Resisitivity Through Copper Wire

Measuring the resistor of hair tele represent of Different Lengths In this report I exit be writing nigh the investigate I volition rent on strapper cable of diverse continuances. The forecastent variable I ordain be meter is the ohmic sub guidance of the Copper fit away. To do this experiment, mavin needs to bewilder mensuratements with a high story of verity, fetching c be of the equipment they manipulation and step to to each one 1 cherish to a certain ten-fold point of accuracy for completely(a) emergences. The problem with measuring the ohmic granting immunity of Copper fit is cod to the properties of slob as a physical.Copper of course has a gloomy foe over cod to it creation a superconductor, meat that it boost has a defense of minute light ins. As it has this property, it is important to consumption a shit electrify specimen that is long full and thin enough to absorb an appreciable confrontation. The normal pry for the oppositeness of dogshit color is ab forth 10-8? m. A 1m space of atomic number 29 cable with a picky secti peer littled land of 1mm? (10-6m? ) terminate be predicted to stick out a resistance of 0. 01?. This net be compute by employ the resistance formula of R=? lA? 10-8 ? m x 1m10-6m2=10-2? The fit I for seize enjoyment is going to be vapourous than this and volition vary in aloofness from 0. -1. 0 metres with a unlikeness of 0. 2m from the preceding(prenominal) telegraph specimen. In total I entrust make water 5 diametric lengths. Apparatus * Voltmeter- Accuracy stated as ( 0. 5% Read. + 1dgt) in the user manual of arms * Ammeter- Accuracy stated as ( 1. 2% Read. + 1dgt) in the user manual * bombing Supply of 6V * Copper cable * 1m regulation in cm * Scissors * electric telegrams * Crocodile dresss * micrometer Method The pursuit function described to a frown place is how I visualize to desc hold on my declarations 1. I forget m easure out the divers(prenominal) lengths of pig electrify I intend to use development a millimetre rule to gain the well-nigh unblemished results I rouse. 2. at a time he lengths are cut, the diam of the bulls eye telegraph I am utilize must(prenominal) be measured. To gain the most accurate result, I allow use a micron and measure the diameter in several places on the wire and take an mean(a) abide by from these meter readings to telescope out the second-rate cross sectional area. 3. I will connect the freshman length of wire into an electrical lot, making sure that online hobo issue with the entire length of the hog wire connected. The circuit will view like this diagram V V A A 4. The potential will be preserve crossways the wire and the new running by means of it. 5. To come about the resistance of the wire I will use the formula V=IR. . The ohmic resistance put forward thus be counterfeited out using the formula ? =RAL where R is the res istance calculated, A is the cross sectional area of the slob wire calculated and L is the length of the copper wire. The criterions shall be unloaded in the following table shown below electric resistance of Wire The physical properties of a wire can either be categorised as being an immanent property or an extrinsic property. The dispute amongst the 2 categories of properties is that intrinsic properties do non depend on the get of secular that is present, whereas extrinsic properties do depend on the amount of poppycock that is present.In the following investigation of the opposition of copper wire, whizz could say that the nurture of the voltage, resistance and modern are all intrinsic properties of the copper wire. The extrinsic determine of the copper wire would be its electrical resistance. The immunity of the copper wire will be dependent on the material itself, which is copper. The impedance of a material can be defined as the resistance of a 1m length with 1m? cross-section(a) area. As the resistivity of material depends in general on the properties of the material itself, each material whether it is copper or pure ti has its own resistivity coefficient.The coefficient for copper is 1. 72 ? 10-8? m. This entertain whitethorn convergem very baseborn for resistivity, just if one were to inhabit that copper is classed as a superconductor meaning that it conducts electricity exceedingly well, they would get laid that in order for the conductance to be very high, the resistivity must be very low. This can overly be explained by the situation that resistivity is the inverse of conductivity (? =1? ). The potential difference across the copper wire (measured in volts) and the flow of prime (the current) by the copper wire are related through the resistance of the copper wire, not its resistivity.In order to find the resistivity, one needs to work out the resistance first by using the comparison R=VI , and then from this t hey can use the formula ? =RAL to find the resistance. The A represents the cross-sectional area of the wire that will be employ in