How the Resistance of a Wire is affected by Cross-Sectional Area

How the Resistance of a Wire is affected by Cross-Sectional Area.

Introduction

Resistance is the opposition a component has on the flow of current and it is measured in Ohms. Resistance occurs as the electrons move along the wire they collide with the metal atoms. These collisions make the atoms vibrate more, which make the metal hotter, they also slow down the flow of electrons causing resistance. Resistance is a measure of how hard it is for the electrons to move through the wire.

There are four factors that affect resistance in a wire.

They are:

1. Temperature: If the wire is heated up the atoms in the wire will start to vibrate because of their increase in energy. This causes more collisions between the electrons and the atoms as, the atoms are moving into the way of the electrons. This increase in collisions means that the resistance of the wire will also increase.

2. Material: The type of material will affect the amount of free electrons which are able to flow through the wire, if the material has very few atoms then there will be high number of electrons causing a lower resistance because the electrons would have less collisions making it easier for the current to flow. But if there were few free electrons there would be more atoms packed closely together making it more difficult for the electrons to pass.

3. Wire length: If the wire is longer, then the resistance will be higher because the electrons will have a longer distance to travel and so more collisions will occur. Because of this the length increase should be proportional to the resistance increase.

4. Cross-Sectional Area 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. Because this increased space between the atoms there should be fewer collisions, and more current will flow.

Resistance can be calculated using this formula R = V/I.

Resistance can be useful in filament lamps and toasters, because if there was no resistance then the wire would not get hot and there would be no light and no toast.

But on the other hand in very big power lines you do not want to waste any electricity in heating up the power lines. That is why in the National Grid they use very wide wires so that there are fewer collisions between the electrons and the metal atoms, that’s why the electricity is transmitted at high voltage and low current. This causes less resistance and less power is lost.

Aim

In this experiment I am going to be investigating what effect changing the cross-sectional area has on the resistance of a wire. Input variables are the things which can be changed in an experiment. In My experiment the input variables are going to be the cross-sectional area of the wire this will be varied from thicker to thinner.

Output variables are things which are predetermined the input variables. In my experiment the output variables are amperes and volts, and these measurements will be used to calculate resistance. My circuit will include a power supply, wires, an ammeter, a voltmeter, and the subject wire.

...

This is a preview of the whole essay

To make this experiment a fair test I am going to keep the voltage to 3 volts, and keep the length of wire to 20 cm. I am not going to change the wires, ammeters and voltmeter. And I am also not going to change any of the other factors only the cross-sectional area of the subject wire.

Prediction

I predict that if the cross-sectional area of the wire decreases then the resistance will increase in proportion to the cross-sectional area.

I think this because of my prior scientific knowledge which shows that the wider the wire the more electrons that will be able to flow through them and the less collisions. But in a thinner wire there is less space for the electrons to move therefore more collisions.

My tables and graphs should support my prediction.

Apparatus list:

Power Supply – used to supply an electrical current and voltage
An Ammeter- used to measure current in amps, connected in series.
A Voltmeter- used to measure voltage. Connected in parallel.
Two different thicknesses of Nichrome wire- used to experiment on.
Two different thicknesses of Constantan wire- used to experiment on.
Meter ruler- used to keep the wire to 20 cm long.
2 crocodile clips- used to connect the subject wire to the circuit.
Connecting wires- to connect all the components.

Safety

I have decided to take some safety precautions by Keeping the voltage at 3 volts because 4 is dangerous, being careful when connecting the wires and while handling the live subject wire.

I also wore goggles and used heat proof mats to prevent the live wire from burning the table.

Method

Firstly I am going to connect the voltmeter to the Power supply.
Connect up all the wires.
Connect the ammeter.
Use crocodile clips to connect the subject wire.
Turn the power supply on to 3 volts.
The circuit should look like my diagram in the aim.
Write down the readings on the ammeter and voltmeter.
Repeat for all the thicknesses of wire.
After all the wires have been done create a table and calculate the resistance of each wire.
Lastly repeat all steps 2 times for reliable results.
And find the averages for the results you have collected.

Preliminary Work

I have decided to use 20 cm of wire as it seemed a sensible length.

I also determined to use 3 volts, because 4 volts melted the wire, and 3 seemed a reasonable, safer alternative. I experimented on which of the two materials to use. (Nichrome or Constantan).

I compared results on two different thickness SWG 32 and SWG 26 and recorded this information in three tables and three graphs.

In conclusion I have decided to use Nichrome wire to experiment on because it has a greater resistance and larger range between highest and lowest resistance.

By using nichrome my results are likely to be more reliable and easier to see how resistance increases as cross-sectional area decreases.

Actual Experiment

I will perform my actual experiment using the method below and considering the safety measures necessary

Apparatus list:

Power Supply – used to supply an electrical current and voltage
An Ammeter- used to measure current in amps, connected in series.
A Voltmeter- used to measure voltage. Connected in parallel.
Four different thicknesses of Nichrome wire- used to experiment on.
Meter ruler- used to keep the wire to 20 cm long.
2 crocodile clips- used to connect the subject wire to the circuit.
Connecting wires- to connect all the components.

