How does the length of a wire affect its resistance?

Physics SC1: How does the length of a wire affect its resistance?

Aim

The aim of this experiment is to investigate how the length of a wire affects its resistance when it is connected to a circuit.

Prediction

I predict that the longer the wire is, the higher its resistance will be because electrons colliding with atoms in the wire cause resistance. The longer the length of wire, the more atoms there will be, so the more chance there is of the electrons colliding, thus causing higher resistance. The resistance and the length should be directly proportional to each other.

Method

Factors that will affect the experiment:

Length – The longer the length of the wire the further the electrons will have to travel along it, increasing the resistance. Because of this the length increase should be proportional to resistance increase. We will be changing the length of the wire each time by 10cm. We will do this by turning off the power and unclipping the crocodile clips and re-clipping them back on 10cm less each time. The wire will be attached to a wooden metre ruler and so this is how we will measure the length of the wire each time.
Cross section of the wire - If the wires width is increased the resistance will decrease. This is because of the increase in the space for the electrons to travel through. Due to this increased space between the atoms there should be fewer collisions. We will use the same piece of wire each time.
Voltage passed through the wire – The higher the voltage the more electrons there will be passing through the wire, this should cause more collisions, causing higher resistance. We will need to keep this the same each time. We will be using a variable resistor to make sure that the ammeter reads the same each time, meaning that the current stays the same each time. If we do not use a variable resistor then the current will change and this will affect the experiment so we will not produce accurate results. The current affects the temperature, which also affects the resistance of the wire (see information below). The rheostat (variable resistor) is used to make sure that the temperature stays the same and the only variable is the length of the wire. We use the rheostat to ensure that the only variable being changed is the length of the wire so that our experiment is fair.
Temperature – Resistance produces heat, but heat also increases resistance. This is because the atoms in the wire vibrate more due to their increased energy. This causes more collisions with the electrons as the atoms vibrate into the path of the electrons. Resistance is caused by collisions with atoms in the wire. We will also therefore not conduct the experiment near any heaters or any other appliance that will majorly affect our investigation.
Type of wire used - The type of material will affect the amount of free electrons, which are able to flow through the wire. The number of electrons depends on the amount of electrons in the outer energy shell of the atoms, so if there are more or larger atoms then there must be more electrons available. If the material has a high number of atoms there will be high number of electrons causing a lower resistance because of the increase in the number of electrons. Also if the atoms in the material are closely packed then the electrons will have more frequent collisions and the resistance will increase. We will therefore use the same piece of wire throughout the experiment.

Some background information:

This is a preview of the whole essay

Some background information:

Resistance is a measure of how difficult it is to push electrons (the particles that carry electrical current) through a wire. The larger the resistance, the more force you have to apply and the more energy you use up to produce a current. The resistance of a wire is: R=r*L/A. L is the length of the wire, A is the cross-sectional area of the wire, and r is the"resistivity" of the material. This information explains what resistance is and how we calculate the resistance of a wire. Long, thin wires have the most resistance. How much the electrons interact with the atoms that make up the material depends on things like the electronic structure of the material, the physical structure, and the temperature. The more they interact with, or "bounce" off of the atoms, the harder it is to keep them going in the desired direction.

What to do

Equipment needed:

Power pack

1m of wire (made out of nichrome)

Metre ruler

Ammeter

Voltmeter

Rheostat (variable resistor)

Crocodile clips x2

Banana clips x4

Set up the equipment as shown in the diagram:

The piece of wire will be attached to a wooden ruler with a piece of metal on the end so it can be connected to the circuit. The wire is attached to the ruler so that it will be easier to measure the length of it each time and we do not have to readjust the circuit each time we change the length.

The variable resisitor will be adjusted so that the current will read 30A each time. This is so the temperature will stay the same and this will not affect the resistance of the wire.

Start the experiment from 100cm and then gradually decrease the length each time by 10cm after each repeat so the last length we will be investigating will be 10cm. The measurements we will be investigating will be: 100cm, 90cm, 80cm, 70cm, 60cm, 50cm, 40cm, 30cm, 20cm and 10cm. Each measurement will be repeated 3 times to ensure our experiment is accurate. If we start the experiment with the wire measuring 10cm, then we run the risk of the wire melting and then we cannot carry on with the experiment. This is therefore why we start the experiment from the longest length of the wire and not the shortest length.

