5.Wire area: If the area of the wire is increased then the resistance will decrease. This is because of the increase in the space for the electrons to travel through. Due to this increased space between the atoms there should be less collisions. This is similar to the wire width but instead of using different swg’s of wire we will double up the wire.
To chose which factor I am going to investigate I am going to consider how I would measure each factor and which factor would be the best and easiest to record.
To measure the wire width I would use different widths of the same length and same material of wire
e.g. thin, medium and thick wire. To record the difference in widths I would use the same voltage and measure the resistance for each thickness. Although it would be easy to obtain and record the data the graphs that I would be able to draw up would not be interesting.
For the temperature of the wire I would not be able to carry out a fair test because it is extremely difficult to produce and control the range of temperatures needed without the correct equipment.
If I chose to measure the difference in the resistance in different materials I would chose a number of different materials and using the same voltage I would record the resistance given by each wire of the same length and width. Although once again it would be simple to record these results the graphs that
could be drawn would not show any connection between the material and the resistance because of the limited number of materials I could test with the equipment available.
If I chose to measure the length of the wire it would be simple to measure and record the findings for this factor and the results collected could show a connection between the length of the wire and the resistance given by the wire.
The final factor is the area of the wire. To do this I would keep adding 1 piece of wire to the circuit every time. This would also be quite easy to set up the experiment and record the results and the results would be quite interesting. This is why I have chosen to investigate this factor.
I chose to use swg 36 because this was the thickness that we had readily available.
To work out the cross-sectional area of the wire I first had to look up its radius. I found this out to be 0.0967mm. From this I was able to use the formula area = r2 to work out the cross sectional area.
(0.0967mm) 2=0.00935mm2 to 5 dp
0.00935mm2*=0.0293mm2 to 4 dp
From this I worked out the cross sectional area to be 0.02932 to 4 dp.
After I chose that the factor that I was going to investigate I had to choose what wire I was to use for the resistance. For this I set up preliminary tests for 3 of the wires that we had available to us. These wires were Copper, Nichrome and Constantine. In this test we were trying to find the wire with the highest resistance because it will give us the most accurate results and reduce the chance of any anomalous results. I set up the circuit as shown on the first page. The length of wire we used was 50cm. In the real test we will increase this length to 100cm because we will want the most accurate results possible and in these preliminary tests it is not as crucial.
These are the results of the preliminary tests:
From these results I can see that the Nichrome wire has by far the highest resistance and so will give us the most accurate results.
But just to make sure that the Nichrome wire will keep giving accurate results as the area increases we did another preliminary test with a larger area of wire.
We see from this second preliminary test that the resistance has gone down steadily with 4x Nichrome wire. This is because the resistance of the test with 4 wires is roughly a fourth of the resistance when measured with one Nichrome wire.
Safety Precautions:
There are not many safety precautions that need to be taken into consideration, in this experiment. The main three I can think of are stated below:
1. We did not carry out the experiment in wet areas, as water is a very good conductor, and thus could be very dangerous.
2. We did not touch the wire when the battery is switched on, because the current would heat up the wire and so could burn us.
3. We also used a safety mat so the hot wires did not damage the table in any way.
Aim: To investigate how the area affects the resistance of a wire.
Prediction:
I predict that if the area increases then the resistance will decrease in proportion to the area. E.g. If with 1 length of wire the resistance is 10 then with 2 lengths of wire the resistance will be 5 I think this because as I know from my scientific knowledge that:
Electric current is the movement of electrons through a conductor. In this experiment a metal wire (Nichrome will be the conductor). So when resistance is high, conductivity is low. Metals such as Nichrome conduct electricity well because the atoms in them do not hold on to their electrons very well. Free electrons are created, which carry a negative charge, to jump along the lines of atoms in a wire, which are in a lattice structure. Resistance is when these electrons which flow towards the positive collide with other atoms, they transfer some of their kinetic energy. This transfer on collision is what causes resistance. So, if we double the area of wire, the space that the electric current has to pass through is larger so it has more space to go through. This decreases the number of collisions and energy transferred by half, so half the amount of energy is required. This means the resistance is halved.
This would also happen if you increased the number of wires by more than one and so if you increased the area of wire by more than one, so if you increased the number of wires to 3 then there would be one third as many collisions and so the resistance would be a third of what it would be if you only used one wire and with four then it would be a fourth. So we can work out a formula for this:
Resistance for one wire (Ohms) = R
Number of wires = N
New resistance (Ohms) = X
X = __R _
N
An example of this is if the resistance for 1 wire if 50 Ohms and if you increase the number of wires to 5 then you can work out the new resistance:
X = __50 = 10
5
So from this we can see that the new resistance is 10 Ohms
My predicted graph is on the following page. It shows what I think the graph of results should be based on my prediction.
