An Investigation into how the Length of the wire affects its resistance

Jenny Arbuthnot

Physics Coursework

Aim: An Investigation into how the Length of the wire affects its resistance

Research:

Resistance is a measure of how hard it is for an electrical current to flow through a conductor. In a metal, current flows through the wire when a voltage is applied across the ends of the wire. The current is free electrons flowing because one end of the wire is made positive. The resistance will vary depending upon how easily the electrons flow through the wire. The more difficult the electrons find it to flow through the wire, the higher the resistance will be. Therefore, resistance can be thought of as how much energy is lost by an electron as it moves along a wire.

The resistance through a wire can be measured using the following equation, providing that the voltage and current passing through the component is known:

Resistance= potential difference (voltage) across a component

Current through the component

A Diagram showing the free electrons and positive ions inside a wire while a current is flowing.

Inside a metal wire, there is a regular array of positive ions. There are also free electrons which travel in between the positive ions like gas molecules, so when a voltage is applied across the ends of the wire, the negative electrons are attracted towards the positive end of the wire and thus a current flows.

Wires have resistance because electrons cannot travel smoothly along it without bumping into the positive ions. These collisions slow the current down because it restricts the flow of electrons and therefore causes resistance. As the electrons bump into the positive ions, some energy is lost and so the more ions they bump into, the higher the resistance and the more energy is lost. This supports the theory that the thinner the wire, the more resistance there is because it is harder for the free electrons to flow along the wire without colliding many times with the positive ions.

As the voltage between the ends of a conductor is increased, the current passing through also increases. If the temperature of the conductor does not alter, the current that flows is proportional to the voltage applied (from Ohm’s law). The following graph shows this effect:

If there is an increase of temperature in the wire, the resistance is also affected. This is because the particles gain energy if the wire is heated and therefore they start vibrating faster. This movement makes it more difficult for the free electrons to move through the wire and carry the current, and therefore the resistance is increased as the temperature increases.

The length of the wire, the factor that I am going to be investigating, also affects the resistance. This is because if the length of the wire is increased, it takes longer for the free electrons to move across the wire as it encounters more collisions with the positive ions.

The thickness of the wire also affects the resistance. This is because the thinner the wire is the less channels of electrons in the wire for current to flow, so the energy is not spread out as much, so the resistance will be higher.

This is a preview of the whole essay

I am going to use a nichrome wire throughout this investigation because it has a higher density than copper wires. This would be an advantage in this investigation because it will mean that the resistance will be easier to measure. This is because as it is denser, it has more resistance in comparison to copper, which is so conductive of electricity that there will not be much resistance. The higher density increases the resistance because there are more positive ions for the free electrons to collide into.

Prediction:

I predict that if the length increases then the resistance will also increase in direct proportion to the length. I think this because the longer the wire, the more positive ions and so the more likely the electrons are going to collide with them. Therefore, if the length is doubled the resistance should also double. This is because if the length is doubled, the numbers of positive ions will also double resulting in twice the number of collisions, slowing the electrons down and increasing the resistance. My graph should show that the Length is directly proportional to the resistance.

If the length of the wire is only half the length of the wire on the same type of wire, there should be half the number of collisions between the free electrons and the positive ions.

If the wire is twice as long, there should be twice the number of positive ions, resulting in twice as many collisions and a predicted doubling of the resistance.

Apparatus:

1 m of Nichrome wire that will be used as the resistor.
Variable resistor is included in the circuit so that I can prove that resistance within a circuit is only relative to the length of the wire, not the current.
An ammeter is included in the circuit to measure the current in the circuit.
Voltmeter is in the circuit because it measures the potential difference across the component, i.e. the nichrome wire.
6 Electrical wires to complete the circuit and join all the apparatus together
Calculator is needed to work out the resistance within a circuit
A power pack is needed because it provides the power needed in order for the circuit to work.
8 Crocodile clips with good contacts or the resistance will be affected. Crocodile clips secure the electrical wires to the components.

A Preliminary Experiment:

In this experiment, I am going to set up the following circuit in order to find out which lengths of wire and what current I am going to use in the main investigation. This is how I am going to set it up:

I am using the variable resistor to make sure that the current within the circuit remains the same, even when the length of the wire changes. In this experiment I am expecting to find out:

How much voltage the power pack should be set to in order for good results to be achieved but at the same time make sure that the wire does not overheat.
The different lengths of wire I should use in order for the difference between the results to be substantial enough to draw a graph that is easy to read.

Results of the preliminary experiment:

See handwritten sheet.

Method for the main investigation:

Set up the equipment as shown in the diagram below:

I am going to make sure that there is a good connection between the components and the circuit.
I am going to make sure that all the components work (i.e. the voltmeter, ammeter and variable resistor) by firstly adding a bulb to the circuit.
I am going to measure the lengths along the wire using a ruler.
When the power supply is turned on, I am going to set the power pack to 4 A.
I am going to place the crocodile clips along the nichrome wire with the desired length in between the contacts (either 20cm, 30cm, 40cm, 50cm or 60cm).
I am going to make sure that the current is set to the desired amount each time (i.e. around 0.4A, 0.6 A or 0.8A) by adjusting the current using the variable resistor.
This is going to be repeated three times for each of the five lengths, each time changing the amount of current to make sure that the resistance is only affected by the wire, not the current.
The results will be recorded.

