I intend to choose one variable to investigate thoroughly, but I will briefly examine the other variables, giving quantitative predictions of resistance in proportion to that variable.
Length:
Quantitative prediction: - double the length would double the resistance.
The longer the wire the more atoms there are therefore the more chance of a collision, thus increasing resistance.
Temperature:
Quantitative Prediction: - Usually the higher the temperature the greater the resistance. The greater the temperature, the more energy the atoms gain therefore the more vibration there is. Because there is more movement the atoms cover a larger area, which increases the chance of a collision consequently increasing the resistance.
In lab conditions it would be extremely difficult to maintain a constant temperature through the whole wire. Also because resistance produces heat it would be impossible to keep the temperature that you are testing constant. Therefore it would not be practical to examine. If the resistance increases over a critical value then heat is produced. We must therefore keep the voltage low otherwise the temperature change will make the test unfair.
Material:
The variable, ‘material’ is not one variable but several. Different materials have different atomic structures which would affect the resistance it includes what the material is made up of, the state of the material, whether oxidation has occurred or whether there are kinks in the wire. Because there are so many variations it would be impossible to give a set quantitative prediction. Because there are so many variations it would not be practical to examine.
Diameter [and prediction]:
Quantitative prediction: - The larger the diameter the smaller the resistance.
In my investigation I intend to examine the variable diameter in more detail.
Hypothesis: I believe that diameter will affect the resistance much the same as length. The larger the diameter, the more atoms there are which would increase the probability of collisions occurring therefore more resistance.
As the diameter increases the resistance decreases. If we decrease the diameter then we decrease the free space that free electrons can pass without colliding. The resistance is therefore inversely proportional to the cross sectional are of the wire:
Resistance ~ 1/cross sectional area of the wire
Resistance ~ 1/ diameter 2
Procedure:
Apparatus:
- Simple circuit including:
- D.C. power supply
- Normal Wires [not to be tested]
- Crocodile clips
- Cell
- Switch
- 8 measurements of wire with varying diameters
- Micrometer screw gauge [an accurate measuring device used to measure a variety of things.]
Circuit Diagram:
= Wire being tested
A simple series circuit with an ammeter in series to the wire being tested.
Method:
To begin my investigation I will first prepare the wire. I shall take 8 samples of wire, each of the same material and the same length which will be 1m. Using a micrometer screw gauge I will measure the diameter of each wire. I will take three readings on each wire, at different place, if there is a difference then I shall be able to calculate an average, ensuring accurate results. I will record the measurements. I shall then connect the wire, using crocodile clips, to the circuit. I will then turn the power on. The power will be set on 1V, keeping the temperature as constant as possible. I will record the current (in amps) passing through the wire at that time. I will repeat the experiment again, but this time I will use 1.5 V, and again record the current running through the wire. I will repeat the experiment once again, this time using 2 V.
I will repeat the same procedure 7 more times; each experiment will use a different diameter of wire.
Safety:
In order to perform a safe experiment I will ensure that the voltage will not exceed 3V to minimalism overheating. I will also be careful not to put the wire into my eye causing damage. I will make sure that there is no current running though the circuit during times when the current is not being observed.
Results.
In order to find the resistance, in relation to the diameter I will have to take the following results for each wire tested:
- Diameter in mm. [I intend to take 3 samples for each wire in order to gain an average so that the result will be more accurate.]
- Amps; a recording for each different voltage setting.
- Resistance; 1 for every different voltage setting.
I will then work out the average resistance.
I intend to put the information into a table, and then into a graph forms.
I expect that the results will have a level of inaccuracy because:
- Human error; if I read or record the results wrong, or if I make errors in the calculations. To prevent this I will have to simple be careful in my observations and double check calculations. I believe that this is the greatest risk to my results, but if I am not careless it poses little risk
- Temperature of the wire. We know all ready that temperature is a variable that can affect the resistance. The wires temperature can be affected by the room temperature, if it is handled (conduction of body heat) and also because electricity causes heat, as the experiment requires heat it may change the temperature. To prevent this I will try to keep the room temperature constant and handle the wire as little as possible, also I will keep the voltage below 2V, and this will make sure that any temperature is minimal and insignificant. I believe that this will not affect my results in any big way
- Condition of the wire; if the wire has corroded in any way, or oxidised, and id the constancy of the wire is equal in all samples. To prevent this I will take a new wire, from a reliable source and use the same material. I do not believe that this will affect my results in any significant way.
Results:
To aid my analysis of these results I will create some graphs, most importantly I will create the graph of diameter by resistance.
Analyses:
[Graph showing resistance by diameter]
This graph will show the average resistance of the wires by the size of the diameter of the wire. The graph that I drew sowed a curved line, beginning from the bottom left (the origin) and curving steeply up towards the right, and the gradient becomes less steep until it becomes almost horizontal.
It shows me that as the diameter increases the resistance decreases. As the wire increases in diameter the resistance drops, until a certain point where the resistance is not affected in any significant way (The horizontal part). This tells me that I used the right thicknesses of wire for my experiment, any thicker and It would not really have affected my results.
In my prediction I stated that as the diameter increases the resistance decreases. I have now proved that theory to be correct, as clearly seen in my results and graphs.
[Graph showing resistance against 1/diameter 2]
This graph will hopefully show that the resistance of a wire is directly proportional to 1/diameter2 . The points gave me an opportunity to draw a fairly straight line, therefore I drew a line of best fit.
The graph showed me that that the average resistance is inversely proportional to diametre2 . I stated in my prediction that resistance would be inversely proportional to 1/diameter2 and I find this theory to be correct.
