Resistance is a measure of how hard it is for charge to flow through something. If the resistance is high then a lot of energy is used up getting the current through. The resistance of a conductor is defined as the ratio of the potential difference across it, to the current flowing through it. A resistor does not stop current from flowing; it just slows down the rate at which it flows.
Charge Flow and Resistance are linked which shows how if current decreases resistance will increase. We know that:
I = Q and R = V
T I
Though there are many factors which affect resistance, including:-
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Length – if we increase the length of the wire, the resistance increases. This means that a longer piece of wire has more resistance than a short one. This is because in one second the electrons could get through a short wire, but if we double the length of the wire it will take 2 seconds instead. This is because there are more atoms and ions in the way so the electrons are slowed down because it is twice as long. So the equation I = Q/t will be halved.
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Temperature – As the temperature rises the resistance goes up as well. This means that in metals, a hot wire has more resistance than a cold one. When a metal gets hot the ions begin to vibrate because they have so much energy. As the temperature is increased the atoms get more energy and vibrate more and so it is harder for the electrons to move through.
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Cross sectional area (the thickness of the wire) – If we increase the thickness we decrease the resistance. Therefore a thin wire has more resistance than a thick one. As the width increases so does the electron number within a fluid time, so that means that there is twice as many electrons when the wire is twice as thick, so the current doubles.
- So the best type of wire to use to affect the resistance would be
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Long in length.
- High in temperature.
- Thin in its thickness.
We have chosen to investigate how the length of a piece of wire affects the resistance of a piece of wire. We have chosen to use this factor rather then one of the others because we are more likely to get accurate and successful results because we have more control over how we measure and gain our results.
Prediction
From an earlier experiment we found that the total resistance (R) of a series circuit is equal to the sum of the separate resistance (R1, R2).
R = R1 + R2 where R equals total resistance of the circuit
R1 = 4.7 ohms
R2 = 10 ohms
A = 0.14A
V = 2.21v
As we are using Constantan wire as a resistor when we increase the length of the wire the resistance should work how resistors in series work. This means that when we increase the length of wire (or add a piece in a series circuit) the resistance should increase too. Due to the increase in the number of atoms and ions between the two terminals it takes the electrons longer to get from one side to the other. For example if we double the length of the wire the resistance will double and the current will halve. Our graph at the end should look something like this:
Length
Resistance
The length and resistance should be directly proportional to each other. So the graph will be diagonal through the origin.
Pre-test
We have done a pretest so that we can decide which thickness of wire to use, and what the highest current we will use will be. From an earlier experiment we know that the thicker the wire is the less likely it is to affect the resistance, therefore it will be ideal to use a thick wire instead of a thin one in our experiment. Therefore we have chosen to use a wire that measures 24 SWG to find out our results. We also have to decide what the highest current we will use will be; we have also done an experiment before for this. It shows that the current (I) is proportional to the voltage (v), this is ohms law. Ohms law is when the current flowing through a metal wire is proportional to the potential difference across it (providing the temperature remains constant.) This is shown by these results from an earlier experiment. Where the resistance is calculated using the formula R = V/I. We found during this experiment that the temperature increased, therefore the resistance was affected. So we now know that the 4.5 D.C is too high for us to use.
Method
- Decide the cross sectional area that you are going to use (24 SWG) and material. Gather equipment including power pack, constantan wire, leads, voltmeter and ammeter.
- Lay constantan wire across a metre ruler from 0cm to 100cm (I am going to work with centimetres, cm, to measure the length. This is because I can be accurate to the nearest millimetre and make sure that the test is fair. The use of mm will also make my work more precise and accurate.)
- Set selected voltage and make sure that the ammeter is set to 10A and the voltmeter on 20V. Now to measure the voltage from 0-10cm for example we connect one of the leads from the voltmeter at 0cm with a crocodile clip and the other at 10cm with a crocodile clip.
- Now we will get a reading at both the ammeter and the voltmeter so we can see what has affected the resistance of the wire if anything. We will repeat 4 times for each length of wire and find the average.
