To investigate the factors affecting current in a wire.
To Investigate The Factors Affecting Current In A Wire
Introduction
The aim of this investigation is to find out the factors that affect current in a wire.
Electric current is defined as the rate of flow of electric charge.
Variables that may affect the resistance of the wire
Every appliance has a resistance. If the resistance is high, the current will be low. If the resistance is low, the current will be high.
The variables that can affect the resistance in a wire are:
- Cross-sectional area of the wire
- Length of the wire
- Temperature
- The material (resistivity)
- Voltage
Cross-Sectional Area
The thicker the wire is, the lower the resistance, therefore the higher the current (given that all other factors are constant).
When a wire is thick, there are more electrons available to carry the current. Free electrons are available in metal (wire), if the metal has a larger cross-sectional area - more electrons will be available. If the wire is thinner, fewer electrons will be available to carry the current. A thick wire has more free electrons and more space. A thin wire has less free electrons and is more 'squashed' together. This means that the electrons are likely to collide more with the metal ions in the wire. Collisions in a metal wire will result in an increase in resistance because the ions from the metal wire will be getting in the way of the flow of electrons. And if there are more collisions, the flow of electrons will be disrupted more. Therefore there'll be less current.
R ? 1
a
Length of a Wire
As the length of the wire increases, the resistance increases. Length is proportional to resistance. And as the resistance increases, the current decreases. As the length of the wire decreases, the resistance decreases hence the current increases (provided that all other factors are kept constant - especially voltage).
In order to explain why this is, one must consider the positive and negative terminals in a wire. All electrons are negatively charged hence they're all attracted towards the positive terminal. But as the length increases, more electrons will become available, but the electrons that are closer to the positive terminal will form a 'barrier'. This 'barrier' makes it more difficult for the electrons on the negative terminal to flow across to the positive terminal. And also the attraction from the positive terminal decreases if there are lots of electrons rushing towards the positive terminal.
Another reason why a longer wire has a greater resistance is because the electrons have a greater distance to travel.
This factor causes more resistance than the fact that a barrier is formed which blocks the way for electrons to flow more freely.
Resistance ? Length
Temperature
When the temperature increases, the resistance increases and so does the length to a certain extent (because when something is heated it expands a little).
When there is more heat in a wire, the positive ions collide more. Since current is the flow of electrons, when the electrons try to flow passed these ions, they will be at risk to more collisions. Hence the electrons get slowed down.
So a higher temperature in a wire will result in a higher resistance therefore a lower current.
The Material (Resistivity)
Different metals have different resistances per 1 metre of length.
E.g. 32 SWG (Standard Wire Gauge) Copper wire and Nickel Chrome wire of the
same length will have different resistances.
The resistivity of a metal is the resistance between the ends of a specimen 1m long and 1m^2 in cross-section.
So at 20 C:
Copper has a resistivity of 1.78 * 10-8 ?
Nickel Chrome has a resistivity of 110 * 10-8 ?
Silver has a resistivity of 1.66 * 10-8 ?
Voltage
The potential difference or voltage is the energy that is given to each charge as it passes through the power source.
The potential difference across a circuit component measures the amount of energy that is transferred to that component as current flows through it.
When the voltage is increased, the current increases too.
Voltage ? Current
V ? I
In my investigation, I am going to keep every controllable variable constant except for length. Length is a non-linear variable because I don't expect it to be directly proportional to current. I previously considered investigating the cross-sectional area of the wire because this factor is probably the most effective one that has the greatest influence on the current in a wire. But instead I chose to investigate the length because it is easier to do practically and is therefore more accurate and reliable.
However, there is a formula to work out the resistance of a wire and it includes the cross-sectional area, length and resistivity of the wire:
Fair Test
In order to see if the length of the wire really does affect the current in the wire, all other factors must be kept constant. This experiment must be conducted under safe and fair test conditions.
All factors (cross-sectional area of wire; temperature; voltage; and material) will be kept constant except the length of the wire. Safety precautions can also be considered as fair test conditions. For example, I am going to make sure that no foreign objects or water come into contact with the experimental apparatus.
