To investigate whether the surface area or the lengths of the carbon putty will affects its resistance
Aim: to investigate whether the surface area or the lengths of the carbon putty will affects its resistancePlanningI am investigating of whether the length or the surface area of the putty will have effect on its resistance.We know from the book of Ordinary Level Physics by A.F Abbott that the resistance of a conductor is affected by several factors:Surface area:Thick wires may be regarded as equivalent to a number of thinner wires of equal area joined in parallel. Doubling the area will therefore halve the resistanceThis means that the surface area is inversely proportional to its resistanceR Ą1ALengthDouble the length of the wire will double the resistance as twice the length of the wire is equivalent to two equal resistance in the series.R Ą lTemperatureThe resistance for a metallic conductor is a constant if the temperature and other physical properties remained constant. In general, for metallic wires, the higher the temperature, the larger its resistance. But for some materials e.g. carbon and semi conductors like silicon and germanium, the higher the temperature, the lower its resistance. The resistance of most of the alloys, e.g. manganin and constantan, is only affected slightly by a change in its temperature.I am investigating the affects of the length and of 1/cross section area (1/A) as both of this factor is connected to its physical effects. It is much harder to record the temperature of the conductor than to measure the surface area or the length of the carbon putty. And the experiments to investigate these factors should hopefully give a good straightforward result. I have chosen to do two, as I was afraid that if one of the experiments failed, I still have a back up data to use.From all of that information predicted that as I doubled the length of the carbon putty, the resistance of that conductor will also doubled and as I halve the cross section area of the conductor of the conductor, and therefore the resistance will be four times bigger.I have done a preliminary test using a similar method below but I have measured the current that goes across the conductor and then calculating the resistance from the data I have collected. In the preliminary experiment, I was trying to measure the current passing the carbon putty, as it is said that R = V and therefore we are Imeasuring the current by varying the length of the carbon putty. We were using a 3 Volts cell and an ammeter to measure the potential differences passing through the conductor putty.We set up the apparatus just as shown in the diagram below 3V cellWireConducting puttyCopper plates and crocodile clipsVoltmeter I did the experiment once
for each reading as I was going for pattern and not accuracy and in overall I took 5 reading as this to give a better picture of the result of this. In this experiment I keep the diameter to be constant at 2.2 cmLength of the carbon putty( cm ) Voltage ( Volts ) Potential difference ( amp ) Resistance =V/I14.5 3 0.18 16.512.5 3 0.19 15.211.5 3 0.20 14.910.5 3 0.25 11.89.5 3 0.27 10.88.5 3 0.31 9.47.5 3 0.38 7.7In this experiment we can see that the pattern is that as we decrease the length of the putty, ...
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for each reading as I was going for pattern and not accuracy and in overall I took 5 reading as this to give a better picture of the result of this. In this experiment I keep the diameter to be constant at 2.2 cmLength of the carbon putty( cm ) Voltage ( Volts ) Potential difference ( amp ) Resistance =V/I14.5 3 0.18 16.512.5 3 0.19 15.211.5 3 0.20 14.910.5 3 0.25 11.89.5 3 0.27 10.88.5 3 0.31 9.47.5 3 0.38 7.7In this experiment we can see that the pattern is that as we decrease the length of the putty, the bigger the potential difference which decreases the resistanceHowever, this process took more time to do as we have firstly to measure the current and then have to calculate the resistance, as we were also provided with ohm meter, I decided to measure the resistance directly. From the preliminary experiment above, I came up with the method below.Apparatus:Carbon putty2 x 5p coins2 x crocodile clips2 x wire2 x board1 x Multimeter1 x bread knifeMethod:To measure length: 1. Roll the carbon putty to the diameter wanted with 2 boards into a long sausage. Make sure that the diameter is uniform all along.The diagram below will show how the rolling of the carbon putty can be done.2 boardsCarbon putty2. Measure the diameter and record3. Cut the carbon putty into the length wanted. ( the diagram on the next page can show how I was cutting the carbon putty into the length I wanted using a bread knife )To measure the cross section