- The readings will be taken at 10cm intervals of 0-10cm, 10-20cm, 30-40cm etc. This will be helpful because we will be able to see just how the length affects the resistance. E.g. if it doubles or triples how does the resistance differ.
Therefore we will have a clear table showing how the length has affected the resistance; we will calculate this using Ohms law (working out the resistance using the formula R = V/I) and drawing a graph. To make sure our experiment is accurate we will be careful when making sure that the leads are connected up at the correct points and that nothing is around it that could affect the results in any way. We will also make it safe by turning the power pack off after taking down each result so that the wire does not get too hot which will also mean that our results will remain accurate. I will make it a fair test by keeping all the variables except the one I am investigating the same. This means that both the material (Constantan) and the cross sectional area (24 SWG). We will also aim to keep the temperature of the wire the same, and to check this we shall plot a current-voltage graph, which if diagonal through the origin shows us that the temperature has not had an effect.
Obtaining Evidence
Results
The following tables show the results of our two experiments.
Analysing and Considering Evidence
Our experiment was very successful and the results we got proved to be quite accurate and precise. Therefore our graphs and result tables provide me with a base to understand just why length affects the resistance. My prediction was that “when we increase the length of wire the resistance should increase too”; my prediction is supported by my results and appears to be correct. At a length of 10 cm (on a 4v D.C) the resistance was at 0.21 ohms however when we tested it at 20 cm we found that the resistance was 0.40 ohms. These results show us that the relationship between resistance and length is almost certainly proportional, and this is supported by graph 2. At 3v D.C a 20cm length of wire has a resistance of 0.40 ohms, a length of wire 40cm long had a resistance of 0.84 ohms, and again we can see just how resistance and length are proportional. The reason that these two factors are proportional is because resistance is caused when electrons find it difficult to get passed the particles within the conductor. The longer the conductor is the more particles there are in the way and so the harder the electrons find it to flow. Resistance is also linked to charge flow, if we change the charge flow it will have an affect on the equation I = Q/t. If the current is changed then this will have an affect on the resistance. So with the help of the formulae I = Q / t and R = V / I we now know that if we increase the charge flow, the current increases and the resistance decreases. Consequently if we double the length of wire the equation I = Q / t will be halved (due to the time increasing) causing the current to be halved and the resistance to be doubled. Therefore my prediction was correct and my results clearly show that the relationship between resistance and length is proportional.
Evaluation
Using my results and my graphs I can clearly tell that my experiment was successful, I can tell this because none of my results have any inconsistent results and my graphs show straight lines which go through the origin. Even after repeating my experiment many times my graphs still remained just as precise and the graph showing the average results of the experiment is a perfect straight line. The fact that I got the similar results each time I did the experiment suggests that is was successful and also reliable, therefore I must have conducted the experiment well. The only anomalous results that I did find while doing the experiments was within my pretest, however this result was probably due to the high voltage not being suitable. This selected result had a much higher current than it should have had, due to the voltage; therefore we chose to use a lower voltage. The way in which we conducted the experiment was good because we made sure that the voltage supplied to the wire was equal each time, the SWG of the wire remained the same, and also that the wire cooled down between each result. The use of mm instead of cm made sure that the length was exact and not longer or shorter. Therefore our results were successful and reliable for us to work from. However this did not mean that the way in which we did the experiment couldn’t have been improved. Having to secure the wire so as to measure the length meant that it was difficult to attach the crocodile clips to exactly the end of the wire. We could not be sure that as we left the wire to cool it was not at a different temperature each time we begun again; this could have affected our results if it had been vastly different.
In our experiment we could have investigated a number of other things, such as the effect of cross sectional area or temperature on the resistance. If we had looked at the affect that the cross sectional area had on resistance we would probably find that as the wire doubled in cross sectional area the resistance would halve. This would be due to there being twice as many electrons so the current would travel a lot quicker and so decrease the resistance. If we looked at how temperature affected resistance we would probably find that as the temperature of the wire increases, the particles within begin to vibrate because they have so much energy, therefore it is much harder for the electrons to move through and so the resistance will rise. So instead of just investigating how length affected the resistance of a piece of wire we could also have investigated the affect of temperature or cross sectional area on the piece of wire.