To keep the temperature constant, I will have to make sure that a large amount of heat doesn't build up in the wire (otherwise it will melt or affect the readings). In order to do this, the power pack will be switched off for a minute or so in between taking readings. I must also keep the surrounding room temperature the same or the particles in the wire will move faster (if the temperature is increased) and this will therefore have an effect on the resistance.
To keep the cross-sectional area of the wire constant, I will note down the SWG of the wire I'm using. And make sure that I'm using the same material.
To keep the voltage constant, I will just make sure the reading off the digital voltmeter is always the same. So if the potential difference across the wire is below the constant value, the rheostat can be adjusted to maintain the p.d across the wire.
The equipment used must be the same when doing repeats etc.
Prediction
Increasing the length will increase the ...
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To keep the cross-sectional area of the wire constant, I will note down the SWG of the wire I'm using. And make sure that I'm using the same material.
To keep the voltage constant, I will just make sure the reading off the digital voltmeter is always the same. So if the potential difference across the wire is below the constant value, the rheostat can be adjusted to maintain the p.d across the wire.
The equipment used must be the same when doing repeats etc.
Prediction
Increasing the length will increase the resistance hence decrease the current passing through the wire. If you double the length, you double the resistance therefore halve the current through the wire.
The reason for this is because as you increase the length, the electrons have to travel a long way. But if the wire is short, the electrons have less distance to travel. And for the potential difference applied in a short length of wire, the electrons can easily travel along this short length of wire with the SAME potential difference.
The other reason why current decreases when length increases is because a longer strip of wire has more electrons available. These electrons will of course be attracted to the positive terminal in a wire. So there'll be lots of electrons on the positive terminal, which form a 'barrier' against the electrons longing to travel to the positive terminal. And also the force of attraction between the electrons and the positive terminal will be less if it is further away in a longer strip of wire.
Resistance ? Length
So if I double the voltage for the same resistance, the current will be doubled. And if I double the length, the resistance doubles therefore the current will be halved.
R = V therefore I = V
I R
Preliminary Experiment
For my preliminary experiment, the following circuit was set up:
The power pack was set to only give out 2V. But in practice, I had to change it to 4V and make sure the reading on the voltmeter was always constant at 2V. The voltage was kept constant by adjusting the rheostat (as explained earlier). I chose a low voltage so that less heat will be produced. Because if I chose I high voltage, the current will be high therefore more heat will be produced. This will affect the results. Whereas a low voltage will show less current therefore less heat dissipation.
A 36 SWG (Standard Wire Gauge) Nickel Chrome wire was used. Nickel chrome is a high resistivity wire and 36 SWG is the thinnest wire available. Thin wires have high resistances. I used a high resistance wire so that there was less current therefore less heat dissipation. And also it would be easier to spot the difference. Because if there was a small error in the reading, it'll have a significant effect on the value of resistance calculated. However, I found that using this was a contributing factor in the heat produced. Because the resistance is very high which in effect causes some heat to be dissipated. I actually felt some heat after switching off the power pack. So in my real experiment I will use 32 SWG Nickel Chrome.
Power Dissipation = V^
R
When V is kept constant, the power dissipated decreases as the resistance increases.
Power Dissipation ? 1
R
A voltmeter and ammeter were included in the circuit so that the resistance can later be calculated. The rheostat was used to alter the voltage so that it always remained constant at 2V when taking down the reading for current. So if the voltmeter reading was above 2V, the rheostat was adjusted so that the voltage was brought back down to 2V. If the voltmeter reading was below 2V, the rheostat was adjusted so that the voltage was brought back up to 2V.
When carrying out the experiment, the power pack wasn't left on for a long time, otherwise heat would've built up thus affecting the results. But unfortunately, I did not leave it off for long enough because I could feel the heat building up. A safety precaution during the experiment was not to touch the wire when live current was flowing through it.
The length of wire used was 100 cm. Then this length was decreased by 10cm each time a reading was noted until it got to 10cm. The wire was connected to the circuit using two crocodile clips, and one of these was moved back by 10cm each time a reading was noted. So in effect, the other 10cm is short circuited out. The results of my preliminary experiment are shown below:
Length (cm)
Voltage (Volts)
Current (Amperes)
Resistance (Ohms)
0
2.00
0.95
2.11
20
2.00
0.46
4.35
30
2.00
0.29
6.91
40
2.00
0.21
9.52
50
2.00
0.16
2.50
60
2.00
0.13
5.38
70
2.00
0.11
8.18
80
2.00
0.09
22.22
90
2.00
0.07
28.57
00
2.00
0.06
33.33
Plan
APPARATUS: - 1m Nickel Chrome wire with a thickness of 32SWG
- Rheostat
- Power Pack
- 6 connecting leads
- 2 crocodile clips
- Voltmeter
- A 0 to 10 amp ammeter
) The circuit will be set up as shown in the diagram above.
