The Cross sectional area will affect the resistance as well because as the area increases the amount of particles increase as well and so do the amount of gaps between them. Therefore the electrons have more space to pass through the wire. See the diagram below for an example.
The material will affect the resistance as well. The purity of the metal will as well, if it is pure it will conduct more than an alloy therefore a pure metal has a lower resistance than an alloy. The density of the metal will effect it as well the denser the metal the higher the resistance because there will be less gaps for the electrons to flow through. The more free electrons there are the lower the resistance will be.
The length will also affect the resistance, as the electrons will have further to travel therefore the longer the conductor the higher the resistance.
Method:
Above is a circuit diagram of how I’m going to set up my experiment.
The voltmeter measures the voltage across the wire. The ammeter measures the current through the circuit. The water bath is to keep the temperature of the wire steady. This is because Ohms law only applies when the temperature is constant so to make it a fair test I have to keep the temperature constant.
I will measure out 8 pieces of wire all at different lengths, 10, 20, 30, 40, 50, 60, 70, 80cm then I will attach the wire to the crocodile clips to complete the circuit and place it in the water bath. Next I will turn the power on and keep the current the same throughout the experiment (Iv chosen 3amps.) I will then record the volts passing through the wire. So now in will have the current and voltage and can work out the resistance from that. I will repeat the experiment 3 times for each length of wire so that I can get an average. As I increase the length I will need to increase the power, as the current will be less as the length of the wire increases.
To make this a fair test I will keep the other factors constant, these include the temperature, the material and purity, and the cross sectional area. To keep the temperature constant I will place it in a water bath. To keep the cross sectional area, the material; and the purity of the material the same I will use the same wire throughout the experiment.
I will test what wire will be best suitable for my experiment. I will do this by taking the 3 wires that are available to me and place them in the circuit above and record their voltage at different currents then work out the resistance. I don’t want a wire that has too much resistance but on the other hand I don’t want a wire to that has no resistance. It also needs to be consistent in its results. To keep this a faire test I will keep the other effecting factors constant, such as the length cross sectional area and temperature. Here are my results from the experiment to see which wire I should use.
I have chosen to use Manganin as my wire because its resistance is constant at all voltages which shows that its tempreature doesn’t increse much when the electrons flow through it. Which shows that it would give me more acurate results when it comes to finding out if and how the length of the wire effects the resistance because it will keep the tempreature constant at hight voltages. It also has the most consistant results.
Prediction: I predict that the longer the wire the higher the resistance. This is because the electrons have further to travel and more atoms to bump into.
I found a formula called the resistivity formula in a text book. The formula was.
R ∝ L
R = Resistance
L = Length (15cm)
This means that resistance is proportinal to length.
To work out the resistance you need to add a constant and the cross sectional area of the wire. So the formula looks like this:
R = PL
A
P = Constant
A = Area (Cross sectional)
The constant for Manganin is 44 x 10-8 which is = 0.000000044
I have chose to use Manganin 24 SWG. The diameter for this is 0.56mm
0.00056m
Therefore the radius is 0.00028
The formula to work out the area of a circle is ∏r2
∏ = 3.141592654
r = 0.00028
r2 = 0.0000000784
∏r2 = 0.00000024630064
A = 0.00000024630064
So now I have all the figures I need to work out the resistance.
R=0.000000044 x 0.15
0.00000024630064
R=0.267 Ω
Here is a table of my predicted Resistances. I predicted these by using the resistivety formula.
Results: Here is a table of my results that I gathered from caring out the above experiment.
Conclusion: I conclude that this experiment shows that the length of a wire directly affects the resistance. This is shown on the graph by a straight line that goes through the origin this means that he resistance is directly proportional to the length of the wire. My result line has a lower gradient than the predicted line. This could be due to the length of the wire not being accurately measured or the crocodile clips not being placed right at the end of the wire, this would have made the length shorter therefore the electrons wouldn’t have as far to travel therefore the resistance would be less. The gradient cant be blamed on an increase in temperature because if the temperature had increased then the resistance would have increased and given a bigger gradient. The graph below shows the difference between my results and my predicted results.
As you can see most of my results are fairly accurate except 50cm this could be due to inaccurate measurements.
My graph has a line of best fit, which sows that the resistance is directly proportional to the length. With out the line of best fit you wouldn’t be able to see that it was directly proportional because some of my results were inaccurate.
From my experiment I conclude that the resistance is directly proportional to the length. What I mean by this is that if the length doubles so does the resistance and if the length is halved so is the resistance for example if the resistance 0.2 ohms when the wire is 10cm the resistance for 20cm should be 0.4 ohms this shows that here is a relationship between the resistance and length.
Evaluation: this experiment went quite well it helped support my theory and prediction. It does this by showing that the resistance is related to the length it also supports that it is directly proportional.
As you can see form my results and graphs the accuracy of my experiment was quite good except for a few exceptions like the 50cm wire which was most probably measured inaccurately therefore giving a bad result.
My results are enough to support my theory that there is a relationship between the length and resistance as shown by my line of best fit. Also my results for the 60 and 70cm wire were exactly as I had predicted this is shown in my results table in the “How far off are my results.”
To improve this experiment if I was to do it again I would use a different wire each time as in this experiment when id done the 10cm wire it would let it cool down if it was hot and use it again this could have made my experiment inaccurate as damage could have been caused to the wire when I first used it. So next time I would cut another wire and use that one. If I had more time I could have done the experiment until I got a constant not an average this would have been more accurate as I would have had more results to back up my prediction and theory.
