What this table should show that as diameter decreases then resistance show increase, this table does not show, that as length of wire increases then so should resistance.
The reason for this is that I only controlled the length of wire, though it does show nichrome has more resistance than constantan.
Method
I will first gather my apparatus together carefully, and then I shall set them up ready for experimentation. I will connect together the components in an arrangement like this:
Fair test
To make this a fair test I will need to measure accurately the length of the wire, the diameter of the wire. I will measure the diameter of the wire using the micrometer, which is accurate to 0.05mm. I shall the measure the length of the wire by using a metre rule, which accurate to 0.5mm.
I will need an extremely high resistance voltmeter and an extremely low resistant ammeter because if the voltmeter had a low resistance connected in parallel then this would create an extra path for the current to flow into. If the ammeter had a high resistance then the current would find it hard to come round again.
Background knowledge
I know that if the length of wire were long there would be more resistance, as there would be a longer line of electrons to go past and not to collide with.
This would be my evidence because the wire type, the diameter and voltage are the same. The only differences are the length, amperes and the ohms, as you can see the amps in the 500mm wire is 3, however the amps in the 700mm wire is 2.10. This shows a larger current can get through the wire more easily.
Therefore when there is a smaller current there would be a larger resistance measured in ohms.
I also know that if the wire were thicker, then this would allow more current to pass freely, therefore less collisions would take place and an easier route would be available.
As you can see the diameter are slightly different, but although voltage is slightly different, the ohms for the 0.56 diameter are much small than the 0.43 diameter.
This does therefore show the there is more area for the current to go through.
I know also that if temperature was raised then the atoms in the actual wire would vibrate more, as heat energy provides energy for the atoms to vibrate. This would then make the current less able to get through as there are so many collisions.
Variables
- Length
- Diameter
- Temperature
Errors
There were many errors when I conducted this experiment as there was a lot of human error involved even though I tried with the best of my ability to keep to a fair test.
First of all there was parallax error which meant my eye sight level could not be level with the measurement so I could have been out by about 0.05 for the voltage. The ammeter was relatively accurate because it was digital reader.
The micrometer was a very accurate tool though it was only 0.05mm out, but also the human error was involved.
To reduce errors it would be recommendable to take many readings or repeat the experiment so then you could take the average to get a more accurate result.
These problems would cause anomalous results.
E.g.
If you had,
0.36, 0.37, 0.38, 0.39, 0.35mm the mean=0.37
Spread of values=0.39-0.35=0.04mm ½ spread=uncertainty 0.02mm
Hence=0.37 +or – 0.02mm
Percentage uncertainty = uncertainty x 100
Mean value
Wire thickness
The wires I used were: 0.19, 0.23, 0.28, 0.37, 0.45, 0.56 & 1.25; for constantan
0.28, 0.31, 0.37, 0.45; for nichrome
Constantan: this wire would be a good wire to test because it only changes by 5% with a high temperature; its resistivity is 4.7x10 to -7.
Nichrome: A wire, which is affected a lot, by heat.
Another problem is that the instrument may be at an incorrect calibration, where by the voltmeter reads 0 but when there are volts applied it reads 5, but it’s actually is 5.2. To remedy this problem I should use a correct one or compensate in the readings.
Also I may without knowing incorrectly use the micrometer by over tightening, or measuring at an angle.
Random errors may errors may also occur as I must judge correctly when I read from the voltmeter scale. Equipment such as the digital ammeter may be different to the other ones supplied, same for the other equipment.
The composition of the wire will always be slightly different due to use, as no two lengths from the same reel will be the exact same.
Finally we had no control over room temperature and because I used wires such nichrome and constantan the may change.
On graphs there also must be errors as there will always be human error, so it always important to take many readings, then average them out to get the best possible outcome. Also when drawing a trend line there must always be error trend lines which show how much one anomalous point is out.
Analysis
As you can see from my table of results I have taken averages of the results and then graphed them. As you can see, as the diameter decreases, along with increasing length this will cause a high resistance and this proves the theory on length.
Also, as current increases you can see that so does the diameter of the wire. This assumption has been proved correct because of my graph, which shows that current is proportional to diameter. However the graph of nichrome is not because of the varying lengths.
Trend line: A graphic representation of trends in data series, such as a line sloping upwards to represent the average. Trend lines are used for the study of problems of predictions, also called regression analysis.
R-squared value: An indicator from 0 to 1 that reveals how closely the estimated values for the trend line correspond to your actual data. A trend line is most reliable when its R-squared value is at 1 or near 1. Also known as the coefficient of determination.
I can see my uncertainty results are all accurate within 15%, although none of my results are perfect as can be expected.
Evaluation
- I can now see that resistance depends on length: L as the longer the wire the greater the resistance so: R α L
- The cross-sectional area so the larger this is then the less resistance there is: R α 1/A
- Finally the resistivity of the material, ρ : R α ρ
A formula can now be established: R= ρL/A
The experimentation that took place was done to work out how variables affected the resistance in a wire. The experiments were suitable to enable us to use formulas we already knew to then finally see what would happen to resistance if anything were done to a wire.
There were many anomalous readings which questioned the suitability of the equipment, but also human error must have been involved. I would repeat the experiment, but I would first need more specialist equipment to rule out many errors.
I would need to work under controlled conditions, which would mean I work in different temperatures to test the plausibility of the resistivity under room temperature.
I would need to have every reading instrument to be digital to rule out any human error when reading a scale, also with it being delicate I must have a brand new one so there is no wear and tear on it and it checked that it is not faulty. The wire I test must be checked to have exactly the right composition and correct length.
I would always need to have connection wire made of a material like silver to reduce the amount of resistance there is.
Due the equipment I was limited to using under 6v because the voltmeter would not go past it, this meant I could not really how internal resistance would affect the experiment. Also the wires to test were already chosen for us so we could not compare a 1mm diameter with a 0.01mm diameter wire.
On the graphs there are anomalous results this may be due to human error when taking results down.
Measuring resistance
Resistance is measured when a voltmeter in parallel with the wire is divided by the ammeter connected in series in the same circuit. (V=IR - R=V/I)
There are three aspects that a resistant wire is capable of upholding:
- The wires resistance increases as the length does.
- The level of resistance also increases when the cross-sectional area of the wire decreases
- Finally the type or material of the wire
The best conductors are copper and silver, which are have the characteristic of having many free electrons, this therefore means that a current is able to pass through more easily than before as the free electrons take the current through the wire
When a voltage is applied across the end of a wire, it is difficult for the electrons to flow so this means that the resistance must be quite high in the material.
Resistance of a metal can measure how much kinetic energy; electrons lose while passing through the end of the wire. This is because the electrons do not travel smoothly down the wire, as they keep attracting positive ions, which impedes their progress. The more collisions a typical electron endures before reaching the end of the wire, the more energy losses when passing through a wire, this leads to increased resistance in the wire.
What happens inside a wire, when a current flows?
The internal part of the metal has a regular array of positive ions (+ve); this is an ion (metal atom), which has lost its free electrons. The free electrons can randomly swim about in the space between the ions like gas molecules. When voltage is applied across the ends of a wire the negative ions (-ve) electrons are attached towards the positive end of the wire and current flows.
Measuring current
Current (Amps) can be measured by dividing charge (Q) by time (t) because 1 amp is the flow of current, where the amount charge on a point per second.
1 amp is the flow of 6x10 18 electrons each second, so the charge on 1 electron is about 1.6x10-19. This means this equation is correct: I=Q/t
This diagram shows the coulombs passing a point each second containing the same amount of electrons per coulomb.
The whole point of measuring amperes is to work out the resistance.
Current and drift velocity
A=Cross sectional area
I =current
n=free electrons per metre (cubed)
e= charge on each electron
v=drift velocity
Formula: I=nAve
Fair test
I expect there to be an internal resistance, this does therefore affect the experiment because less voltage can be applied through the circuit, hence a lower amount of coulombs per second.
Kirchhoff’s second law states ‘Around any closed loop in a circuit, the sum of the E.M.F.’s (Electromotive force) is equal to the sum of the p.d.‘s (Voltage).
Є = IR + Ir