2) The rheostat will be adjusted so that the reading on the voltmeter is exactly 2.00V
3) The readings on the ammeter were recorded.
4) The experiment was repeated thrice with the following lengths of wire, connected between the two crocodile clips.
100cm
90cm
80cm
70cm
60cm
50cm
40cm
30cm
20cm
0cm
When taking the readings, I had to be prompt then immediately switch off the power pack. This condition especially applied when taking down readings near the range of 10cm. Because it is here that the current passed through is at its highest therefore it will heat up quicker.
When putting the crocodile clips on the wire, I made sure that it was exactly on the desired point.
I made sure that the wire was flat so that it wasn't over 1m etc.
Safety: Because this experiment involves electricity, it can be considered as a
dangerous experiment. Therefore normal safety procedures apply. So the wire
should not be touched when the power pack is on. And if the power pack is
switched off, great care should be taken when touching the wire, as it will be
hot.
Great care will be taken when conducting the experiment, so that no water
comes in to contact with the experimental apparatus. Because water can
conduct electricity.
Other Observations
No real changes had to be made to my original plan except for the fact that I used cello tape to hold down the wire to the metre ruler. This was done to make it more convenient when putting on the crocodile clips on the desired locations. So that the wire was completely flat therefore more accurate.
Before measuring the current through 10cm of wire, the power pack was left off for a long time. So that the wire could completely cool down.
Results
The results that were recorded there and then were in a tabular format. After the experiment was completed, these results were transferred to an excel spreadsheet. And the resistance was calculated using the formula:
R = V
I
From these results, two graphs were drawn, for use in the analysis of the investigation.
Another extension I could do is maybe investigate how the other variables affect the current in a wire. So if I were testing whether the cross-sectional area affects the current in a wire, I would have to keep all other variables constant. Then I would test different diameters of the same length, material, temperature and voltage.
I would expect the current to increase as the cross-sectional area increases. Because increasing that would increase the number of electrons available to carry the current. And also it has more space for the electrons to travel therefore they won't be bumping (colliding with each other) as often. But if it were a thin wire, there would be more frequent collisions between the electrons and the ions. Hence the electrons get slowed down.
RADIOACTIVE DECAY CURVES EXPERIMENT
Analysing Evidence:
Simple Conclusion - From this experiment, I found out that for both isotopes, the activity decays with time.
Processing Evidence - From the 2 graphs, I calculated that the half-life for isotope A is approximately 8 minutes and the half-life for isotope B is approximately 1 minute. These are fairly constant over the given time interval.
Therefore the half-life is consistent for both isotopes.
So I conclude that isotope A is STRONTIUM 93 and isotope B is either STRONTIUM 94 or PROTACTINIUM 234.
Explanation and Comparison with Prediction - The prediction stated that radioactive isotopes have a constant half-life and that different isotopes can be identified by their half-lives. Both these statements are true to a certain extent. Because the half-life for each isotope is not exact, however both the isotopes have a different half-life therefore they are different isotopes.
Isotopes are atoms with the same number of protons but different numbers of neutrons. Isotopes that emit radioactive particles are called radioactive isotopes.
When the nucleus of a radioactive isotope emits an alpha or beta particle - it is said to decay. Note that a gamma ray won't do anything because it has no mass.
The definition for half-life = the time taken for half the atoms initially present to decay into their new element.
Radioactive decay is a random process. So there is no way of predicting when a particular nucleus will decay. But when huge numbers are involved - there are general statistical patterns.
So if you take some radioactive material, you'll find that the activity will slowly decline. Because there are fewer and fewer nuclei left that can decay.
The whole point why a radioactive isotope decays is that it is trying to become stable.
The results did agree with the prediction.
However the half-life can vary a lot because it mostly depends on how the best-fit curve is drawn. And the isotope is meant to be decaying but there are slight fluctuations (increases) in the activity. This is probably due to experimental error or the wrong background radiation reading.
Evaluating Evidence:
Simple Evaluation - In my opinion, I think there were sufficient results to draw a conclusion, but I don't think these results were accurate enough. Therefore I think there were faults in the method that led to these inaccurate results.
Anomalous Results - There were points that were just off the best-fit line. However, I still believe there are many anomalies. This is especially evident for isotope B. Because the activity increases at certain points and the activity sometimes even goes into the negative values. These are circled in red on the tables. These errors were probably caused by the count for the background radiation (65). Because this value was recorded for a period of only 5 minutes. So the background radiation is probably higher than expected which caused some of the values in the table to go into the negative values.
Another explanation is that there were experimental errors when doing the experiment.
Accuracy and Reliability - Because of these anomalies, I don't think that the results were reliable enough to support a firm conclusion. And I also don't think that I managed to obtain an accurate value for the 2 half-lives. This is because the best-fit line can vary so easily. Therefore when calculating the half-life, it is bound to vary.
I do think there were enough measurements but I don't think that the range was suitable. For example, I think that when measuring the background radiation, a longer period of time should've been used. And the number of counts from each isotope should've been measured every second for one hour.
A source of error that could be eliminated is doing the experiment away from areas where there is a high background radiation count.
Improvements - One obvious improvement is repeating the experiment. Or accurately measure the exact background radiation count. Or use a larger amount of each isotope and record the counts over a longer period of time. These changes should be made to give more accurate results and to avoid those fluctuations (increases) in count rate. And also to avoid values going into the negative values.
Extension Work - To extend this investigation, I would take large amounts of STRONTIUM 93, STRONTIUM 94 and PROTACTINIUM 234 and I would do the same experiment (with improvements included) to determine accurately the count rate and hence the half-life. Because I am still not sure whether isotope B is STRONTIUM 94 or PROTACTINIUM 234.
Another way I would extend this investigation is that I would record the count rate for that particular isotope for a very long time (one year or so) and see if the line ever reaches zero. I predict that it will reach zero but no one can ever predict when. That is why the graph is called an exponential decay curve.
Analysing Evidence
Simple Conclusion
From this investigation, I have found out that decreasing the length of a wire increases the amount of current flowing through it, provided that all other factors are kept constant. These other factors include the potential difference across the wire, the temperature of the room, the cross-sectional area of the wire and the resistivity of the wire.
I have also found out from my second graph of length against resistance, that increasing the length increases the resistance of the wire.
Identification of Trends
My first graph of length against current is a curve and it is non-linear. Because the difference between each 1 is not the same (which I had worked out earlier).
Length
This best fit curve on this graph in exponential.
This graph agrees with my prediction. Because if you double the length, the current halves. For example:
At 20cm the current is 0.50A
But at 40cm the current has halved to 0.25A
At 50cm the current is 0.20A
But at 100cm the current has halved to 0.10A
My results table is very accurate. But for some readings like the 10cm one, the current that passed through it is 0.99A. But according to my prediction it should be 1A. But if you look at my graph this is within experimental error and it is only out by 0.01A.
This graph is a curve because each time you halve it from the 10cm mark, it will produce a curve.
My second graph of length against resistance is a straight line through the origin. Even though I didn't test 0cm of wire, it is common sense to assume that 0cm of wire will give 0? in resistance.
This graph is a liner graph and it shows clearly that:
Length ? Resistance
The best fit line shows three points that are out, but these are not that far out and is within experimental error. These results have been highlighted on the graph.
This graph shows that as you increase the length of the wire, the resistance increases proportionally to it. For example:
At 20cm, the resistance of the wire is 4.00?
Then at 30cm, the resistance of the wire is 6.06?
Then at 40cm, the resistance of the wire is 8.00?
This shows that as the length increases by 10cm, the resistance increases by approximately 2?. These slight inaccuracies are not anomalous results because they are within reasonable experimental error (which is shown by my graph because it is near enough to the best fit line).
My results did agree with my prediction.
The results fully support my predictions, so the reasoning in the predictions appears to be sound (this applies to both the qualitative and quantitative predictions).