Safety

I have decided to take some safety precautions by Keeping the voltage at 3 volts because 4 is dangerous, being careful when connecting the wires and while handling the live subject wire.

I also wore goggles and used heat proof mats to prevent the live wire from burning the table.

Method

1. Firstly I am going to connect the voltmeter to the Power supply.

2. Connect up all the wires.

3. Connect the ammeter.

4. Use crocodile clips to connect the subject wire.

5. Turn the power supply on to 3 volts.

6. The circuit should look like my diagram.

7. Write down the readings on the ammeter and voltmeter.

8. Repeat for all the thicknesses of wire.

9. After all the wires have been done create a table and calculate the resistance of each wire.

10. Allow wire to cool before continuing to the next stage.

11. Lastly repeat all steps 3 times for reliable results.

12. And find the averages for the results you have collected.

Results

Results on following pages

Analysis

Looking at my results I can see that my results are positively correlated and also I have noticed some trends in the results they are, in experiment one when the thickness of nichrome wire is at SWG 26 the resistance is 1.48 Ω and at SWG 28 the resistance is 2.19 Ω and also on experiment two when the thickness is SWG 26 the resistance is 1.46 Ω, and at SWG 28 the resistance is 2.12 Ω.

The results show that as cross-sectional area decreases the resistance of the wire increases. Because the wider the wire is the easier it is for the electrons to pass, and the narrower the more difficult it is for the electrons to pass. This agrees with my prediction because in my prediction I stated that if the cross-sectional area of the wire decreases then the resistance will increase in proportion to the cross-sectional area. I think this because of my prior scientific knowledge which shows that the wider the wire the more electrons that will be able to flow through them and the less collisions. But in a thinner wire there is less space for the electrons to move therefore more collisions.

My prediction has been proved correct by the results, because the results show that as width increases the resistance decreases. In Experiment one when the thickness of nichrome was SWG 26 the resistance was 1.48 Ω however when the thickness of nichrome was SWG 28 the resistance was 2.19 Ω, this clearly shows that the resistance increases as the thickness decreases.

Scientific Knowledge

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. Because this increased space between the atoms there should be fewer collisions, and more current will flow.

The method I used to collect the data was quite successful because it is very easy to understand what the results show, and it proves that my prediction was correct.

Evaluation

I think that the experiment was also quite successful and the results were reasonably accurate, apart from some anomalies which are circled on the graphs, the anomaly in experiment one was far off the line of best fit and I have decided to re-experiment on this anomaly in graph one SWG 30 which its resistance was 2.24 Ω, this anomaly may have been caused by the wire heating too much, possibly the wire was not connected properly, or I may have misread the readings. The other anomaly was not too far off the line of best fit so felt that it would be acceptable not to redo that one. The results shown on the graphs have a great range difference between the highest and lowest resistance, and all the points are close or on the line of best fit in all the graphs apart from some anomalies. To improve these results it would help to take the first measurement on the ammeter and the voltmeter before the wire begins to heat or to keep the wire cooler by either cooling the room or by placing the wire in cool water, this would not be so dangerous because the voltage that was used is not very high at all.

I think that my results are not 100% accurate because I know that mathematically in a scatter diagram to be sure of accurate and reliable results you need to plot 5 or 6 points, but in my graphs I have only plotted 4, because only four thicknesses were available to me, so I could not use more thicknesses. If I did my investigation again I would want to use more thicknesses to ensure reliability and I would also use analogue volt and amp meters to ensure precision readings.

Accuracy

To make my current investigation more accurate I will re-experiment on the anomalous result in experiment one (circled on graph) to ensure my average is reliable. I will carry out the experiment three times and find the average results, and plot graphs for these. I will use the average result to re-plot the graph showing that this would have been a successful result had it gone to plan. I will use the same method to take the readings, however I will not allow the wire to heat up before taking the readings. Having redone the experiment I am now able to see an improvement on the average graph, due to the re-experiment the average graph no longer has a predominant anomaly, proving that the error was caused by the wire overheating.

Results for Re-Experiment to Follow (at end of Evaluation)

To improve accuracy I could also consider an alternative method for the experiment the method follows:

Method

1. Firstly I am going to connect the voltmeter to the Power supply.

2. Connect up all the wires.

3. Connect the ammeter.

4. Use crocodile clips to connect the subject wire.

5. Turn the power supply on to 3 volts.

6. The circuit should look like my diagram.

7. Write down the readings on the ammeter and voltmeter.

8. Repeat for all the thicknesses of wire.

9. After all the wires have been done create a table and calculate the resistance of each wire.

10. Allow wire to cool before continuing to the next stage.

11. Lastly repeat all steps 3 times for reliable results.

12. And find the averages for the results you have collected.

As I am aware that heat affects the accuracy of the results I have added a stage to allow the wire too cool, therefore reducing the possibility of an error