How the resistance of a piece of wire changes with length

GCSE Science

Planning

Research;

Electricity is the flow of electrons from negative to positive: the opposite direction from which they are measured.
Electricity flows, due to the outer electrons in a metal being loose and hence they can flow.
The free electrons are moving very fast inside the metal (1/1000 of the speed of light) but another electron will be moving in the opposite direction with the same speed. This means that there is no net flow of charge and so no current
When connected to a circuit, the power source creates kinetic energy in the electrons. These accelerate and collide with the metal
Resistance is caused due to the atoms in the metal colliding with the flowing electrons. The metal ions will then gain vibrational energy, which is converted into heat. The electrons lose kinetic energy.
As there is a higher length of wire, so will there be more metal atoms for the flowing electrons to collide with. Hence, as the length of the wire increases, so will the resistance of the wire.
Resistance can be calculated using Resistance (ohms)=Voltage (Volts)

Current (Amps)

This had led me to make my:

Prediction;

I predict that as the length of wire increases, so will the resistance of the piece of wire increase. This is because of the increased amount of metal atoms for the electrons to collide with. If the length of the wire doubles, the electrons have twice as much metal ions to collide with, so there is double the amount of friction over the piece of wire.

To work out the resistance of any piece of wire this formula can be used;

R=pL/A, where R= Resistance, p= resistivity, L=Length & A= Area of the cross section of the wire.

This shows that if you double the length of the wire the resistance will double. This is because the length is directly relative to the resistance. It also shows that if you double the CSA (cross-sectional area) the resistance will decrease twice over.

Range and variables

I will be changing the length of wire, using every 10 cm, up to 100 cm. I will keep the thickness of the wire the constant (by using the same wire throughout the experiment) and I will also try to keep the temperature constant. I will use a low voltage (2V, 3V) so as to not increase the current, as this will cause inaccurate readings, as well as being dangerous

Preliminary experiments;

We found a suitable range of voltages so that the wire did not get too hot. We also found a suitable range ...

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Range and variables

Preliminary experiments;

We found a suitable range of voltages so that the wire did not get too hot. We also found a suitable range to use, and the right number of repeats to take.

Safety;

Safety is not much of a problem in this experiment. The only problems we could come across are the wire getting too hot, due to the current being too high, or if water was spilled near the experiment. I will make sure that neither of these things will happen.

Apparatus;

We will require;

An ammeter
A voltmeter
A metre long strip of Constantine wire
A power supply
Crocodile clips
A metre rule
Tape

Method;

We will set up the circuit in the following manner;

The wire will be placed on to the metre rule, and one lead of the voltmeter will be left loose, so that taking measurements simply requires the loose end to be touched at the required length on the metre rule. This makes taking measurements quick and easy. The wire that we will use will be Constantine, which is an alloy, and has a resistivity of 49x10-8 ΩM. It has a diameter of 0.02mm.

Observations

I made sure I did this with precision and skill by ensuring that the loose voltmeter wire was touching at exactly every 10cm. I also waited 3 seconds before each reading, to make sure that the reading was constant. I also made sure that the current reading was EXACTLY accurate, as this could adversely affect the resistance calculations.

Analysis

This graph shows that as the length increases, so does the resistance. It shows positive correlation. This is because as the length increases, so does the number of metal ions present. This would mean that there are more ions for the electrons to collide with, just as I had stated in my prediction. My results show this very conclusively. It also shows that as current increases, the resistance is unchanged. This can be confirmed by rearranging the formula R= V/I to leave V=IR, meaning that the voltage across the piece of wire is proportional to the resistance, as the current is a constant unless the power input is changed. I think that the slight differences between the gradients of my graph are due to the slight inaccuracies of the experiment.

This is what is shown on my graph. It also shows that if you double the length, the resistance also doubles. If any point on the x-axis of my graph is taken, e.g. 20cm, if this is doubled, the reading on the y-axis will also be double, hence the formula R=pL/A

I have taken the value of the resistivity of Constantine to be 49x10-8 ΩM, (this was found out of a textbook), however, I could calculate this using p=RA/L. Using the thickness of my piece of wire (0.02mm), I could calculate this to find out that it equals 0.00183, using values from my graph. This is quite a difference from the value in the book, but I would think this would be due to the inaccuracies on my graph, together with my reading for wire area maybe not being quite accurate.

All of these things lead me to think that my results support my prediction very well, and, hence the experiment was probably quite accurate.

Evaluation

I think that my experiment went very well. My results are very good, and they fit very well onto a graph, and are not far from the best fit line.

We chose to do five repeats to ensure that each average we took was as close as possible to the correct result. This would mean a greater accuracy of results. We took an average to ensure that the results could be easily graphed, and to ensure a greater quality.

Most of my results are very close to being double at the appropriate points. This would mean that our results were accurate, as they would fit my theories about the direct proportionalities of length and resistance.

The reason that I think my results were accurate is because of the major lack of anomalies. This is probably due to the accuracy of the equipment used. Both the Ammeter and the Voltmeter were accurate to 2dp, and so are very suitable for the task. However, there were also problems, and these could have caused anomalies. The wire, when placed on the meter rule, was nigh-on impossible to get perfectly straight. Also, at the end of the ruler, it was hard to get a good point for 100cm, as the rule ends here! This meant that the lengths measured may be untrue, and may account for the slight inaccuracies in the values. Another problem was that it was hard to find the correct place to put the loose Voltmeter end. It may also explain why our graph lines don’t fit perfectly over themselves.

These problems could be solved by;

Using wire that has been pressed for a day or so, to ensure that it is straight, and without kinks or buckles
Using a ruler that is slightly longer than a meter, to allow space for the Voltmeter end to be placed on the ruler, and easy measurement.
Use of a triangular-tipped loose end to the Voltmeter. This would mean a greater accuracy of results, as the end has a very small surface area, and is easier to position correctly.

However, despite these possible blemishes, I would say that I am quite confident that our results are reliable. I think that our results are sufficient to support my conclusion, although I would like to try a few other variables to check how other factors can affect our results. This might give me a better impression of how our experiment was inaccurate. Some of these variables are:

CSA (cross-sectional area) of wire

If I were to investigate CSA, I would use 5 different CSAs of wire. I would then decide on a fixed length, and take 5 repeats for each piece of wire. As the wire gets thicker, the resistance would increase, again due to there being more ions for the electrons to collide with

Current

If I were to look directly at current, I would use a fixed length, and just change the current entering the piece of wire. I would use 5 different currents, and, again, have 5 repeats.

Type of wire

If I investigated the type of wire, I would use wire made out of Constantine, Copper, Nichrome, Aluminium and Manganin. I would then choose a fixed length, and take 5 repeats for each type of wire. The better conductors (Copper, Aluminium) would provide less resistance due to them being better conductors.

Temperature of experiment

I would use a fixed piece of wire, and length, and change the temperature, if I were to investigate this. I would use 5 different temperatures, and have 5 repeats. As temperature increases, resistance would increase, due to the metal ions having more energy, and vibrating more, causing more collisions, and hence the electrons would be slowed more.