Figure 3
This diagram compared to figure 1 shows how the theory of resistance is affected by the alteration of the cross-sectional area of a wire. When the cross-sectional area of a wire is increased then the resistance will halve because the electrons have more space to move freely and less collisions will occur. The width in figure 3 is double the width in figure 1 resulting in half the number of collisions and a predicted halve of resistance.
Figure 4 Figure 4a
RESISTOR 1 - is a rheostat. I am using this to vary the current in my circuit. A rheostat works as a sliding contact moves.
Figure 4b
RESISTOR 2 - is two wires connected to crocodile clips, which will move across the length of nichrome wire, against a metre ruler. This varies the voltage in the circuit.
Apparatus:
● Power supply (Power Pack)
● Voltmeter
To measure the resistance.
● Ammeter
To measure the resistance.
● Rheostat ~ (Resistor 1)
● Nichrome Wire + Metre Ruler + Crocodile Clips ~ (Resistor 2)
Wires - Different lengths and cross-sectional area but the same metal.
Metre Ruler - To measure the wire being tested to ensure a fair test.
Crocodile clips - To connect the wire being investigated to the rest of the circuit.
● Connecting Wire
To connect the above items and to complete the circuit.
Method:
1) The apparatus is collected.
2) The apparatus is set up as shown in figure 4 above.
3) Adjust the sliding contact in variable resistor 2 to the desired current (0.4 A)
3a) Adjust the sliding contact in variable resistor 2 to the desired current (0.5 A)
4) Change the length of the wire by adjusting the sliding wire connectors (crocodile clips)
4a) Change the cross sectional area of the wire.
- Record results during observation period.
Fair test: to make it a fair test I must consider all these variables and make sure they remain constant.
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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 path of the electrons. This increase in collisions means that there will be an increase in resistance.
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Material: 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.
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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. Due to this the length increase should be proportional to the resistance increase.
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Wire cross-sectional area: 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 less collisions.
I must ensure that I control all these variables so that my results are consistent with my prediction and I’m only testing one variable at a time.
In order to plot a good graph I need to ensure I have at least 5 sets of results for each experiment and for each trial I will test the wire with two corresponding currents so that I can calculate an average resistance.
Risk Assessment:
- I will handle the power supply carefully.
- I am going to only use a low current and voltage.
- I will be careful when handling live wires.
Results:
Result 1:
From these results I have drawn a graph.
Result 2:
From these results I have drawn a graph.
Analysis:
From the results shown on the graphs on the previous page I can see that the resistance of the wire is proportional to the length of the wire. I know this because the line of best fit shows that if the length of the wire is increased then the resistance of the wire will also increase. I can also see that the graph for the cross-sectional area is proportional to the resistance. This conflicts with my original prediction so I can’t be sure as to why the results have had this outcome therefore I can’t fully analyse the results as they are not what my scientific research shows that it should be.
Saying that however, I do know that the cross-sectional area of a wire is inversely proportional to the resistance of a wire, as previous experiments have proven. To be clearer of this, take a fuse for example and a thick piece of wire of the same length and material, (controlled variables) and if we were to test this out in a controlled environment with a controlled voltage we would find that the resistance within the fuse is so high that the wire heats up and melts whereas the thicker piece of wire has a lower resistance in comparison.
Conclusion:
If the length increases, than the resistance will also increase in proportion to the length. From my graph I have shown that my prediction was correct, as the line of best proves that the resistance of the wire is proportional to the length of the wire. The length of the wire affects the resistance of the wire because the number of atoms in the wire increases or decreases as the length of the wire increases or decreases in proportion. 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 will be a larger number of collisions, which 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. Also if the length of the wire was trebled or quadrupled then the resistance would also treble or quadruple.
If the cross-sectional area of a wire increases, the resistance will decrease inversely proportion to the width. Despite my results show an outcome that shows otherwise an ideal set of results would show my prediction to be accurate. This is because when the cross-sectional area of a wire is increased then the resistance will halve accordingly as the electrons have more space to move freely and less collisions will occur. The fewer the collisions the lower the resistance. If the cross- sectional area is therefore trebled then the resistance would halve trebly.
Evaluation:
From my results table and graph I can see that my results that I collected are not very reliable. It is clear to see my result table 2 isn’t scientifically correct and my result table 1 shows many individual anomalous results. Also on the graph I can see that some of the averages plotted are anomalous because the results do not line up. During my experiment I have noticed several modifications I could make to improve the Investigation.
The first of these modifications would be to use a large range of widths to give a clearer result table.
Secondly I would use a digital voltmeter instead of an analogue meter. I would do this because a digital voltmeter is a lot more accurate than an analogue because if the needle in the analogue voltmeter is bent then the readings given off will be false whereas a digital voltmeter does not rely on a needle or any other manual movements.
The next modification I would make would be to use pointers instead of crocodile clips. I would do this because pointers would be more accurate, as 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 different conducting metal wires of the same length to see how this affects the resistance. I can predict through my research that the type of material will affect resistance as the amount of free electrons, which are able to flow through the wire, varies from material to material. 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.
As temperature is such a huge variable and not constant it would be hard to measure this factor or test it as it can become quite dangerous so I have chosen not to further investigate this factor. Through my research, however I have found that temperature does indeed affects the resistance in a wire and so to that extent does the materials. My research shows that the temperature of a wire heats up the atoms in the wire, which 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 path of the electrons. This increase in collisions means that there will be an increase in resistance.