The gradient of the straight-line graph can be worked out using the formula:
Gradient = y step
X step
= 4
20
= 0.2
The length of the wire affects the current (therefore it also affects the resistance) because as the resistance increases, the current decreases. As the length of the wire decreases, the resistance decreases hence the current increases (provided that all other factors are kept constant - especially voltage).
In order to explain this, one must consider the positive and negative terminals in a wire. All electrons are negatively charged hence they're all attracted towards the positive terminal. But as the length increases, more electrons will become available, but the electrons that are closer to the positive terminal will form a 'barrier'. This 'barrier' makes it more difficult for the electrons on the negative terminal to flow across to the positive terminal. And also the attraction from the positive terminal decreases if there are lots of electrons rushing towards the positive terminal.
Another reason why a longer wire has a greater resistance (hence less current) is because the electrons have a greater distance to travel. And these electrons will be colliding more with the positive ions of the metal wire over a longer period of time because they have to travel a longer distance. This factor arguably has a greater influence on the current rather than the 'barrier' formed.
So if the length is doubled, the resistance is also doubled but the current halves.
Evaluating Evidence
Simple Evaluation
In my opinion, I thought that my method was a very good way to obtain a decent set if results to see if length affects the current in a wire. I think that I carried out the experiment very well given the resources that were available. My results were extremely consistent therefore my procedure can be assumed to be successful.
The only bit of my plan I had changed was that I used cello tape to hold down the wire. This was in actual fact an improvement so that I could put the crocodile clip on the exact spot. And it kept the wire down so that there weren't any kinks in the circuit.
Anomalous Results
I had no results which were outside reasonable experimental error. A result that is just off the best-fit line of a line graph is within experimental error (hence OK). I did not have any points that were significantly further away from the others.
My graph showed no anomalous results.
However, the points that are just off the best-fit line can be explained:
For example, for my length against resistance graph (straight line), at 70cm, the resistance should've been 13.80? instead of 13.33?.
At 80cm, the resistance should've been 15.80? instead of 15.38?.
And at 90cm the resistance should've been 17.80? instead of 18.18?.
The reason for these results is probably down to reasonable experimental error. Maybe the crocodile clips weren't making a secure enough connection. Or the wire could've been corroded or kinked at a certain point. Or even the connection in the socket wasn't secure enough. However, as the wire was getting longer, I did find it quite difficult to stretch it out.
Accuracy and Reliability
My results were reliable and accurate enough to support a firm conclusion.
I think I did take enough measurements for a suitable graph and I think I did cover a wide enough range of variables. When repeating my results (3X) I got exactly the same results.
Improvements
To improve accuracy, I could maybe try more lengths or take more repeat readings. I could maybe use a multimeter to measure the current. Because they give the results to a greater degree of accuracy and maybe I could've spotted whether the significant figures affected the outcome of a particular result. For example, 0.2A is the same as 0.16A. A multimeter is less likely to make this assumption.
A straighter piece of wire could've been obtained so there would be no corroded or kinked bits in the wire.
Then next modification I would make would be to use pointers instead of crocodile clips to attach to the wire. I would do this because pointers are more accurate in measuring the length of the wire.
In the experiment, I did not control the room temperature but instead just assumed it was kept constant. So maybe the room temperature could be adjusted so as not to make it very hot, otherwise the resistance of the wire would be greatly affected.
I found that I had plenty of time to spare at the end, so maybe next time I could wait longer between readings so as not to get any heat effect at all.
These changes would improve the accuracy and reliability of the experiment.
Extension Work
To further the investigation, I could maybe keep the current constant to measure the heat dissipation.
Or I can take an unknown length of wire (that can't be measured because it's so long). So this unknown length of wire will be rolled up like a coil. And I can use this experiment to find the length of it (provided that all other factors are kept constant for a fair test). So what I would do is measure the current through that wire and keep the voltage constant at 2V. Then I can use the formula: Resistance = S x 1 .
Length
Then using that formula, I can work out K (a constant value). If I'm using the same sort of wire and same thickness (Nickel Chrome 32SWG) then from my earlier calculations, I know that K = 10. So I can work out the length of an unknown nickel chrome 32 SWG wire by the following calculations:
Page 1 Varun Sivabalan