An Investigation into the factors, which affect the electrical resistance of a length of wire.

I predict that as I increase the cross sectional area of the wire the resistance of the wire will decrease. This is because as the cross sectional area of the wire increases so does the amount of space through which the electrons can travel. This makes it less likely that the electrons will collide and therefore the wire gives less resistance to the movement of the electrons. I also predict that the resistance of the wire is inversely proportional to the cross sectional area of the wire.

Plan

Firstly I will set up the circuit, which will look like the one below using a power pack, ammeter, voltmeter, covered wire and the wire I will be testing.

I then placed the crocodile clips 30.0cm apart on the length of wire and turned the power pack on at 5 volts. I then recorded the current in amps and the volts to the nearest two significant figures. I then repeated this using lengths of 35.0, 40.0, 45.0, 50.0, 55.0, 60.0, 65.0, 70.0, 75.0 and 80.0 and at the end used the earlier stated equation to work out the resistance of the wire.

I also repeated the entire of the above experiment using the three SWG's I decided to use which were 22, 34 and 36.

Results

This table shows the results I took from the first experiment in which I used wire with an SWG of 22.

Length

Voltage (V)

Current (A)

Resistance (?)

30.0

3.13

2.88

.09

35.0

3.27

2.59

.26

40.0

3.38

2.37

.43

45.0

3.46

2.26

.53

50.0

3.61

2.05

.76

55.0

3.66

.94

.89

60.0

3.71

.84

2.02

65.0

3.79

.76

2.15

70.0

3.84

.64

2.34

75.0

3.95

.56

2.39

80.0

4.02

.48

2.72

This table shows the results of my second experiment in which I used wire with the SWG of 34.

Length

Voltage (V)

Current (A)

Resistance (?)

30.0

3.94

0.66

5.97

35.0

4.08

0.56

7.29

40.0

3.97

0.44

9.02

45.0

4.23

0.42

0.07

50.0

4.32

0.42

0.28

55.0

4.37

0.39

1.21

60.0

4.39

0.36

2.19

65.0

4.42

0.34

3.00

70.0

4.40

0.31

4.19

75.0

4.43

0.29

5.28

80.0

4.45

0.28

5.89

This table shows the results of my third experiment in which I used wire with the SWG of 36.

Length

Voltage (V)

Current (A)

Resistance (?)

30.0

4.84

0.74

6.54

35.0

4.91

0.69

7.12

40.0

5.00

0.62

8.06

45.0

5.08

0.55

9.24

50.0

5.13

0.52

9.87

55.0

5.22

0.45

1.60

60.0

5.29

0.41

2.90

65.0

5.30

0.41

2.93

70.0

5.32

0.38

4.00

75.0

5.40

0.36

5.00

80.0

5.41

0.33

6.39

I calculated the resistance using the following formula:

Resistance = Voltage / Current

I also got a second graphical representation of the resistance by analysing the gradient of a graph of voltage against current (see graph 1).

Conclusion 1: length of wire

Graph 3 gives fairly good straight line, which shows the results have a positive correlation. This is saying that an increase in the length of the wire gives an increase in its resistance. As it goes through the origin it is also suggests that the change in the length of wire is directly proportional to the change in resistance in the wire. This goes with what I said earlier in my prediction and can be explained by the fact that resistance is caused by free electrons colliding with the ions in the metal lattice of the metal of the wire. When an electron collides with an ion in the metal lattice the electron loses sum of its speed and energy in the form of heat, this is resistance. This is also is proportional to the length of the wire as the longer the wire gets the more times the electrons collide so therefore there is more resistance.

Conclusion 2: Cross sectional area

On the graph I have plotted, with the resistance against the cross sectional area it shows that there is a negative correlation. This means that they are inversely proportional and that an increase in the cross sectional area of the wire leads to a decrease in the resistance. This is in agreement to what I said in my prediction and can be explained by the fact that resistance is caused by free electrons colliding with the ions in the metal lattice of the metal of the wire. When the cross sectional area is increased so is the amount of space that the electrons have to travel through the wire and therefore means that there are not as many collisions and that therefore there is less resistance. This also supports my earlier statement, which states that, the cross sectional area of the wire is inversely proportional to the resistance of the wire.

Evaluation

I think that the results I got were good and gave me good straight lines on my graph. There were some anomalous results, which were probably due to the wire heating up and therefore changing the resistance of the wire, which is quite possible as I used a relatively high voltage and it was probably the source of the large majority of my errors. Another thing could have been due to the fact that the wire was not absolutely straight and therefore there could have been deviations in the length of the wire. This would have meant that not all my results were completely accurate.

I think the apparatus I used and the way I recorded my results worked well as a got a good set of results that I could draw a clear conclusion from. They clearly showed that the length of the wire was directly proportional to the resistance and that the cross sectional area of the wire was inversely proportional to the resistance. My experiment probably would have been more accurate if I had taken several readings for each variation in the experiment to get an average and if I had used previously cooled wire so that it ruled out the possibility of bad results due to the temperature of the wire changing. Also I could have used straightened wire to make sure it was a fair test.