However, I was not happy that I had found a metal which was sufficient for the test, I wanted to check that there was no others which would suit this investigation better, so I tested another metal to see if that would be better. I tested copper to see how whether it would be a better material to use. My results back up why I used constantan instead of copper. They are shown below:
This table shows that the current did not change at all , neither did the voltage and so in turn the resistance did not change throughout.
As I went on I plotted a graph and my results showed a clear positive correlation between length and resistance. Before even beginning my investigation I have observed that the resistance increase is directly proportional to the length and as the length increases, so does the resistance. This is very similar to the theory of ohms law which states that The potential difference (voltage) across an ideal conductor is proportional to the current through it.
Method
This method outlines how I will go about my investigation and the steps I will take. I also include a fair test and any other relevant information which I need.
How will I do the experiment?
- I will collect the appropriate equipment which I need as shown in the equipment list.
- I will set up the electrical circuit as shown in the diagram on page 1.
- I will take a meter length of constantan wire and measure 10cm from one end.
- I will then take the crocodile clips and put one at the end of the wire and the other 10cm along the wire.
- I will then, using the variable resistor, take 5 measurements of the voltage and current, which using the following equation will allow me to calculate the resistance.
Volts
÷ = Resistance (Ω)
Current
- I will then take an average resistance of the five so that I have the most accurate equation.
- I will then plot a graph of my results so that I can analyse the results.
I have decided to use measurements over one metre as I feel that the distance will be about right to show varied resistance and have not chosen a shorter length as I feel it would get too hot and the readings would then not be reliable as I am only testing how length affects resistance, not how heat does as well.
Fair test
To make my experiment fair, I will be making sure that I am only getting results for resistance affected by length and not by anything else. To do this I have to make sure I take into account what other things can affect resistance.
Temperature: To make sure that the temperature stays constant, I will use a longer piece of wire and I will make sure I am in an atmosphere where the room temperature will stay constant. I am hoping that the temperature of the wire during the test will stay constant during the test and I have decided to use a metre length of wire instead of a 10cm piece or its equivalent.
Length: I am using a ruler so that my measurements are accurate, however this is what I am changing so this will be changing anyway.
Thickness: Before doing the test, I measured the thickness of the wire at small intervals to make sure that the wire was the same length all the way along. This proved that the thickness of my wire was constant. I measured at 10cm intervals and found that the wire was 0.23mm at all points checked. I used a micrometer to obtain these measurements.
Material: I used constantan as my wire as it proved to be a very good metal in showing varying levels of resistance. To make sure that the material was kept constant, I used the same piece of wire. This is because constantan is an alloy (60% copper 40% nickel) and generally it is in the ratio 60:40, however there could have been a mistake during production meaning that constantan was produced at a ratio of say 59:41 then my results could be different. This is why I used the same piece of wire.
Predicting using the formula
We can calculate the resistance using a formula. This allows me to avoid the hassles of actually doing the true experiment. This formula is:
R= (ρ÷A) x L
Resistance = ρ ÷ area x length
ρ = electrical resistivity
electrical resistivity = 47 x 10-8 Ω/m*
*From science data book- Oliver and Boyd Pg 60
ρ÷area
This will be constant and so the only part of the formula which will be changed will be the length which will be changed according to my plans (at 10cm intervals).
From this information I can work out a table and plot a graph of resistance which should in theory be the same as the results from my test.
My results
These are the results of my experiment.
I calculated the resistance from the readings of voltage and current which I had acquired. To calculate the resistance, I used the equation:
Resistance= V ÷ I
V= voltage (volts)
I= current (amps)
This is my finished graph:
My graph clearly shows that resistance is proportional to the length. I have proved that as the length of the wire increases so does the resistance. My graph has very clear positive correlation which shows the link between length increase and resistance. The line of my graph seems to be quite clear and is relatively straight, however, the results around the 60cm mark seem a little unusual and if I was to do the experiment again then I would definitely retest at that particular length. As my graph has quite a regular pattern of results, I fell I could predict further patterns of the graph if it continues in the same pattern. A few of these results are shown in the table below:
I have followed the general pattern of the graph to produce this. I have rounded my predictions to whole numbers but there seems to be a pattern interval of around 1.25 Ω
Evaluation
I think the experiment went quite well and I think I did quite well. I found doing the actual experiment quite easy, however, I have found the write-up a lot more difficult. I think my results were pretty accurate, however, my result at 60cm, does seem a little unusual, however I did re-test at this length at seemed to get around the same result.
To improve my experiment, I could have done the same test with another wire, increased the number of tests I did on each wire, for example going up to 200cm or a metre. To get a better idea of resistance, then I could have tested on one of the other things which affect resistance. For instance, not only testing at different lengths, but also at different thickness as well. I could also have controlled some of the other factors such as temperature, by keeping the experiment in a temperature controlled area, and making sure the experiment is conducted as quickly as possible so as to avoid the wire over heating.
To make sure my results were as they should be, I could use the equation to make sure my results complied as well as possible. This equation is r = (ρ÷A) x length.
To extend the investigation, I would need to increase the width of the wire. To do this, I would need to use the circle equations and circular prism equations. These are:
π r 2 to find the area of a circle, or the face area of a circular prism.
To calculate the area of a circular prism, use this equation:
(π r 2 ) x length of prism.