My predicted graph shows that the resistance should decrease as the area of wire increases. This means they will be inversely proportional to each other .The graph is based on my scientific knowledge and Ohms law (Ohms law is stated in my conclusion.
Results:
We conducted 2 tests and then we found an average resistance from these results. We set up the experiment as shown on the first page. We started with one length of 100cm Nichrome 36 and then added one each time until we had 6 wires attached to provide resistance.
The 2 tables of results are below followed by the table with the average resistance.
First test
Second test
Average resistance
I have plotted the resistance against the area of the wire in a graph on the following page.
Analysis and Conclusion:
The first thing that you notice when you look at the graph is that it is curved. The graphs show that the area of wire is inversely proportional to the resistance. This is true to my prediction. This proves Ohm's Law as he states that if the area of the cross section of the wire is uniform then the resistance of the wire is inversely proportional to the cross section/area. So in simple terms the smaller the area the wire, the higher the resistance and the larger the area of the wire, the lower the resistance. This is because there are electrons in a circuit. These electrons travel around the circuit at an even pace. When they come to the wire I placed in the circuit the electrons have to slow down in order to be able to pass through it. This causes a resistance. The electrons will bump together, and the more they bump the higher the resistance of the wire. In a thin wire these electrons have to squeeze tightly together in order to pass through, however in a thick wire these electrons do not have to squeeze together as much to be able to pass through. So the more they squeeze together, the higher the resistance.
Summary of Ohms law
The current flowing through the circuit is directly proportional to the voltage applied to the circuit. (If you double one, you double the other.)
The cross sectional area is inversely proportional to the resistance of the wire. (If you double the cross sectional area, you halve the resistance.)
Ohms's law states that:
V = I*R and
= RC/L
V = voltage applied, I = current
R = resistance of the circuit, C = cross sectional area
L = length of the wire, and = resistivity of the wire.
This is correct in my results because as the area is doubled (from one wire to two) the resistance goes down by almost half (from 37.30 to 19.65). Then when the area is tripled it goes down from 37.30 to 12.01 and 12.01 is very close to a third of 37.01.
Evaluation:
From my graph I can see that my results that I collected are very reliable. I know this because my graph does not show any individual anomalous results. I can see on the graph that none of the results plotted are anomalous because all the points lie along the same curved line.
When I was measuring the lengths of the Nichrome wire, my measurements might have been slightly inaccurate as the rulers used might not have been exact, and it was difficult to get an accurate reading of length by eye, as the wire was not completely straight, so it may have been of different thicknesses throughout the length. This would have contributed as a slight error in my results. As this factor probably only made a slight difference, it did not affect my results.
The crocodile clips and the connecting leads could have affected the fairness of the experiment. They are a different type of metal from the Nichrome wire and may have different properties and therefore different resistance. Therefore the resistance of the Nichrome wire showed up on the ammeter and the voltmeter was slightly more than it actually was. To solve this problem, I would have found out the resistance of the connecting leads and crocodile clips before each experiment and minus it from the overall resistance of the Nichrome wire plus the connecting leads plus the crocodile clips.
c = a - b
a = overall resistance of Nichrome wire, crocodile clips and connecting leads
b = overall resistance of crocodile clips and connecting leads
c = resistance of Nichrome wire
To make my experiment possibly more accurate I could have got 3 sets of results and found an average but this would be too time consuming.
I don’t think I could really improve on the way the experiment was done because my results were very accurate, as I had no anomalous results.
I also found that the experiment was quite easy to set up, as it was simple and uncomplicated.
Further experiments I could do related to the resistance in a wire, would be to see whether the following factors would make a difference in the resistance of a wire: (I have made a prediction for each factor from my own scientific knowledge on how I think the resistance would change in a wire for that particular factor )
1. Wire width:
I think that if the wire width is increased the resistance will decrease. This is because of the increase in the space for the electrons to travel through. Due to this increased space between the atoms there should be less collisions.
2. Temperature:
I think that if the wire is heated up the atoms in the wire will start to vibrate because of their increase in energy. This causes more collisions between the electrons and the atoms as the atoms are moving into the path of the electrons. This increase in collisions means that there will be an increase in resistance.
3. Material:
I think that the type of material of the wire will affect the amount of free electrons, which are able to flow through that wire. This is because the number of electrons depends on the amount of electrons in the outer energy shell of the atoms, so if there are more or larger atoms then there must be more electrons available. If the material has a high number of atoms there will be high numbers of electrons causing a lower resistance because of the increase in the number of electrons. Also if the atoms in the material are closely packed then the electrons will have more frequent collisions and the resistance will increase.