area1. Roll the carbon putty to the fattest one you can, but make sure that the length is sufficient enough to be used in the experiment e.g. 8 cm2. Do the experiment and repeat3. Then roll the carbon putty to get a different cross section area, and then do the experiment.4. Repeat method 3 again.Method to do the experiment1. Place 2x two pence coins at each end of the carbon putty.2. Attach crocodile clips to the end of each 2 p coin 3. Attach these wires, which is connected to a multimeter to both the crocodile clips.4. Measure the resistance.5. Repeat the reading again.In the preliminary experiment, I was trying to measure the current passing the carbon putty, as it is said that R = V and therefore we are Imeasuring the current by varying the length of the carbon putty. We were using a 3 Volts cell and an ammeter to measure the potential differences passing through the conductor putty.We set up the apparatus just as shown in the diagram below 3V cellwireConducting puttyCopper plates and crocodile clipsVoltmeter I did the experiment once for each reading as I was going for pattern and not accuracy and in overall I took 5 reading as this to give a better picture of the result of this. In this experiment I keep the diameter to be constant at 2.2 cmLength of the carbon putty( cm ) Voltage ( Volts ) Potential difference ( amp ) Resistance =V/I14.5 3 0.18 16.512.5 3 0.19 15.211.5 3 0.20 14.910.5 3 0.25 11.89.5 3 0.27 10.88.5 3 0.31 9.47.5 3 0.38 7.7In this experiment we can see that the pattern is that as we decrease the length of the putty, the bigger the potential difference which decreases the resistanceHowever, this process took more time to do as we have firstly to measure the current and then have to calculate the resistance, as we were also provided with ohm meter, I decided to measure the resistance directly by setting up the apparatus as shown on the diagram below.Conducting putty2p coins and crocodile clipsWiresOhmmeterCollecting the dataIn collecting the data, we use plastic glove as this carbon putty is messy and afterwards it was a wise thing to do to wash our hands as this material is toxic if swallowed.In the experiment to investigate whether the length of the carbon putty, I was trying to keep these factors constant:1. The resistance of the wire2. The cross sectional area of the putty3. The temperature of the putty4. The amount of contact between the 2p coin and the puttyThe diameter of the carbon putty is kept constant to 2.5 cm and I started with 10 cm long carbon putty and try to get 5 readings with 1 cm intervalI repeated the reading five times as I in my preliminary experiment I keep getting a changing reading. By doing this I was able to eliminate anomalous result and take an average readingLength (cm) Reading 1( £[ ) Reading 2( £[ ) Reading 3( £[ ) Reading 4( £[ ) Reading 5( £[ ) Average( £[ )10 8.4 8.9 8.8 8.2 8.5 8.69 6.8 7.3 6.7 6.4 6.5 6.78 6 6.2 5.2 5.4 5.6 5.67 4.8 4.3 4.3 4.8 4.2 4.56 3.4 3.8 4.1 3.9 3.8 3.85 3.6 3.1 4 4.3 3.8 3.9In the experiment to investigate whether cross-section area has affect on the resistance of the carbon putty, I was trying to keep the factors below constant:1. The resistance of the wire2. The contact resistance between the 2p coin and the putty3. The length of the putty used4. The voltage across the puttyIn this experiment I keep the length constant to 8 cm, it was difficult to get the diameter I wanted with a constant interval, and therefore I was just trying to get 3 cm and 1.5 cm as this is the one I will use in my analysis Diameter( cm ) Reading 1 ( £[ ) Reading 2 ( £[ ) Reading 3( £[ ) Reading 4 ( £[ ) Reading 5 ( £[ ) Average( £[ )3 4.5 4.7 4.3 4.6 4.3 4.52.7 5.2 4.5 4.9 5.1 5.2 4.92.5 7.1 6.0 6.2 6.2 6.2 6.22.2 13.2 12.9 11.8 11.7 9.8 11.81.8 13.4 13.9 13.5 12.5 13.3 13.31.5 15.4 14 14.8 14.9 14.6 14.9To find out the cross section area from the diameter I was using this formula:Cross section area: ƒàr2For example: The diameter is 3 cmThe cross section area is therefore ƒà* 1.52 = 7.07Cross section area (cm2) I/ A( 1/cm2) Resistance Reading 1( £[ ) Resistance Reading 2 ( £[ ) Resistance Reading 3 ( £[ )Resistance Reading 4 ( £[ ) Resistance Reading 5 ( £[ ) Resistance Reading Average ( £[ )7.07 0.14 4.5 4.7 4.3 4.6 4.3 4.55.72 0.17 5.2 4.5 4.9 5.1 5.2 4.94.91 0.20 7.1 6.0 6.2 6.2 6.2 6.23.80 0.26 13.2 12.9 11.8 11.7 9.8 11.82.54 0.29 13.4 13.9 13.5 12.5 13.3 13.32.41 0.41 15.4 14 14.8 14.9 14.6 14.9The result that I think is anomalous is shaded.I took the reading up to one decimal place because to make it simple yet pretty accurate as we are only to see the pattern of this experiment AnalysisGraph 1 shows that the resistance of the conductor varies with different length of the conductor. It shows a positive correlation