To show how different factors affect the resistance of a wire and to what degree

(b) The independent variable will be the cross-section area. The different rods all contain one metre of constantan but each one has a different cross-section area. To measure the resistance of the wire I will insert the two wires of the ohmmeter in to the two sides of the rod. I intend to take seven results, the cross-section area ranging from 0.0256mm² to 0.2025mm². I do not intend to repeat any results unless they are very different from what I have predicted.

(c) The resistance will be measured when different materials are use for the wire. The rods all contain different materials, they are used in the same way as in (b). I intend to take 5 results with the materials: constantan, manganin, nichrome, brass and steel being used. The length (1 metre) and the cross-section area (0.45mm²) will remain constant in all of the rods.

Hypothesis

I believe that the length and resistance will be proportional to each other:

Resistance

Length = constant

The reason behind my prediction can be referred to the water model, when the pipe is doubled in length the friction between the water and the pipe will also double because the water has to be pushed through twice as much of piping. If this theory is applied to an electrical circuit it means that the resistance of the wire will be double if the wire is twice as long.

I believe that the relationship between the cross-section area and the resistance will be proportional, however, it cannot be written as:

Resistance proportional to cross-section area but as:

Resistance proportional to 1 .

cross-section area

This is because the larger the cross-section area the smaller the resistance therefore the cross-section area has to be divided by 1.

My reason for predicting this, again, came from the water model. When the pipe is halved in cross-section area, the friction between the same amounts of water going through the pipe will double as the water molecules are pushed into a much thinner pipe, which means the molecules are under higher pressure. When this theory is applied to an electrical circuit it means when the cross-section area is halved the resistance is twice as much.

If my predictions are correct, the graph for a proportional relationship should have a straight line going through the origin.

Obtaining Evidence

Results

(a)

Resistance

(?)

Length

(cm)

2.2

0

4.1

20

6.0

30

8.0

40

0.0

50

2.0

60

3.9

70

5.9

80

7.8

90

9.19

00

(b)

Resistance

(?)

Cross-section area

(mm²)

3.3

0.2025

4.0

0.1600

6.3

0.1024

7.5

0.0784

0.5

0.0625

5.5

0.0400

25.0

0.0256

(c)

Resistance

(?)

Material

3.3

Constantan

3.0

Manganin

6.8

Nichrome

0.7

Brass

.5

Steel

The experiments were carried out exactly as I described in the method, no changes were made during the experiments.

Analysing Evidence and Drawing Conclusions

Graphs

I have plotted 4 graphs (p.t.o.):

(a) To show the relationship between length and resistance

(x) To show the relationship between cross-section area and resistance

(b) To show the relationship between 1 . and the resistance

cross-section area

(C) To show the relationship between materials and the resistance

Conclusion

The graphs 1 and 3 have straight lines going through the origin; this indicates that the relationship is proportional. It can be written as a mathematical expression:

. resistance = constant

length

3. resistance . = constant

/cross-section area

I have drawn a graph showing the relationship between resistance and the cross-section area of the wire to confirm that only the resistance and 1/ cross-section area are proportional.

For experiment (a) the reason behind the conclusion can be referred to the water model, when the pipe is doubled in length the friction between the water and the pipe will also double because the water has to be pushed through twice as much of piping. If this theory is applied to an electrical circuit it means that the resistance of the wire will be double if the wire is twice as long.

For experiment (b) the reason, again, came from the water model. When the pipe is halved in cross-section area, the friction between the same amount of water going through the pipe will double as the water molecules are pushed into a much thinner pipe, hence a higher pressure. When this theory is applied to an electrical circuit it means when the cross-section area is halved the resistance is twice as much.

This conclusion and the results match my predictions exactly; the results show this by a straight-line graph going through the origin.

Evaluating Evidence

I think the way I carried out the investigation was appropriate, the apparatus had been specially prepared for easy use and accuracy for this investigation so I had little control over them, and hence it would be difficult to make mistakes during the experiments.

If I did the investigation again I would have preferred it to be carried out in a constant temperature e.g. in a water bath using water resistant apparatus. This would have given me even more accurate results. I do not know how precise the rods were for experiments (a) and (b), however, I am sure they are much more accurate rods which I could have used to carry out the experiments in order to gain truer results.

I found the conclusion was easy to foresee, as it was a simple investigation, also the water model helped me greatly to forecast the results. Therefore when the results matched my hypothesis I was certain that they were accurate.

I had some slightly anomalous results in experiment (a); when the length was doubled the resistance was slightly under what it should have been. This could have been due to the fact that an extra centimetre of constantan was needed to be bolted to the wood, however this would have increased the resistance, not decrease it. Another factor could have been that the screw that was used to fix the constantan was made of iron; iron has a lower resistance than constantan so this is probably the reason the resistance was slightly lower than what it should have been.

I would carry out experiments to see how temperature would affect the resistance of the wire, also I would like to find out if the shape of the wire's cross-section would have any effect on the resistance. I could extend experiment (a) further to see if the relationship would still be proportional if different materials are used.

Sean Fang 9DW