In my investigation I am going to look at two different variables- the length of a wire and the cross sectional area of a wire.
Firstly I am going to investigate the length I will measure and record the resistance, it will be the dependant variable. The independent variable will be the length and the temperature, material and cross sectional are will all be controlled variables. To control the temperature of the wire we will use a long piece of wire so it doesn’t overheat and affect the resistance, and we will also remove the key in the apparatus after each reading. I f we did not do this the experiment would not be reliable because there was more than one in input variable.
I am going to measure the resistance by calculating the gradient of the graphs of voltage against current. In the first experiment of the length, I will put in different lengths of wire ranging from 0.5m to 1.5m and record the voltage and current using a special programme for the computer. I would record 3 sets of data for each length and take an average. I would use roughly 5 or 6 different lengths. This also means that accuracy is not a problem as the computer will not misread information.
If I were to complete the experiment for length I would be able to predict the following: if the length increases then the resistance will also increase in proportion to the length. I think this because the longer the wire the more atoms and so the more likely the electrons are going to collide with the atoms. So if the length is doubled the resistance should double. If I where to draw a graph of this, resistance against length, the graph would show that the length is proportional to the resistance, as it would be a straight line graph through the origin.
Also I know that the resistance in the circuit is the sum of all the resistances, these could be length of wire in this experiment.
Method
1) Setup apparatus which consists of:
Computer
Interface
6 different lengths of wire
Ammeter
Voltmeter
Crocodile clips
Philip Harris data logging programme.
As shown:
2) Choose program to measure the resistance- Philip Harris Data logging program.
3) Carry out a battery test and select the Ammeter and Voltmeter on channels 1 and 2.
4) Adjust current to 0.1 of an amp and add in a wire of length 0.5m to start. Set up ammeter to 0-1Amp max.
5) Press spacebar to measure current and voltage on the screen.
6) Take out the key and increase the voltage after putting key back in.
7) Repeat the above steps increasing the voltage a little higher each time.
8) Then change wire and repeat procedure for each different length of wire.
9) Plot graph of voltage against current.
10) Measure gradient of the line using the programme which is the resistance.
I have also included a page showing details of how to setup and use the Data logging program on the computer.
Safety
Remember lab rules and make sure that all bags are out of the way.
Keep a small current so the there is no overheating. Also wear goggles over eyes in case the wire should recoil. Also make sure that the wire is not wound up during the experiment as it may short current out a bit of the length so the readings may not be exact.
Results
When I get the results I would draw out a good results table and print out all of the graphs of voltage against current and get the computers accurate measurement of the gradient hence resistance.
Obtaining Evidence.
For this section I would include my results table.
Interpreting and Evaluating.
I could best represent my results on graph of resistance against length and in a results table.
From the graph I would be able to see a clear straight line through the origin. Showing that my prediction was true and that the resistance is directly proportional to the length of the wire.
From this I can add the equation
R=kL
This equation also fits in with
R=(PL)/A
This suggests that the constant (K) is the Resistivity (P)
I think that this was the best way of doing this experiment because if we had of done it manually we could have made mistakes very easily for example reading the results wrongly. It would have also taken far longer. You could also have made a mistake drawing the graph or calculating the gradient wrongly and its also hard to know where to draw the line of best fit.
The way we did the investigation using the computer eliminated many of these problems. Although there is still a chance of making a mistake.
However the computer method is very accurate.
If I were to do the experiment again I would use more wires. In this experiment I would use more than 6 to get a clearer result. I would also use longer lengths of wires and increase the range of lengths for example 0.5m up to 3m.
I could also take more values of voltage and current which may perhaps add more values to the graph making it even more accurate and hence the gradient i.e. the resistance.
From doing this experiment I am confident that the graph you would plot had you done the experiment correctly would prove that the resistance is proportional to the length.
If the cross sectional area of the wire 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 fewer collisions.
I will now go on to explain and carry out the investigation for the variable cross sectional area. The plan for this experiment is similar to the plan for the length but is different in some parts.
To carry out an investigation dealing with resistance and electricity, we firstly need to know about what resistance is. The resistance is the opposition of a conductor to current. It occurs when electrons travelling along the wire collide with the ions in the wire. It could also be described as a measure of how hard it is to move the electrons/ions through a wire.
The current is the rate of the flow of charge and the voltage is the energy transferred per unit charge.
To measure the resistance you need to know the current flowing through a circuit and also the voltage. These can be measured by using an ammeter for current and a voltmeter for voltage.
The relationship between voltage, current and resistance is known as Ohms law. Resistance is measured in Ohms.
Ohms law states that the current through a metallic conductor is directly proportional to the voltage across it providing its temperature and physical conditions remain the same.
The equation connecting resistance to voltage and current is V=IR, where V is voltage, I is current and R is resistance. Conductors intended to have resistance is just the sum of all the resistances.
In a parallel circuit the total resistance is always less than the branch with the smallest resistance. The equation for this is R=R1+R2+R3.
Another equation which is also useful is the equation for Resistivity. This is:
Resistance also depends on temperature, because if the wire is heated up the ions in the wire will start to vibrate because of their energy increase. 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.
In planning for this experiment I came across yet another equation which may be useful. This is the equation for Drift Velocity:
I=nAeV
Where:
n= number of electrons per m3
A=cross sectional area
E=charge on the electron (-1.6×10-19)
V=drift velocity.
I also know that as the drift velocity decreases the current decreases and so the resistance decreases. This happens with a longer wire.
For this experiment the independent variable is the CSA (cross sectional area). The dependant variable is the resistance and the controlled variables are the temperature, material and the length.
My prediction for this is that as the area increases the resistance will decrease. Therefore I predict that the resistance will be inversely proportional to the CSA. The reason for my prediction is that the total resistance of the resistors in parallel is always less than the resistor with the smallest resistance.
I would also predict that as you would double the area the resistance will decrease by ½.
I would plot my results on a graph of Resistance against are which would show that the relationship between them would be inversely proportional and I would also plot another graph of resistance against 1/CSA, which would be directly proportional proving that the relationship between CSA and resistance is inversely proportional.
I will carry out this experiment by getting 6 different thicknesses of wire, each with a different diameter and from this I would work out the CSA. To work out the cross sectional area I would firstly use a Micrometer screw gage to get the diameter. To get the CSA I will use the formula πd2
4
I would measure the diameter at roughly 6 points along the wire to make sure that the wire was not elliptical but circular. I would take an average and work the CSA out from that average.
I will use a range of thicknesses from 18 to 36 SWG.
Method.
The method for the CSA experiment is very similar to the experiment for the length of wire and includes the same apparatus as below:
1) Setup apparatus which consists of:
Computer
Interface
6 different lengths of wire
Ammeter
Voltmeter
Crocodile clips
Philip Harris data logging programme.
As shown:
2) Choose program to measure the resistance- Philip Harris Data logging program.
3) Carry out a battery test and select the Ammeter and Voltmeter on channels 1 and 2.
4) Adjust current to 0.1 of an amp and add in a wire of diameter 18 SWG to start. Set up ammeter to 0-1Amp max.
5) Press spacebar to measure current and voltage on the screen.
6) Take out the key and increase the voltage after putting key back in.
7) Repeat the above steps increasing the voltage a little higher each time.
8) Then change wire and repeat procedure for each different thickness of wire.
9) Plot graph of voltage against current for the 6 wires.
10) Measure gradient of the line using the programme which is the resistance.
Again refer to sheet on setup of data logging program on computer.
Safety.
Again the safety aspects of this experiment are the same as before.
Remember lab rules and make sure that all bags are out of the way.
Keep a small current so the there is no overheating. Also wear goggles over eyes in case the wire should recoil. Also make sure that the wire is not wound up during the experiment as it may short current out a bit of the length so the readings may not be exact.
Results
When I get the results I would draw out a good results table and print out all of the graphs of voltage against current and get the computers accurate measurement of the gradient hence resistance. I would also plot the graphs of resistance against area and resistance against 1/CSA.
Obtaining evidence.
Here is a table of my results:
Interpreting and Evaluating.
For CSA the way that I can represent my results best is by using the graphs that the program on the computer recorded. From the graphs you can see that each of the graphs includes detail of the resistance the voltage and the current. It also includes a table of results for each wire. The graphs are numbered for wires 1-6. The gradient of each graph represents the resistance.
I have also plotted graphs of resistance against area and resistance against 1/area.
From these graphs it is clear to see the pattern of resistance is inversely proportional to the CSA, as the graph of resistance against area is a curve. But the resistance is proportional to 1/area, as the graph of resistance against 1/area is a straight line graph.
I can now also say that the conclusion shown by these graphs fits in with my prediction. The points are also close to the best fit line showing how it is a strong relationship.
To explain what happened we firstly need to have the definition of resistance. It is “the property of any object or substance to resist or oppose the flow of electrical current.”
The object in this case is the wires and it has different factors which make it more or less resistant. In this case we were investigating how the CSA affected the wire. From my graph I can see that as the CSA decreases the resistance increases. This is because the electrons in the current travel down the wire the hit off the atoms in the wire so it takes them longer to go down the wire therefore increasing the resistance. Also each time an electron hits an atom it loses energy therefore increasing the resistance further as it takes a longer time to get down the wire.
In a wire with a larger area the electrons will not lose as much energy as they have a larger space to travel through and less resistance as a result of not hitting as many particles. I can also say that the theory that the sum of resistors in parallel is always less that the resistor with the smallest resistance can also be applied here.
I can also see from my results that as the area doubles the resistance decreases by roughly ½.
As the Resistance is inversely proportional to the Area:
R 1/A
R=k×1/A
K=PL
As the length is always 1m:
K=P
So again the constant is the Resistivity.
We can go on to form an equation for Resistance:
Resistance=area × 1/K
I can also determine the resistance from the graph of resistance against 1/area.
Resistance =Resistivity x length
CSA
Resistance = Resistivity x length x 1/CSA
The length is constant; 1m
Therefore the gradient of the line = y2-y1 4.3-2.1 x 10-5
X2-x1 81-37.7
Also Ώm2 = Ώm
M2
The resistance is 5x 10-7m.
I think that this was the best way of doing this experiment because if we had of done it manually we could have made mistakes very easily for example reading the results wrongly. It would have also taken far longer. You could also have made a mistake drawing the graph or calculating the gradient wrongly and it’s also hard to know where to draw the line of best fit.
The way we did the investigation using the computer eliminated many of these problems. Although there is still a chance of making a mistake.
However the computer method is very accurate.
If I were to do the experiment again I would use more wires. In this experiment I would use more than 6 to get a clearer result. I would also use thicker or thinner wires and increase the range of SWG of the wires.
I could also take more values of voltage and current which may perhaps add more values to the graph making it even more accurate and hence the gradient i.e. the resistance.
From doing this experiment I am confident that the graph you would plot had you done the experiment correctly would prove that the resistance is inversely proportional to the CSA.