To repeat the experiment we will turn off the power pack and disconnect and reconnect the crocodile clip from the wire. This is so we are truly remeasuring the different voltage each time and not just remeasuring the previous length. We will also readjust the rheostat for each repeat. This is so we will achieve creditable and realistic readings that we can draw a firm conclusion from and produce a graph with noticeable patterns and trends that we can also draw a firm conclusion from that will fit in with the background information found and will prove the prediction I made to be true.

The setting on the power pack will be 6v so that it is not too powerful and will not cause the wire to melt too soon.

To make this experiment safe we will follow the usual safety guidelines that we always use with electricity; we will make sure that the wires are not frayed and they are safe to use, we will make sure that we have dry hands when conducting this experiment and we will make sure that there is no danger of spilling any chemicals or water around this experiment. We will act sensibly and we will make sure that the plug is turned off before dismantling the equipment after the experiment and before disconnecting and reconnecting the clip to the wire to avoid the risk of an electric shock.

Carry out the experiment using the guidelines stated remembering to readjust the rheostat and disconnect and reconnect the crocodile clip on the wire each time for every repeat. Record the voltmeter readings and these will be used to take an average which will then be used to plot the graph of results.

We need to produce reliable results each time so we can draw a correct and accurate graph and identify trends in the graph and our results. We can therefore come to a firm conclusion using our results obtained. So, replicates are essential for all measurements, i.e. getting the same answer at least 2 times out of 3 after repeating each measurement.

Results

Results table to show how the length of a wire affects its resistance

*Please see separate results graph*

From the results achieved we can see that as the length of the wire decreased, the voltage readings also decreased. This means that as the length of the wire decreased, so did its resistance. If we carried on shortening the wire then evenually the wire will have melted. This proves my prediction to be true, as I predicted that the longer the wire is, the higher the resistance will be. As there were less atoms present in the wire to collide because the wire was short, there was only a small chance of the atoms colliding so the resistance of the wire was low. We can also see that the resistance of the wire was proportional to the length of the wire; when the wire was long, the resistance was high, when the wire was short, the resistance was low. We can see from the graph an obvious pattern, the one we have already described; the resistance of the wire is proportional to the length of the wire; when the wire was long, the resistance was high, when the wire was short, the resistance was low. We can see from the steep gradient of the graph that the resistance of the wire is low. So when the graph gets steeper, we can tell that the resistance of the wire is lower.

Conclusion

We can see from the results table and the graph that my prediction has been proved to be true; the longer the wire is, the greater its resistance. This is because electrons colliding with atoms in the wire cause resistance. The longer the length of wire, the more atoms there will be, so the more chance there is of the electrons colliding, thus causing higher resistance. The positive correlation of the graph shows that as the length of the wire increases, so does its resistance. This fits in with the background information that I found out.

Evaluation

The evidence achieved fits in with the background information I found so this must mean that the experiment went well as we achieved a set of results that proved the prediction stated to be true. We can also come to a firm conclusion from these results. We can see from the graph an obvious pattern, the one we have already described; the resistance of the wire is proportional to the length of the wire; when the wire was long, the resistance was high, when the wire was short, the resistance was low. I expected the correlation of the graph to be postive as this would be showing that as the length of the wire increased, so did the resistace, and the graph does show positive correlation.

The repeated results are all very similar to eachother meaning that we were accurate with out experiment and measuring. I think that therefore my results are reliable and I trust them enough to state an accurate conclusion from them. We can see that there are no anomalous results in the graph indicating that the experiment was carried out efficiently and accurately. The experimental method was satisfactory because it produced reliable and accurate results. This must also mean that our experiment was also fair aswell as accurate because the results are accurate and reliable. If we carried on shortening the piece of wire then it would have eventually melted.

However, if we were to improve the experiment we could take more care with our measuring when we change the length of the wire and when repeating measurements.

To extend the enquiry of factors that affect the resistance of the wire we can also investigate changing the following factors: