Scientific Explanation
A metal wire is made up of millions of metal atoms and each atom has one or two electrons, which are loosely held. As the electrons are negatively charged, if one is lost from an atom the atom becomes positive and is then called an ion. The wire is made up of positive ions surrounded by ‘free’ negative electrons. The ions vibrate around their fixed positions and the electrons move randomly in the wire. When a battery is attached to the wire the free electrons are repelled by the negative terminal and attracted to the positive one so the all move in the same direction towards the positive terminal. These moving electrons are the electric current. But the electrons collide with the vibrating ions and his makes it more difficult for them to get past and they are slowed down. These collisions are what cause the resistance. Using this explanation I predict that doubling the length of the wire doubles the amount of ions that the electrons must pass, doubling the number of collisions, therefore doubling the resistance for the electrons.
2 x length = 2 x ions = 2 x resistance
Preliminary Work.
Results table
For my preliminary work I will not be using any length of copper wire because its resistance is to low to be measured precisely and it is too like the wires used within the circuit. I have also decided not to use 24 SWG constantan because the resistance is too low to be measured accurately, unless I use the longer lengths. The longer length would cause problems in accuracy because the wire twists, making it difficult to measure the length accurately. The 32 SWG constantan would be good to use for my investigation because it has a good range of resistances within a length of 1m and they are large enough to be measured with precision. I will use lengths of 25 cm, 40 cm, 55 cm, 70 cm, 85 cm and 100 cm. I will use this range of 5cm steps because I think that it will give better-spaced results. I am not going to use lengths lower than 25 cm the resistance would be too low to measure accurately and I will not use lengths longer than 100 cm because the twists in difficulty in handling could cause problems in accuracy when measuring the lengths against the metre rule.
Main Investigation
Diagram
Method
The apparatus will be set up as shown in the diagram. The wire will be secured to a meter rule with adhesive tape, with a crocodile clip fixed at the zero end (‘A’) of the metre rule and another crocodile clip movable to the length of wire being measured at the time (‘B’) as shown. The length of the metal wire will be measured as shown on the diagram from the inside edge of the crocodile clips as read against the meter rule. I can adjust the crocodile clip (‘B’) position so I can measure the resistance for 5 different lengths so I can plot a graph. For each length I will record the current from the ammeter and voltage from the voltmeter, I will then calculate the resistance using the following equation
CURRENT / VOLTAGE = RESISTANCE
I will measure the resistance for each length three times. I will do this by adjusting the current for each length by turning up the D.C. power supply to give three different current settings. I will not use any current higher than 0.40 amps because the current would heat the wire and thus would affect the resistance. I will not use a current lower than 0.20 amps because I want the chances of inaccuracy and error in reading to be as low as possible. This is because the smaller the current, the bigger the chances of error in the readings.
E.g.
0.01A in 0.20A = 1 in 20 chance of error
0.01A in 0.10A = 1 in 10 chance of error (too high)
For each pair of meter readings I will calculate the resistance. This will give me 3 resistances for each length. I will us the three values to calculate the average resistances. I will control the wire’s thickness and material by using just one wire from one reel throughout the experiment. I will control the temperature by staying in the same environment kept at a constant temperature throughout the experiment. I will keep the current low and switch off the power supply between readings to also ensure temperature is kept as constant as possible. If I were to not control the current, the wire may heat up and possibly burn myself or other surrounding materials.
Results Table
Analysis
My graph has a straight line through the origin so this tells me the resistance is directly proportional to the length. My prediction was correct as the graph shows an increase in length does increase the resistance. My mathematical prediction was correct because doubling the length doubles resistance. I can use values from my graph to show this.
- When the length is 25cm the resistance is 2.1 Ohms
- When the length is doubled to 50cm the resistance is also doubled to 4.2 Ohms
Scientific Knowledge
I have found that by increasing the length of the wire I am increasing the number of ions along the length therefore increasing the number of collisions the moving electrons have to encounter. I now know that doubling the length of the wire doubles the amount of ions vibrating around their fixed positions that the electrons must pass. This doubles the collisions between the moving electrons and the ions thus doubling the resistance. This formula I predicted is correct.
2 x length = 2 x ions = 2 x resistance
Evaluation
I believe my results are accurate because all 5 points on my graph are close to the line of best fit. I have no anomalous results because I controlled all the variables well and ensured lengths were as accurate as possible.
Reliability
For each length the three resistance results are close together therefore I think my results are reliable. I can work out the percentage variation using this equation.
% Variation = largest value – smallest value X 100%
Average value
For all 5 lengths my percentage variations are below 10 percent. And in fact all but one are below 5%. My results are reliable.
Validity
My conclusion is really only valid for the lengths tested, material used and SWG value used. However, if I were to repeat this investigation using different lengths I am confident the line of best fit would pass through the origin on a straight-line graph as shown. I believe that the conclusion would apply to both shorter and longer lengths because my results are so good.
Comment on Method
My method has proved suitable but it could be improved. I could have also controlled the temperature better by using smaller current. However this would require a more sensitive Voltmeter and Ammeter to ensure precise readings. I would need a meter that read to 0.001A and 0.001V. Another way of improving my method is by ensuring the wire had a constant diameter along the whole length of the wire. I could do this by checking at various points of the wire with a micrometer that measures to 0.01 mm. In order to ensure the correct lengths of wire were maintained throughout the experiment I could have used smaller crocodile clips that would have a much tighter hold on the wire to prevent any slipping altering the measured length.
Additional Work
In order to obtain extra evidence and support and further my conclusion I could measure the resistance of smaller lengths of 32 SWG constantan wire. However this would require a different technique in which I would have to measure the resistance directly, using a multimeter set on the Ohms scale. Alternatively I could measure the resistance of small lengths by adopting the circuit used previously. I could use a variable resistor in order to enable finer control of the current. This method would require more sensitive ammeters and voltmeters, as the readings would be smaller.
