Find out how the length of a piece of wire affects is resistance.

Antoine Allen

The effect of the length of a piece of wire has on its resistance

Aim

To find out how the length of a piece of wire affects is resistance.

Background information

Conducting materials such as metals have resistance. They oppose the flow electrons through them.

Resistance - This is a measure of how hard it is for the electrons to travel through a part of the circuit (measured in Ohms (Ω)-From S-cool.co.uk

Resistance is the force, which opposes the flow of an electric current around a circuit so that energy is required to push the charged particles around the circuit. Resistance is measured in ohms. A resistor has the resistance of one ohm if a voltage of one volt is required to push the current of one amp through it.

Resistance occurs when the electrons travelling along the wire collide with the atoms of the wire.

These collisions slow down the flow of electrons causing resistance. Resistance is a measure of how hard it is to move the electrons through the wire.

Wire length: If the length of the wire is increased then the resistance will also increase as the electrons will have a longer distance to travel and so more collisions will occur with the positive nuclei in the wire. Due to this, the length increase should be directly proportional to the resistance increase. From Nelson Physics

To measure and record the results for this factor is simple; the results would be collected and could show a connection between the length of the wire and the resistance given by the wire.

Ohms law, V= IxR. This says that for a certain current there will be a greater voltage across the wire if it has more resistance.

This tells me that the voltage measures the amount of energy used up in getting each coulomb of charge through the wire. The units of volts are the same as joules per coulomb. Therefore, Ohms law says the more resistance means more energy used to pass electrons through the wire. Resistance is a measure of how much energy is needed to push the current through something. The electrons carrying the charge are trying to move through the wire, but the wire is full of atoms and the electrons keep colliding with the positive nuclei that keep colliding in the way and making the electrons use more energy.
If there is a rise in temperature the positive nuclei that are colliding with the electrons, gain more energy and start to move about increasing the resistance.

Resistivity is a mass property of material describing how well that material inhibits current flow. This is the physical property unlike resistance, which is not. If we consider current flowing through a unit cube of material, resistivity is defined as the voltage measured across the unit cube's length (V/m) divided by the current flowing through the unit cube's cross sectional area (I/m2). This results in units of Ohm m2/m or Ohm-m.

Things that can effect resistance

Temperature
Cross sectional area

Current- This is a measure of the flow of electrons around a circuit (measured in Amperes or Amps (A))

Voltage- This is a measure of how much energy the electrons are carrying around to the things in the circuit (measured in Volts (V)) from S-cool.co.uk

Plan

I plan to find out if the resistance does vary upon the length of a piece of wire. I plan to study the information I find out immediate as I obtain it. I am going to do a preliminary so I can see if ...

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Things that can effect resistance

Temperature
Cross sectional area

Current- This is a measure of the flow of electrons around a circuit (measured in Amperes or Amps (A))

Voltage- This is a measure of how much energy the electrons are carrying around to the things in the circuit (measured in Volts (V)) from S-cool.co.uk

Plan

I will need a circuit like this:

Prediction

I think the longer the wire is the higher the resistance will become. The reason I think this is because the longer the piece of wire the electrons will have more particles to collide with, than a shorter wire. I plan to take reading of voltage and current.

Scientific reason for thinking this

Diagram

Short piece of wire larger piece of wire in

In the circuit the circuit

If the temperature rises the positive nuclei will vibrate more, subsequently increasing the resistance, which means more collisions are induced. As the electrons collide energy is transferred as heat. The resistance is higher.

The resistance is directly proportional to the length of the wire. If consider this however hard it is for electricity to flow through 1 metre of the wire, it must be twice as hard to flow through 2 metres and 4 times as hard to flow through 4 metres etc. for constant cross section.

As long as everything else about the wire remains the same, the thickness and temperature and finally material. Doubling the length will double the resistance.

If we plot this on a graph, we get a straight line as shown below. This is from my research

These collisions slow down the flow of electrons causing resistance. Resistance is a measure of how hard it is to move the electrons through the wire.

If the length of the wire is increased then the resistance will also increase as the electrons will have a longer distance to travel and so more collisions will occur. Due to this, the length increase should be directly proportional to the resistance increase

Preliminary

I am going to assemble the apparatus as shown in the circuit at the beginning of my plan. I am going to check the apparatus gives the right trend as predicted. I am doing this to check that the range of lengths of wires I have chosen gives a good set of results. Also I am doing to see if the results show my prediction and if my plan is appropiate.

Conclusion:
my results show that there is a proportional change between the length of wire and the resistance. Also it shows that I managed to control temperature, as there is no anomalous results. It shows at 300mm it has more than double the resistance that is at 100mm. Proving my prediction right. From this I have obtained that my experimental techniques are suitable enough to provide sufficiently accurate data to compose an accurate analysis and resistance graph.

Variables –.

There are many variables like

Temperture-once the curret is passing through the wire it will heat up and this will be added resistance, I have chosen not to use this variable so I will only place the current on the wire longer enpough to get the reading, thiis will prevent the temperture from rising

Safety/Fair:
I am going to make it fair and safe by only using 4 volts on the power pack. So it does not burn and cause a fire. A wooden board will be places underneath the wire. We will stand up and make sure there is no water or liquid near the apparatus. To make it fair we will repeat the experiment. We will only hold he connects on the wire for a few seconds, to it does not heat up. We will allow cooling time for the wire in case it does heat up.

Accuracy

I have used a table so I can record methodically and accurately. I am going to do it in mm so be precise. Also I will take the reading from 2 dp. I will repeat the experiment too obtain an average. I will study the data when it is collected, if it appears to be anomalous then I will carry out further repeats so I can ignore the anomalous results when working out the average. We must also make sure that the wire is straight when we conduct the experiment. If it is not, short circuits may occur and bends and kinks in the wire may effect the resistance, also.

Controls

Controls are used to see if there is a reaction coming from the apparatus, to make it a fair test.

We will only place the connects to the wire for a few seconds so it does not eat up, and obscure the results.

Method

I will place my apparatus together as shown in this diagram.

I will measure 100mm, 200mm, 300mm, 400mm and 500mm at the board that the wire is mounted on. I will make sure I use the same metal that I did in the preliminary. Also I would have already checked it was appropriate in the preliminary.

We will observe the reading on the voltmeter change and the amp meter we also observe a general increase in the voltage as the length of wire we use gets longer.

Equipment list

Volt meter

Amp metre

Power pack
Ruler
Length of wire
Connection Wire

Michrome – 0.55

Results

Table

Analysis

In my prediction, I stated that, if the length increases than the resistance would also increase in direct proportion to the length. My graph shows that as the results are all on or next to the line of best fit I know this because the Line of Best Fit is a straight line through the origin showing that if the length of the wire is increased then the resistance of the wire will also increase in proportion to each other. The reason for this is the longer the piece of wires the more positive nuclei the electrons have to collide with, so the resistance is increased. The resistance of a wire depends on the number of collisions the electrons have with the atoms of the material, so if there is a larger number of atoms there winl be a larger number of collisions that will increase the resistance of the wire. If a length of a wire contains a certain number of atoms when that length is increased, the number of atoms will also increase. This is described in detail in my plan.

The resistance at 100mm is 0.49 and at 200mm it is 0.92, this shows that the resistance has doubled by the double in length. Showing that the resistance and the length of wire must be directly proportional.

Also I can work out the resitivity

I think if we went to length of wire higher than 500mm it would not make a difference. I have learnt this from my graph; because 100m is still as proportional as 500mm, therefore 500mm would be as proportional as 2500mm.

The data shows my prediction was correct.

Anomalies

I had no anomalous results; this was because I worked with precision and skill. This shows my results are reliable. This is shown on my graph, as my results are all on or next to the line of best fit.

Evaluation

I am pleased with my finding s as they match my prediction. I have managed to prove that up to 500mm of wire the resistance is proportional to the length of wire. I had no anomalies. I am pleased with this because if the temperature had changed during the experiment I would have had some. This shows I worked with skill to stop this from acquiring. The difference in the resistance is in the 0.40 at all the points. This shows the accuracy was obtained throughout the experiment

Improvements

To get a more general conclusion we could go up to 5m. Also we could investigate the cross sectional area and temperature. I think the cross sectional area will come up with the same outcome as the length of wire. On the other hand I think the temperature will give a more abundant outcome, as the particles would be moving more with the higher temperature.

Extend

The modifications I would make would be to use pointers instead of crocodile clips; I would do this because pointers would be more accurate. The pointers would be more accurate because the tips have a much smaller area than the crocodile clips giving a more accurate measurement of the length of wire.

As well as making these modifications I would also improve my Investigation by testing the same wire but different widths of that wire. I would do this to expand on my Investigation.

Also we could try and involve the temperature.