To find the resistivity you need a table showing the resistance, the length
and the area. This table is shown below.
Material Resistance(Ohms) Area (mm ) Length (Metre) Resistivity (nm x 10 )
Constantan 2.19 0.126 1 0.28
Manganin 1.84 0.126 1 0.23
Copper 0.06 0.159 1 0.01
Radius(mm) Area(mm )
0.195 0.126
0.195 0.126
0.225 0.159
To find the area, you use the formula:
Pr
3.14 x (radius x radius)
From the table above, you can work out resistivity by using the formula, and then rearranging it to give you:
p= RA Resistivity = Resistance x Area
l Length
Example:
p = (1.84 x 0.126) = 0.23184 (round up the figure) = 0.23
1 metre
The results obtained above are the results obtained when doing the experiment on the different materials that affect resistance but with the same length. I used three different types of wire (Constantan, Manganin and Copper). The Constantan wire used during the experiment was 28 SWG
The Manganin wire used during the experiment was 28 SWG. The copper wire that I used during the experiment was 26 SWG. The readings that I received were accurate as not only did I keep to the safety procedure by turning off the power supply when not needed but I also tried to keep it as fair a test as I could manage. While obtaining the results I realized that my hypothesis before the experiment was accurate no matter what voltage the power supply is on, the resistance is always the same, and it also obeys Ohm's law.
Analysing results:
Experiment 1 - Length
The results that I obtained from this experiment on different lengths with the same (material) wire were good. The Constantan wire that I used during the experiment was 26 SWG. I had to do five trials as shown before to accomplish the experiment and obtain accurate readings, which then lead on to accurate results.
Even though the results were accurate in the end leading us to a formal line of best fit on my graph, I did incur a little anomalous reading in my results table as shown in the results table. Therefore for me to make the results for the experiment accurate I had to revolve and figure out a solution to my problem. In this case I simply deducted the reading anomalous reading which was '3'. Then to make sure a line of best fit could be attained I simply added up the other remaining readings which were 1.3, 1.29 and 1.29 (not the 3) then simply figured out the average and concluded my experiment successfully.
Experiment 2 - Cross-sectional area of a wire
The results that I obtained during this experiment on the different Constantan wires were pristine and accurate. The wires that I had used were 22 SWG, 26 SWG, 34 SWG and 36 SWG.
Experiment 3 - Material of the Wire
The results obtained above are the results obtained when doing the experiment on the different materials that affect resistance but with the same length. I used three different types of wire (Constantan, Manganin and Copper). The Constantan wire used during the experiment was 28 SWG
The Manganin wire used during the experiment was 28 SWG. The copper wire that I used during the experiment was 26 SWG. The readings that I received were accurate as not only did I keep to the safety procedure by turning off the power supply when not needed but I also tried to keep it as fair a test as I could manage. While obtaining the results I realized that my hypothesis before the experiment was accurate no matter what voltage the power supply is on, the resistance is always the same, and it also obeys Ohm's law.
Measuring resistance:
Resistance can be measured using an ammeter and voltmeter. This can be done when the resistance of a conductor can be found by measuring the current through the potential difference of a wire, when it's applied across it.
Method for measuring Resistance:
The way in which to measure resistance is to use an ammeter so that it can be measure the current through the component and also have to use a voltmeter to measure the potential difference across it. The following figures show two different circuits in use. It shows you where the voltmeter measures the current of flow. The diagram shows you that it has a voltmeter to measure the resistance of wire and an infinite resistance ammeter. The first circuit is unknown if component X has a low resistance, whereas the second circuit is the one to use if component Y has a higher resistance. To work out the value of X it is merely worked out by using the ratio of both readings of the voltmeter and ammeter.
Electrons move more easily through some conductors than others. The opposite of any conductor to a current is called a resistance. A good conductor has a high resistance; there are three main aspects that a resistant wire is capable of upholding are as follows:
1) The resistant wire increases as the length increases
2) Resistant wire increases as it's cross-sectional area decreases
3) Is dependant on the material
A material of long thin wire has more resistance than a short thick wire. Both the wires have the same materials. The best conductor of a wire is copper and the second best conductor of a wire is aluminium. Aluminium is used more because not only does it conduct electricity exceptionally well. But it is cheaper and easier to use. Copper is expensive but has a longer life expectancy than aluminum and is guaranteed to deliver the best source of electricity that it can provide. Aluminium is a good conductor of electricity and is also cheaper than copper but aluminium is not expected to have as long a life expectancy as that of copper. For every 2% of aluminium used 1% of copper is used. Although aluminium is cheaper copper would be more ideal as it is guaranteed to receive the best of its ability.
When a voltage is applied across the end of a wire, if it difficult for the electrons to flow then the resistance of the metal is higher. Resistance of a metal can measure how much energy electrons lose while passing through the end of the wire. This is because the electrons do not travel smoothly down the wire they keep attracting positive ions, which then impedes their progress. The more collisions a typical electron endures before reaching the end of the wire, the more energy it losses, when it passes through along the wire, which then allows the wire to have more resistance.
What happens inside the wire when a current flows?
The inside of the metal has a regular array of positive ions (+ve); this is when an ion is a metal atom, which has lost its free electrons. The free electrons can 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.
