Prediction
From my general knowledge I think as the cross sectional area of a metal wire decrease, therefore the greater the resistance will be present in the wire. This is because to have an electric current to exist we must have a flow of electrons, which carry the electricity from the negative end to the positive end, and in any electric circuit their will be always be a resistance. This is the opposing force of the current or the movement of electrons in the circuit, therefore the more resistance there is, the harder it is for electrons to move in the circuit. Therefore if we decrease the cross sectional area we are narrowing the 'path way' for the electrons to move, meaning more electrons would collide with the atom in the wire or the electrons, meaning less electrons would reach the positive end and would get a loss of energy. This is due to the small gap that the electrons must pass between the atoms of the wire and also means that less electrons could pass through a thin wire than a thick wire because the wire get congested and more energy is needed for the electrons to push and squeeze into the gap to carry on to the positive end. This energy is called the voltage, which is the 'driving force' that pushes the current or electron round the circuit, therefore if we increase the voltage then more current will flow.
Not just the cross sectional area of a metallic wire can affect the resistance but three other factor, which is described and stated in the secondary sources I used: "Physics for you' and 'GCSE Physics'. As the length of the wire increases so does the resistance increases. This is because as I described before, about the electrons would collide more if they travelled through a narrow gap, this would happens again but5 in a different matter.
As there is a longer distance for the electrons to travel in a long wire, there would be a big chance of collision happening between the electrons and the atoms or the electrons in the wire. This will result in energy loss and maybe heat loss from the electrons and this energy and heat loss are transferred to the atoms of the metal and this will cause the wire to increase in temperature. When the electrons collide with the atoms of the wire, the electron loose energy and they slow down and make themselves weak to move through the wire and increasing the resistance.
Another factor that will effect the resistance is the rise in temperature. As you increase the temperature the resistance will increase as well because as the temperature rises through the wire it makes the atoms of the metal wire vibrate more, therefore the electrons collide more or get intercepted with the vibrating atom and with the fast moving electrons in the wire and collide, causing the resistance to increase.
The last factor is depending on what the material of the wire it is because some material like metals allow a current to pass through them because they have free flowing electrons between the atoms, making them a very good conductor. On the other hand some material like non-metals do not allow a current to pass through them meaning they are insulators. We can explain that metals allow the electrons to move away from the nucleus of the atom is because the outer layer of electrons in metals, have special properties which allow these electrons to become free electrons and as a result not belonging to any particular nuclei in the metallic molecule so they are called delocalised electrons. This creates a sea of negatively charged electron around the positive metal ions, which we call actions. This means that if a potential difference (which is also known as voltage) is applied thorough the metal wire, the delocalised electrons will move towards the positive end of the circuit and so there is a current. Non-metals however, don't have this property so they are usually known as insulator, which does not conduct

electricity but one exception is graphite. This is because of its structure it has which allow free electrons, which aren't shared to move between the individual layers of the carbon molecule in graphite.
Likewise all these factors must be counteracted, so I don't get a very big resistance value but the cross sectional area of the wire must change because that is what
I am investigating on. Recapping, resistance is in fact the slowing down of electrons and this is because of the collision of the electrons with the metallic atoms, impurities and other electrons in the wire.
A theory of resistance is that the resistance of a conductor is the ratio of potential difference divided by the current, and is always constant provided that the physical conditions like temperature are the same. The current in a circuit is directly proportional to the applied potential difference and also inversely proportional to the resistance. This theorem has made a formula for resistance but has been rearranged from the formula: -
V = IR
Where V equals to voltage, I is the current and R is the resistance; and when the formula is rearranged to work out resistance it should look like this: -
R = V/I
The resistance is measured in ohm's, which is named after the man who discovered the theory of resistance, ohms is also written in a Greek symbol

(called omega).
Remember that the wire used is made out of constantan, which is an alloy of copper and nickel, which can also affect the resistance given. This alloy is made with 55% copper and 45% nickel. Constantan is used in many resistors like in standard resistor and heating elements because so much resistance is built up in the wire which opposes the electron and builds up immense heat. The two metals are bonded by special bonds called metallic bonding (term found in the book 'Chemistry for you'). And the metals are molten together and allowed mixing together and causing them to bond. This is because the metal receives high energy and the electrons become free and these 'actions' become surrounded by pools of negative electrons and the electrons from the cation start to move freely around all the electron, because the electrons move freely they form quit strong bonds and hold the two metals together and they act as one. This is like sharing electrons in non-metals but instead sharing in the whole structure of the constantan.
The resistance of the constantan has an irregular pattern in the structure because of the different size atoms, which are mixed in constantan, and they don't form a regular pattern.
This cause the electrons to collide more with the big atom or use loose energy when moving round the atom; therefore increasing the resistance. Good thing about having this property is because it strengthens the metal making it firm.
The resistively of constantan is 49

10
-8 
and using this I can work out the predicted resistance of constantan and below is the results: -

SWG
21
24
28
30
34
36
40
42
44
Radius (mm)
0.4065
0.2795
0.188
0.1575
0.117
0.0965
0.061
0.051
0.0405
1
π
(r

10

3
)
2
2.51

10
6
4.075

10 6
9.006

10
6
12.83

10
6
23.25

10
6
34.18

10
6
85.54

10 6
122.4

10
6
194.1

10
6 m
2
Calculated resistance
(ohms)
0.745992
1.5974
3.530352
5.02936
9.114
13.39856
33.53168
47.9808
76.0872
By plotting a graph using these data, this will give me a rough idea how the experimental graph should look like. And when plotting these results it gave me: -
Resistance vs Cross sectional area
80
70
60
50
40
30
20
10
0
0 50 100 150
Cross Sectional Area (m
2
) x 10
6
200 250
You can see it is a perfect straight line with a constant increase and that is what my graph should look like.
Looking at the configuration of a circuit, more resistance is in a Series than a parallel circuit because if we think about it more electron will be flowing through one wire and the wire will get congested with electron causing more resistance, where as in a parallel circuit there are many wire and if one wire get congested it can move trough another wire, making a lower resistance.