the experiment. The resistance of the wire is expected to double in time entertain when the length of the wire manifold in size. The resistivity however, should stay about enough the same end-to-end all of the repeats conducted. Reducing the skepticism in the resultsThere are virtually particularors which could affect the accuracy of my results in the experiment of the resistivity of copper wire. superstar of the parts which could affect the accuracy of my results is to do with the measuring devices I use to conduct the experiment. any(prenominal)(prenominal) measuring device can provided be used to measure to a certain spot of accuracy. It is this certain degree which determines how accurate your results are to the confessedly value. In my experiment, I am using a 3? Digits Multifunction Multimeter (DMM) to measure the current through t he circuit and the potential difference (p. d. ) across the copper wire.The main advantage of using a DMM compared to using an analogue voltmeter is the fact that they allow you to record a value to a certain number of decimal places by having different ranges which correspond to the direct of precision of the reading. In the experiment I am conducting, I will be measuring the p. d. to a resolution of 0. 001V using the 2V range on the multimeter. Having the resolution to this degree of measuring rod ensures that I get a voltage reading to 3 decimal places join on the accuracy of the reading and allowing me to bugger off a closer value to the true value.The accuracy for the ammeter has been produce as being 1. 2% of the reading + 1 lysergic acid diethylamide for the range (200mA) and resolution (0. 1mA) I will be using for the current. This means that the value I will record will be 1. 2% of the true value of the current +0. 1mA. I am using the 200mA range rather than the 20A r ange because the resolution of the result is greater than that of the 20A range. This will record a much accurate result which reduces the dubiety in my results. Similarly the range I will use on the voltmeter which is at 2V has an accuracy of 0. 5% of the reading + 1 LSD, which is yet more accurate.Another factor which can affect the resistivity of the result is the temperature of the copper wire. This can affect the resistivity by changing the value of the resistance to make the resistance slight proportional to that of the length of wire. Normally the resistance of a wire will outgrowth as the length of the wire developments due to their being more atoms in the wire for the electrons to overpower by in order to get the through the entire length of wire. As the increase in resistance ? increase in length, the resistance should double when the length of the copper wire is doubled.In order to establish and make sure the resistance is not affected by temperature, I will connec t the copper wire up into the circuit at a low voltage so that the copper wire will not warm up and increase in resistance due to the atoms inside vibrating more. I will also be using a micrometer to measure the diameter of the wire. I am using a micrometer sooner of a standard cm ruler because the level of suspense is far less than that of a ruler. The micrometer allows me to record a value for the diameter of the wire with an question of 0. 0005mm, whereas with an ordinary ruler with mm markings, the incredulity would be 0. 1mm. ResultsThese are the results I lay in from the experiment carried out. All of the entropy is stark naked data that I halt unruffled myself and has not been manipulated in way at all. N. B- The diameter of the wire was measured to be 0. 435mm. The cross sectional area was calculated as being 1. 48? 10-7m2. This value was used throughout the experiment to work out the different resistivity set using the resistivity compare as stated previously. R epeat Length of Wire (m) electromotive force (V) online (A) Resistance (? ) Resistivity (? m) 1 0. 2 0. 044 1. 911 0. 023 1. 71E-08 2 0. 2 0. 042 1. 907 0. 022 1. 64E-08 3 0. 2 0. 043 1. 909 0. 23 1. 67E-08 1 0. 4 0. 088 1. 882 0. 047 1. 74E-08 2 0. 4 0. 085 1. 879 0. 045 1. 68E-08 3 0. 4 0. 087 1. 869 0. 047 1. 73E-08 1 0. 6 0. 132 1. 839 0. 072 1. 78E-08 2 0. 6 0. 135 1. 845 0. 073 1. 81E-08 3 0. 6 0. 129 1. 839 0. 070 1. 74E-08 1 0. 8 0. 158 1. 748 0. 090 1. 68E-08 2 0. 8 0. 163 1. 741 0. 094 1. 74E-08 3 0. 8 0. 159 1. 745 0. 091 1. 69E-08 1 1. 0 0. 207 1. 739 0. 119 1. 77E-08 2 1. 0 0. 209 1. 738 0. 120 1. 79E-08 3 1. 0 0. 201 1. 710 0. 118 1. 75E-08 From the table above, I also worked out the averages of the results measured from the experiment.Repeat Length of Wire (m) Voltage (V) intermediate V Current (I) Average I Resistance (? ) Average R Resistivity (? m) 1 0. 2 0. 044 0. 043 1. 911 1. 909 0. 023 0. 023 1. 71E-08 2 0. 2 0. 042 1. 907 0. 022 1. 64E-08 3 0. 2 0. 043 1. 909 0. 023 1. 67E-08 1 0. 4 0. 088 0. 087 1. 882 1. 877 0. 047 0. 046 1. 74E-08 2 0. 4 0. 085 1. 879 0. 045 1. 68E-08 3 0. 4 0. 087 1. 869 0. 047 1. 73E-08 1 0. 