The resistance on a wire depends on several factors. A long wire has a larger resistance than in a short wire. A fat wire has a lower resistance than in a thin wire. Resistance is proportional to cross-sectional area; and it depends on a property of the material called resistivity, so
Resistance = Resistivity x Length
Area
Resistivity p, is a property of the material (whereas resistance is a property of a component). Resistivity is a measure of how the material opposes the current through it. Metals have a low resistivity; insulators have a high resistivity. Semiconductors as their name implies, are somewhere in the middle. The table 1 lists typical values of resistivity (bottom right).
For example the resistance of 100 m of copper wire, cross-sectional area 1.5mm , is:
R=pl = 1.72 x 10-8Wm x 100m
A 1.5 x 10-6 m2 = 1.15W.
Why does the wire have resistance?
The electrons don't travel smoothly down the wire because they keep bumping into positive ions and this impedes their progress. Its collision restricts the flow of the
Experiment 1:
Aim:
How resistance depends on the length of the wire
Hypothesis:
For this experiment I predict that my results will obey Ohm's law. When the length increases so does the resistance
Resistance Decreases Length Decreases
Resistance Increases Length Increases
Apparatus:
} Power Supply
} (2) Crocodile clips
} (3) Black Circuit Wires
} (1) Red Circuit Wire
}Voltmeter
}Ammeter
} Different Constantan Wires (26 SWG wire Constantan)
Method:
Firstly I shall have to prepare all my apparatus that I need to precede with my experiment, and then I will cut exactly one metre of constantan wire. Each time I have successfully taken down the necessary readings from one length I will then reduce the constantan wire by 20cms. I will then attach the crocodile clips to either end of the constantan wire. After doing this I will connect my wire to the voltmeter and ammeter and then switch my power supply on. Then I will record my readings and add them to my results table.
connecting the wire to the power supply I will induce voltages of 2v, 4v, 6v and 8v and then quickly note down my results, then turn the power supply off so the wires don't overheat and the add my readings to my result table.
Trial 5:
For this trial I must reduce the wire by 20cms, leaving us with a wire, which has a length of 20cms. Then I will attach either end of the wire with crocodile clips. Then after connecting the wire to the power supply I will induce voltages of 2v, 4v, 6v and 8v and then quickly note down my results, then turn the power supply off so the wires don't overheat and the add my readings to my result table.
While taking down the readings for each trial one must switch on the power supply while using a voltage of 2v, note down the results quickly and then instantly switch off the power supply. The same must be done with the voltages of 4v, 6v and 8v. The reason for this being so that accurate readings can be attained. If one was to keep the power supply on while switching voltages the wires would overheat and inaccurate readings would be obtained.
Diagram:
Outline of graph:
This is just an outline of my graph for resistance against length (RxL). I think my graph will appear to be like this as it goes through the origin; my graph will probably be a straight line, which will go through all the points, leaving from the origin therefore should be a straight line graph (y = mx+c)
Experiment 2:
Aim:
How resistance depends on the cross-sectional area of the wire
Apparatus:
W Power Supply
W (2) Crocodile clips
W (3) Black Circuit Wires
To 4v, 6v and 8v and then quickly noting down the results turning off the power supply and adding my readings to my results table.
Trial 3:
Firstly I must get a constantan wire 26 SWG. I then have to measure it and cut it at exactly one metre and then proceed with my experiment. I have to attach the wire to the crocodile clips and then turn the power supply to a voltage of 2v. After doing that I must then turn on the power supply quickly and then almost instantly after noting down my results quickly from the ammeter and voltmeter turn off the power supply. Therefore there is minimal chance of the wire overheating. Then I must repeat this experiment again by turning the power supply to 4v, 6v and 8v and the adding my readings to my result table. I will then need to calculate the resistance as well as the diameter, radius, the area and 1/area.
Trial 4:
Firstly I must get a constantan wire 22 SWG. I then have to measure it and cut it at exactly one metre and then proceed with my experiment. I have to attach the wire to the crocodile clips and then turn the power supply to a voltage of 2v. After doing that I must then turn on the power supply quickly and then almost instantly after noting down my results quickly from the ammeter and voltmeter turn off the power supply. Therefore there is minimal chance of the wire overheating. Then I must repeat this experiment again by turning the power supply to 4v, 6v and 8v and the adding my readings to my result table. I will then need to calculate the resistance as well as the diameter, radius, the area and 1/area.
For all of the trials above after you have obtained all the readings needed for the five trials you need to calculate the resistance (R) that is measured in Ohm's (W). What you then do is divide the voltage by the current as shown then rearrange the formula:
Voltage = Current x Resistance
REARRANGE
Resistance = Voltage
Current
The diameter of the wire is already given to you and from that, you have to find out the radius, the area and 1/area.
To find the radius, you simply:
Calculate the diameter and then divide the diameter by two
To find the area you simply use the formula:
Pr
3.14 x (radius x radius)
To find 1/Area you simply:
Calculate the area, and then divide it by 1
After all your calculations you input your information into a table:
SWG Diameter(mm) Radius(mm) Area(mm ) 1/Area(mm )
Diagram:
Results: Showing different SWG wires.
SWG Power (Volts) Voltage(Volts) Current (Amps) Resistance(Ohms) Average(Ohms)
The results above are the readings I had obtained from the second experiment on different Constantan wires. The wires used were 36 SWG, 34 SWG, 26 SWG and 22 SWG.
Results: showing the area and 1/area.
SWG Diameter(mm) Radius(mm) Area(mm ) 1/Area(mm )
