: R ∝ L.

This is because the wire has impurities in its makeup, and it also has ions in. when a wire is polarized, electrons flow through it on end to the other. This is electricity. When these electrons hit ions in the wire, the are slowed down. This is resistance. Because the amount of ions in a given length of wire is always roughly the same,(given that the wire is made of the same material and the same quality), the amount of ions, and therefore resistance doubles when you double the length of the wire. I will now find out exactly what the resistance-to-length relationship is for this type and quality of wire.

R ∝ L

∴ R = k L

∴ k = R/L

subst. When L = 10, R = 1.98

∴ k = 1.98/10

∴ k = 0.198

∴ R = 0.198 x L

I have found that the formula for the resistance in this piece of wire was approximately 0.198 x the length of the piece of wire. I can now determine the resistance for any length of this type and quality of wire.

Evaluation

I think that the method we used and the results we obtained were both suitable and acceptable for the experiment, because they both fitted quite neatly with the experiment itself. The results were in the range I expected, and the method was not over-complicated, but it was still fairly practical. Looking at my title and introduction, I have done what I set out to do.

I think that the least accurate part of the investigation was probably me, because my measuring probably could have been a lot more accurate if I had taken more time and care over it, but I am happy with the results and method I got.

There were no highly anomalous results, and those that were slightly out of sink, I have explained in my ‘anomalies’ section. If I were to do this investigation again, I think I would probably not change much, but just try and be a little more accurate.