Errors in the Experiment
- If the temperature of the wires or room rises there will be a greater resistance as the atoms in the wire will be moving making the electrons need more energy to move along the wire. To minimise this error I will conduct all the readings on the same day to prevent room temperature rises and will switch off the circuit to stop the wires heating up.
- The placing of the crocodile clips is exactly on the mark to prevent less or extra length of wire being used which would directly increase or decrease the resistance. I will solve this problem by using a ruler with clearly identifiable markings and placing the wire on the rule above the scale.
- Faulty connectors and wires would lower the current flowing through the wire I will eliminate this by performing a preliminary experiment so I will be able to check if there’s a lower current than predicted.
- Twisted wire that would increase the length of wire, stretching the wire along the ruler will solve this.
Preliminary Experiment
I am going to conduct a preliminary experiment to find out which diameter of nickel chromium wire was optimum to tests its resistivity. The choice of diameters I have are; 0.30, 0.45 and 0.55mm. I performed the experiment using the same apparatus listed above and in the same set-up.
I am going to use the 0.45 mm wire as the resistance is a integral number so will be easier to calculate with to find the resistivity of the wire. I also wanted to do this experiment to familiarise myself further with the method; if I had any problems I could correct them there and then. This would mean I would obtain precise and reliable results in my main experiment when investigating the connection between the length of the wire and the resistance of the wire.
Safety
I am going to only use a voltage of 1.5 volts so the wire will not burn.
Be careful when the wire is connected, as it will get hot.
Be careful when cutting the wire.
Make sure the circuit is off when removing the wire from the circuit to be measured.
Justification of Procedures
Length of the wire: - At the beginning when I did a preliminary experiment I was using crocodile clips instead jockey keys to connect the wire to the circuit. Although the crocodile clips made it easier for me to measure the length of the wire I found it very difficult to keep the wires in these clips since it kept slipping out so the wire wouldn’t get connected successfully to the circuit. I therefore decided to use jockey keys because these keys made it easier for the wire to be measured accurately using a meter ruler. I decided to chose 8 different lengths between 30-100cm because these lengths will give me accurate results and that 8 readings are sufficient enough for me to plot a straight line graph and draw a good line of best fit through the points. Micrometer screw-gauge: - I decided to measure the diameter of the wire at 3 different positions on the wire. I then calculated the average diameter from the 3 measurements taken to enable me to measure the diameter of the wire as accurately as possible. Switch:- I have decided to use a switch in the circuit to prevent the wire from overheating by breaking the circuit once a result has been obtained. If the wires’ temperature increases the resistance will increase also, causing me to gain an anomalous result.
Justification
I am going to conduct the experiment in this way to get a resistance (R), value across a length of nickel chromium wire. This R value along with the length (L) will allow me to plot a graph of R= P L Resistivity (P) Area (A)
A
Y=m x +c making the gradient P allowing me to find P as I know the values of R, L, and A.
A
Results
Results of testing the diameter of Nickel Chromium
The average diameter of the nickel chromium found by using a micrometer is 0.455 or 0.46 mm to two decimal places. I will use 0.46 mm in the equation Area = π (D x 10 ³)² 2
Conclusion/calculations
Resistivity formula R=PL
A
Formula found from graph R= P L +0
A
Y= m x +c
Gradient = Y = 5.8 = 6.9 Ω/m
X 0.85
Area = π (0.46 x 10 ³)² Area = 1.66 x 10
2
P = Gradient P= Gradient x Area
A P= 6.9 x 1.66 x 10
P= 1.14 x 10
P= 114 x 10 Ω m
From my graph on the previous page, I can see that the resistance of the wire is directly proportional to the length of the wire. I know this because the Line of Best Fit is a straight line through the origin showing that if the length of the wire is increased then the resistance of the wire will also increase in proportion to each other. The line of best fit is a straight and it goes though (0,0) if there is no length, there is no resistance proving that the resistance of the wire is directly proportional to the length of the wire.
The length of the wire affects the resistance of the wire because the number of atoms in the wire increases or decreases as the length of the wire increases or decreases in proportion.
The resistance of a wire depends on the number of collisions the electrons have with the atoms of the material, so if there is a larger number of atoms there will be a larger number of collisions that will increase the resistance of the wire. If a length of a wire contains a certain number of atoms when that length is increased, the number of atoms will also increase.
If the wire is half the length of a certain wire, it would have has half the number of atoms, this means that the electrons will collide with the atoms half the amount of times. In addition, if the length of the wire was trebled or quadrupled, then the resistance would also treble or quadruple. This is indicated on my graph, with the length being 100cm and the resistance being 6.83 Ohms. This in theory would mean that at 50cm there would be a resistance of 3.45 Ohms. From the graph it is easy to tell that the theory is correct and therefore my results reliable. From my results table and graph, I can see that my results that I collected are very reliable and accurate as all the points lie exactly on the straight line.
Evaluation
My results are very reliable as they all lye on the best fit line so I can confirm my prediction and support a conclusion. I know this because outside resources (Textbooks and Britannica) say that ‘the length increases in direct proportion to the resistance.´
Possible errors
- The wire had actually increased in temperature due to a change in room temperature or the circuit had been left on for long periods of time. I tried to reduce the temperature increase, if any, by switching off the circuit as soon as possible once I had obtained a result.
- The wire I used was taken off a reel of nickel chromium wire so was new with no twists or kinks and could be very taught once taped on the ruler. During the placing of the wire on the ruler a few bends had been made in the wire, these would be straightened easily and only added a negligible increase in length.
- Placing the jockey keys on the exact length of wire being tested was difficult because the ends of the keys had a very small area. They often slipped down the wire so the wire I tested was actually a few millimetres longer/shorter this meant I needed to repeat the test once I’d noticed this change in length.
- The apparatus I used might have been faulty due to loose connections but I would have noticed the discrepancy in results when I conducted my preliminary experiment as I used the same apparatus.
Percentage Errors
All experiments conducted have a certain error on them, as not all apparatus is 100% accurate. The apparatus I used has a certain percentage error found by using the equation:
Percentage Error = Sensitivity x 100
Reading
Error = 0.10 x 100
30
= 0.33%
Error = 0.01 x 100
0.46
= 2.17% in millimetres
= 8.69 % as the cross sectional area is squared
Error = 0.01 x 100
0.18
= 5.56%
Error = 0.01 x 100
1.23
= 0.81 %
Total error = 15.39%
The most sensitive measurement was the reading on the micrometer as it could be + 8.69% due to the squaring of the cross sectional area. This means that my average diameter could be + 8.69%.
Numerical Error = Diameter x 8.69 = 0.04 mm
100
The resistivity of nickel chromium that I found using the equation R = PL has a total error of 15.39 % so the resistivity could actually be a different value. A
The error in numerical value has a + 175 x10 Ω/m. Found by Error = Resistivity x 15.39
100
I had no systematic errors as my best fit line found on my graph runs through the origin (0,0). Random errors are:
- I found that the experiment was quite easy to set up, as it was simple and uncomplicated. The only problem I can see is the calculations once all the results have been obtained as very small numbers are used and a simple mistake can lead to a wrong answer being produced.
- Temperature increase
- Battery running out (current reduced)
- Faulty apparatus
I had no anomalous results as all the points lye exactly on the bast fit line. This proves I conducted the experiment very well making sure all the apparatus I used was working and of good quality. I also made sure all my tests were done fairly by keeping all the variables constant except the length of wire and I tried to do the experiment to the best of my ability. I also gained a good set of results by testing the lengths from 100-30 cm then 30-100 cm so using the average would solve any difference in voltage results. I found no need to repeat any lengths as my first and second set of results were very close to each other. I wanted to repeat the experiment for a third time to make sure there were no anomalous points that may have been found twice.
If I were to conduct the experiment again I wouldn’t change the way I performed it at all because my results were so accurate. If I were to perform the experiment again I would choose a different variable such as:
I think that if the wire diameter 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 less collisions. I would also test to see if diameter if also directly proportional to resistance.
I think that the type of material of the wire will affect the amount of free electrons, which are able to flow through that wire. This is because the number of electrons depends on the amount of electrons in the outer energy shell of the atoms, so if there are more or larger atoms then there must be more electrons available. If the material has a high number of atoms there will be high numbers of electrons causing a lower resistance because of the increase in the number of electrons. Also if the atoms in the material are closely packed then the electrons will have more frequent collisions and the resistance will increase.