because the resistance increases as the length increases but the relationship is not a proportional one as the graph does not pass through the origin. My prediction that the resistance will doubled as we doubled the length of the carbon putty was right. In the table, we can see as we double the length we roughly have doubled the resistance. The graph and table give some example. When the length is doubled from 5 cm to 10 cm the resistance doubled from 3.9 ohm to 8.4 ohm.A reason for this can be seen from this diagram5 cm putty 5 cm puttyIf each 5cm long of carbon putty have a resistance of 3.9 ohm, therefore two 5 cm carbon putty put in series will have a resistance of roughly 7.8 ohm. In my experiment my result was 8.4 which was close enough and from this data we can see the pattern of this.Final conclusion for the length experiment.From this graph I can say that as we doubled the length of the conductor, we will also doubled the resistance. Therefore resistance changes is proportional to the length changes.Analysis for the cross section area experimentFrom my table I managed to produce graph 2 of my experiment to investigate whether the cross section area of the carbon putty will change the resistance of it. However, the result does not meet my prediction.The graph is in a concave curve, meaning that as the 1/a increased, the resistance increased but not proportionally, however it shows a positive correlation between them.I predicted that if I halve the cross section area, I would increase the previous resistance by 4 times. As we can see from the table that the resistance when the cross section is 5 cm2 which is 5/5.72 * 4.9 ohm = 4.3 ohm does not increased by 4 to 17.2 ohm or a reading near that. The resistance when the cross section area is 2.5 cm2 is 2.5/2.54 * 14.9 ohm = 14.6 ohm.However we can see that as we increased the cross section area, we decreased the 1/A , this have effect on how the resistance decreased as the cross section area increased and 1/a decreased. Graph 2 shows this clearly which was able to show a smooth curve graph.From the table we can see as we decreased the cross section area from 7.07 cm2 to 2.41 cm2, we increased 1/a from 0.4 to 0.41, which resulted on the increased of the resistance from 4.5 ohm to 14.9 ohm.R ƒÑ 1/A , this means as we increased the 1/A we also increased the resistance as this experiment has proven. EvaluationI think that my experiment went quite well, as I was able to produced a quite accurate data and produced a graph. I had some anomalous results because of some errors. However, my results supported my conclusions.The errors on this experiment is that the wire also had some resistance, and therefore the ohmmeter did not only measure the resistance of the carbon putty but also the resistance of the wire. The second biggest mistake is that the difficulty to put a uniform contact every time, this is quite difficult to do, but have the biggest effect. To reduce errors on this, I repeated the readings 5 times. The third one is that the 2p coin have some rust in them, this will affect the measurement of the resistance a way to solve this to rub the 2p coin with an emery board to use it. The carbon putty it self is a difficult medium to work with. It is malleable but hard, and once being taken out of its original form, it¡¦s difficult to shape them into the diameter and the length that I wanted without leaving any air gap.It was also difficult to make the diameter of the putty uniform all along, and as I cut the end of the putty with a bread knife, I also squashed the end, this might have some affect on this experiment. And improvements of cutting the length of the carbon putty can be done by using a cheese wire instead of a bread knife to cut the end. And we are able to use a core borer to make the diameter uniform or some metals rollers of different diameter under the base board so the diameter will be uniform and the putty can not be rolled thinner There are some limitations on this experiment as the carbon putty took so long to shaped and the experiment itself took long to do. As we also only have a specific amount of putty, we were not able to make an extra long carbon putty or to make an extra fat one.I would like to increase the range of my reading as my reading range is very small, and therefor I was only able to get a small view of the real graph, but If I was doing the experiment in a bigger range, I might have a better picture of the result. For further experiments I would like to measure the temperature of the room to see whether a small temperature change have effect on the resistance of the carbon putty as we were doing the experiment in couple of days time and therefore during that time, there must be some temperature changes.