Reliability of Results:

I am going to do each length three times with the current changing each time then I am going to take the average of the three results.

Everything else must be kept the same except for the length of the wire and the current.

Accuracy of the Results:

Read results precisely and then round all the answers to 1 d.p.
Make sure that the calculations are right by repeating them.
When measuring the length of the nichrome wire, I am going to measure the length to 1 d.p.

Safety Precautions:

The entire circuit should be kept far away from water as otherwise there will be the hazard of electrocution
If the wire looks like it is evidently too hot, I will switch off the current for a while so that it can cool down.

Fair Test:

Ensuring that the experiment is a fair test is important because otherwise the results will not be accurate. To make sure that this investigation is a fair test, I am going to make sure that:

I use the same piece of nichrome wire throughout the investigation so I know that the cross sectional area or density is not different.
I am going to use the same apparatus and components throughout the experiment so if one particular component has a problem, the test will still be fair because each every part of the experiment will be done using the same apparatus.
Everything will be kept the same except for the lengths of wire and the amount of current being passed through the circuit.
Each length will be repeated three times using different amounts of current and then an average of the three results will be taken.

Results:

See table on handwritten sheet and hand-drawn graph.

Analysing Evidence and Drawing Conclusions:

In order to obtain the resistance of each length, I used the following formula from Ohm’s law:

Resistance (Ω)= Voltage (V)

Current (A)

Once the three resistances were found out for each length of wire, I found the average of them by adding the figures together and then dividing the answer by three.

For example: For the 30cm length of wire, the results were as follows:

Current (A) voltage (V) Resistance (Ω)

0.401 0.80 0.80 / 0.401 = 2.00 (2 d.p.)

0.600 1.21 1.21 / 0.600 = 2.01 (2 d.p.)

0.802 1.61 1.61 / 0.802 = 2.01 (2 d.p.)

Then, I added the three answers together and divided them by three so that I could get the average resistance. 2.00 + 2.01 + 2.01 = 6.02

6.02 / 3 = 2.006

= 2.01 Ω (2 d.p.)

I plotted the average of each length of wire to get the graph ad then drew a line of best fit.

As the line is straight and goes directly through the origin, I can deduce that the length of the wire is directly proportional to the resistance. This is because if the wire is longer, it takes longer for the free electrons to move across the wire. This is because if the wire is longer, there are going to be more positive ions for the free electrons to collide into and therefore slow them down.

The resistance is directly proportional to the length of the wire because if there is double the amount of wire, there is going to be double the number of positive ions for the free electrons to collide into. This means that the free electrons collide into the positive ions twice as many times as it would in a wire which was half the length, so if the length is doubled, the resistance is doubled. This means that the theory is similar to a hallway because a shorter hallway would allow people to move quicker and at a higher rate than a long hallway.

My results show that my prediction is correct because I predicted that the length of the wire would be directly proportional to the resistance and so when the length of the wire increases, the resistance would also increase. The results also more or less support my quantitative statement because I thought that if the length of the wire doubled, the resistance would also double. This is correct because my graph shows that the average resistance for a 20cm length of wire is 1.3Ω, while a 40 cm wire, double the length of 20cm, has an average resistance of 2.6 Ω, which is exactly double the resistance of the 20 cm resistance. Therefore, my results support the prediction that I made at the beginning of this investigation.

Evaluation:

My graph shows that my line of best fit is straight and goes straight through the origin. Also, the points that I plotted are either on the line or extremely close to the line, so there are no anomalous results.

I believe that the procedure that I used was reliable and successful. I got reliable results and they were just as I had predicted.

From my graph I can see that although some points are not exactly on the line of best fit, they are extremely close and therefore cannot really be classed as anomalous. I think that the main reason why the points were slightly off the line of best fit was because I rounded the resistances to 2 d.p. Then, I took the average of the three resistances, therefore meaning that the actual results may not be as accurate as they could have been. This is because I found the average of numbers that had already been rounded up or down, so it could have been a bit less accurate then it otherwise would have been if I had found the average of the resistances before they had been rounded. Therefore, if I had to improve on my method, I would find the average of the three resistances before they had been rounded and then round the average at the end in order to get more precise results.

Another factor which could have slightly affected the results and caused them to be slightly off the line of best fit was the fact that the temperature of the wire may have varied. This would have caused the positive ions to vibrate more and this movement would make it harder for the free electrons to move through wire. This could also have slightly affected my results.

I believe that as there were no anomalous results and the results were as I had predicted, the results are sufficient to be able to draw the conclusion that length and resistance are directly proportional. If I had more time, I could check if the results were completely accurate by repeating the experiment again and making sure that I could reproduce the same results again.

If I were to carry on with this investigation and to explore resistance further, I would find the resistance of more lengths and I would try using more than just three currents. This expansion of my investigation would support my results further. Also, I would repeat the currents and the lengths that I did again to make sure that I could get the same results, which would support my conclusion of this investigation.

If I could improve on this investigation, I would change the type of ammeter and voltmeter that I used so that it would give a reading of more than two decimal places. This would help give more accurate results.

Reference Books Used:

I used the following books in order to help me find the scientific knowledge: