My hypothesis regarding this investigation is that the longer the wire, the higher the resistance. This is because the longer the wire, the more collisions will take place, since the free electrons will have a greater distance to travel and will therefore collide more than in a short wire. More collisions will therefore mean more energy being converted into heat and therefore the resistance of the wire will increase.
Furthermore, I predict that the length is directly proportional to the resistance, since by doubling the length, the number of the collisions will also double and so will the amount of energy lost in collisions.
Graph showing voltage against current
Plan
1m length of 0.457mm Constantan wire (S.W.G. 26)
Metre ruler
Ammeter
Voltmeter
Crocodile clips
Low voltage unit
I shall first collect all the equipment and set up the apparatus as shown in the image below:
To begin my experiment, I shall fix 1m length of SWG 26 Constantan wire onto a metre ruler. I shall then use two crocodile clips to connect the low voltage unit to the ammeter and to the 5cm position on the wire. I shall then use two more crocodile clips to connect the voltmeter to the wire at the 0cm and the 5cm position.
To identify the best voltage for my investigation, a preliminary experiment was carried out and the following results were obtained:
After performing the preliminary experiments and studying the results, it was decided that 4V will be used in our actual experiment and that we will have a difference of 5cm between each length.
After setting up my experiment, I shall then turn on the power supply for the low voltage unit and switch on the ammeter and voltmeter. In order to maintain safety in the following experiment, a low voltage will be used so there will be minimal overheating and so the wire will not burst into flames.
After taking a reading of the voltmeter and ammeter, I shall then record the results in a table. I shall then turn off the power supply and move the crocodile clip from the 5cm to the 10cm position, repeating the procedure above. I shall therefore repeat the steps for each length, taking 10 readings, and shall therefore repeat the investigation two more times for accuracy.
Results Anomalies = *
I shall now plot the following results onto a graph and shall use the graph to analyse the results of my experiment.
Analysis
By studying the graph above it is obvious that my prediction was correct and that by increasing the length of the wire, the overall resistance would also increase. This is because resistance is caused by free electrons colliding with ions in the material and the energy provided by the applied voltage being converted into heat, which consequently decreases the electron’s speed and increases the resistance. Therefore when I increased the length of my wire, the number of atoms also increased. By increasing the number of atoms in a wire, the chance and the number of collisions between the free electrons and ions in the material also increased. These collisions cause electrical energy to be converted into heat which in result decreases the speed of the electrons and increases the resistance of the wire.
The graph shows a strong trend of a straight line and this therefore means that the length of the wire is directly proportional to the resistance. Hence when you double the length, the resistance also doubles. For example, when the wire is at a length of 5cm, the average resistance of it was 0.16 ohms. Whereas when the wire length is doubled to a length of 10cm, the average resistance also doubles to 0.32 ohms.
The relationship between the length and resistance of a wire can be expressed by the following formula:
Rl
Where R is the resistance of the wire and l is the length.
Evaluation
In my opinion the experiment was very successful. Studying the graph with the line of best fit, it is obvious that the results are accurate since they are all close to the line and there is nearly a perfect straight line. After studying the error graph it is evident that most of the recorded results have a high reliability because of the similarity between them. It is also evident that the results contain two anomalies which could have been caused by several factors: a misreading of the ammeter or voltmeter, using an incorrect length, not allowing the wire to cool down or using the incorrect voltage on the low voltage unit.
We repeated the experiment 3 times and therefore were able to average out the results to increase the reliability. We used a wide range of results ranging from 5cm to 50cm. If we were to use higher values in our investigation, then the pattern would have carried on since the length is directly proportional to the resistance.
In my initial experiment I failed to control some of the variables. Since we used crocodile clips, the length of the wire was not accurate and varied by several mms. As well as that, we did not let the wire cool down between measurements and this therefore meant that the temperature of the wire increased and so did the resistance of the wire.
To improve the overall accuracy and reliability of my experiment I would alter the method of the investigation. In order to control the temperature variable in the experiment, I would leave the wire to cool completely during measurements or would use several wires of the same material and width. To improve the accuracy of the measurement of the wire I would use clips smaller than a crocodile clip so therefore the length of the wire would be as accurate as possible. As well as that, since the voltmeter and ammeter only gave the readings to 2 decimal places, improve my accuracy I would use equipment that is more accurate and that gives the readings to more decimal places, such as a to computer.
In conclusion, the investigation has shown me that by increasing the length of the wire, the resistance also increases in direct proportion. To further extend my investigation, I could test another variable and investigate its affects on the resistance of a wire. For example, I could test the affect of the temperature or the cross-section area on the resistance of the wire and could find the formula that expresses their relationship.
