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What factors affect the Resistance of a Wire?

Extracts from this document...

Introduction

Richard Lai        Physics Sc1        29/05/2003

4th Form FI                MATH

Sc1- What factors affect the Resistance of a Wire?

In this experiment I am going to find out what factors and how they affect the resistance of a wire.

Prediction[a]

There are three given factors that can affect the resistance of a wire: length, cross-section area (abbrev CSA) and material. The two factors that I am going to work on are the length and the cross-section area.

1.) Length

My prediction of how the length can affect the resistance of a wire is the length is proportional to the resistance, i.e. if the length of a wire is doubled, then its resistance will also be doubled (see right). The equation that I referred to is this:

If the constant terms “ρ” and “A” are taken away, then we are left with “R” and “L”, which means that the resistance should be proportional to the cross-section area:

R∝L

Hopefully the results of this experiment will be the same as I have predicted.

2.) Cross Section Area

My prediction of how the CSA can affect the resistance of a wire is the resistance is inversely proportional to the CSA, i.e. the greater the CSA of the wire is, the lower the resistance is:

R1/a

The reason for this is because the thicker the wire, the more space there is for the current to travel through, and since the current finds it easier to travel through the thicker wire, the resistance would be lower. The diagram on the right is an example: if the wire is doubled in its radius, the resistance will be halved; therefore showing that the resistance of the wire is inversely proportional to the CSA.

Method

1.) Length

Middle

0.440Ω

0.680Ω

I have decided to use 0.14mm-radius wire for the length investigation, since it gives significant ranges of resistance, which can be shown clearly on a graph; for the CSA investigation, I have decided to use 80cm as the length for the wires. 90cm would be ideal, but I found it difficult to connect the copper wires together – they were simply not long enough. I want to make sure that the clips are clipped properly throughout the investigation, so I think 80cm would be a safer length, and yet still gives great ranges.

Results[b]

All my processed results are written down in 3 significant figures, so that they are all fair.

Length

Constant variables: same wire [radius (0.14mm), wire material (constantan)], current (0.5A)

 Length (cm) P.D. 1 (V) P.D. 2 (V) P.D. 3 (V) Aver. P.D. (V) Current (A) Resistance (Ω) 5 0.21 0.23 0.25 0.230 0.5 0.460 10 0.43 0.56 0.46 0.480 0.5 0.960 15 0.64 0.71 0.67 0.670 0.5 1.34 20 0.86 0.88 0.88 0.870 0.5 1.74 25 1.09 1.11 1.10 1.10 0.5 2.20 30 1.28 1.31 1.31 1.30 0.5 2.60 35 1.49 1.54 1.52 1.52 0.5 3.04 40 1.70 1.77 1.75 1.74 0.5 3.48 45 1.90 1.96 1.99 1.95 0.5 3.90 50 2.13 2.20 2.18 2.17 0.5 4.34

Length – measured with Ohmmeter

Constant variables: same wire [radius (0.14mm), wire material (constantan)]

Clips resistance: 0.2Ω

Conclusion

I can set up the same apparatus as the one I used for my experiment, but replacing the wire-board with a graphite. I will need graphite leads in different thicknesses for the “resistance against CSA” investigation, and, optional, graphite leads in different hardness’s for investigating the relationships between the hardness of the graphite lead and its resistance. I will need an insulator to hold the graphite lead up on the working surface so that there will be less risk of electric shock.

I will be using an ohmmeter to measure the resistance of the crocodile clips that I am going to use, so that its resistance can be excluded from the actual reading of the total resistance. Then I will do the same procedure as I did in the experiment for constantan wire, e.g. preliminary experiment to find out the sensible CSA for the “resistance vs. length” investigation and length for the “resistance vs. CSA” investigation, the number of readings, lengths, repeats, average, etc. I will bear in mind of what to be careful of, such as clearing the area around the apparatus, and not to leave the current on for too long.

I would guess that the graphite’s resistance would behave in the same way as the metallic wires do, but since this is something which I have never done before, I have no confidence that my prediction will be right, so in the future I might try and carry this investigation out.

[a]Planning: 5/8

[b]Obtaining Evidence: 8/8

[c]Analysing: 5/8

[d]Evaluating: 5/6

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