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Investigating a factor affecting the electrical resistance of a wire.

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Introduction

James Crowe

SC1 Investigation 2003

A factor affecting the electrical resistance of a wire

Free Electron Model:

        The free electron model is the representation of a metallic solid as a container filled with a gas composed of free electrons (i.e. those responsible for high electrical and thermal conductivity) and fixed metal ion particles:

The fixed particles, arranged as a crystal lattice, merely vibrate on the spot. The more kinetic energy they have (which can be affected by a rise in temperature) the more violently they vibrate. The free electrons are able to move around randomly within the metal. When a voltage is induced in the wire a current flows, this is because the electrons are attracted to the positive end and repelled by the negative end, as a result of this they move circularly around the circuit.

The origin of electrical resistance is that when the free electrons flow around the circuit, they often collide with the fixed vibrating metal ions which obstruct the flow, this is resistance. As this happens, the collisions cause friction which results in a temperature rise giving the particles more kinetic energy. This means more violent vibrations and so more collisions. Therefore, if a current flows for too long the wire will heat up and the resistance increase. Ohm’s law is a way of using the known voltage and current in a circuit to find out the resistance. Ohm’s Law means a steady increase in voltage would, in a circuit with constant resistance, produces a constant linear rise in current. It is a formulation of the relationship of voltage, current and resistance expressed as V = I x R.

Variables:

        There are many variables which could affect the electrical resistance of a wire. These are the diameter of the wire (its thickness)

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Middle

Wire 4:  0.315

Wire 5:  0.376

Here are the results of my preliminary work:

Wire Number

Diameter of Wire (mm)

Length of Wire (cm)

Voltage (Volts)

Current (Amps)

Resistance (Ohms)

1

0.193

10

1.25

0.71

1.76

1

0.193

100

1.4

0.08

17.50

2

0.234

10

1.16

0.91

1.27

2

0.234

100

1.38

0.12

11.50

3

0.274

10

1.07

n/a

n/a

3

0.274

100

1.36

0.17

8.00

4

0.315

10

0.98

n/a

n/a

4

0.315

100

1.35

0.23

5.87

5

0.376

10

0.88

n/a

n/a

5

0.376

100

1.34

0.31

4.32

This work clearly shows that wire 1, with the thinnest diameter and therefore the highest resistance, has the widest range of results. Therefore I am going to use wire 1 for my investigation as it will give me the best results. Interestingly, wires 3-5 did not even give results for 10cm within the range of the ammeter as their resistance was to low, and therefore the current to high to give a readable current. It is possible that infact the thicker wires would have given a wider range of results, which is a problem, but the ammeter provided couldn’t read their results so this is unimportant.

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Conclusion

For further work I would like to investigate the variable of the diameter of the constantan alloy wire. I would investigate whether the diameter of the constantan wire and the resistance of the wire were directly proportional. I would do this by using the same method as my original investigation, but doing so on each of the five wires. This would have given a much more detailed investigation and would also have shown whether the fact that length and resistance are directly proportional is true for every diameter of wire, and if so to what extent. It would also show clearly the relationship between diameter of the wire and resistance. Problems with this would be that doing so many experiments would mean a much higher likelihood of anomalies. It would also be very time consuming to get so many results, so a way of needing to take fewer results for the same conclusion would also be helpful. Problems with equipment and wires heating up and changing resistance would also be more prominent in this further investigation, so these problems would be analyzed more in my further work. I predict that this further work would show that infact the diameter of the constantan alloy wire and the resistance of the wire is indirectly proportional. Therefore if I increased the diameter of the wire the resistance would decrease. This can be shown from the use of the free electron model:

This shows that for the same distance of wire if the diameter doubles then the number of free electrons doubles with the same probability of collisions occurring. Therefore there are twice as many free electrons to flow around the circuit resulting in half the resistance. This means that as they are indirectly proportional then doubling the diameter of the wire would half the resistance. This is what my further work would show, in investigating the variable of the diameter of the constantan alloy wire.

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