6 0. 132 0. 132 1. 839 1. 841 0. 072 0. 072 1. 78E-08 2 0. 6 0. 135 1. 845 0. 073 1. 81E-08 3 0. 6 0. 129 1. 839 0. 70 1. 74E-08 1 0. 8 0. 158 0. 160 1. 748 1. 745 0. 090 0. 092 1. 68E-08 2 0. 8 0. 163 1. 741 0. 094 1. 74E-08 3 0. 8 0. 159 1. 745 0. 091 1. 69E-08 1 1. 0 0. 207 0. 206 1. 739 1. 729 0. 119 0. 119 1. 77E-08 2 1. 0 0. 209 1. 738 0. 120 1. 79E-08 3 1. 0 0. 201 1. 710 0. 118 1. 75E-08 Uncertainties indoors my results Before creating the graph of my results, I calculated the overall uncertainties of each measurement at heart this experiment, so that I could reassure where the most indecision of the average resistivity value comes from.To calculate the precariousness for each measurement, I took the average measurement that had the biggest difference from its original data. The p lowshare of uncertainties of each measurement was as follows * Percentage distrust of the Voltage V= 0. 2060. 005 V suspicion in V= 0. 0050. 206? light speed%? 2. 43% * Percentage unbelief of the Current I=1. 7290. 019 A skepticism in I=0. 0191. 729? atomic number 6%? 1. 10% * Percentage of Uncertainty in Resistance R=V/I Uncertainty of R=1. 10%+2. 43%? 3. 53% * Percentage of Uncertainty in Length Uncertainty=0. 60. 001m Uncertainty in L=0. 0010. 6? 100%? 0. 17% Percentage of Uncertainty in Area The Diameter of the wire is 0. 4350. 0005mm The high hat area where the diameter is 0. 435mm A=? 0. 21752? 0. 1486mm2? 1. 486? 10-7m2 The upper limit area where the diameter is ? 0. 4355mm A=? 0. 217752? 0. 1489mm2? 1. 489? 10-7m2 The negligible area where the diameter is ? 0. 4345mm A=? 0. 217252? 0. 1482mm2? 1. 482? 10-7m2 So the area is 0. 1480. 0004mm2 with a parcel uncertainty of A=0. 00040. 148? 100%? 0. 27% * So the component uncertainty in the Resistivity can be calculated as the sum of all the uncertainties in the experiment ? =RAL=3. 53%+0. 27%+0. 17%=3. 97%The percentages of instrument defect are as follows * Voltmeter reading is 0. 0005V slavish error in Voltmeter= 0. 00050. 206? 100? 0. 24% * Ammeter reading is 0. 0005A Instrumental error in Ammeter=0. 00051. 729? 100? 0. 03% * Micrometer reading is 0. 0005mm Instrumental error in Mircometer=0. 00050. 435? 100? 0. 11% * The total instrumental error is the total of each instrumental error stated above which would be 0. 38%. represent 1 Graph 2 Data Analysis In all of my results that I look at collected, on that point is a substantive relationship amongst the increasing length of wire and the value for the resistance.One would expect this strong correlation between the resistance and the length since one of the unsubdivided laws of electrical resistance is that it increases proportionally with the increase in the length of the wire. One can explain this through the understanding of elect rons in a circuit and the atoms arranged at heart the components in a circuit. With my experiment of copper wire, a current passed through my circuit once a voltage was use to the circuit. When the electrons were given energy to move they passed through the circuit to the copper wire where they go through the resistance which was calculated.As the lengths of the copper wire increase, the amount of fixed atoms within the structure of the wire increases. Due to this the electrons have a high chance of colliding with the fixed atoms, which causes the wire to affectionateness up and increase the resistance. One can see the certainty in the correlation between the average resistance and the length of the copper wire by feeling at the incline of the line of trump fit within graph 1. The side shows that R? =0. 9984, showing an extremely strong positive correlation between the two variables.From the equation of the side displayed in graph 1, the average resistivity can be calculate d which takes into account all of the points within the data collected. The gradient of the line shows the equation Resistance (R)Length (L). In the computing for resistivity, one not only needs the value of RL, but also needs the cross sectional area of the wire. If the cross sectional area of the wire is multiplied by the gradient, then the average resistivity can be calculated ? =RAL=0. 1192? 1. 486? 10-7m2? 1. 77? 10-8? m In Graph 2, the percentage of uncertainty of each average resistance was displayed in the vertical error bars.The percentage of uncertainty of the length of the wire was so small that it was not worth adding to the graph since it is extremely hard to see on the graph. From these percentage uncertainties of the average resistance in the experiment, one can calculate the supreme and the borderline values for the resistivity from looking at the gradients like we did for graph 1. To calculate the nominal gradient, I took the gradient of the line from the utte rmost uncertainty in the lowest resistance to the minimum uncertainty of the highest resistance.I did this to obtain the shallowest gradient possible from all the points on the graph. I then multiplied this gradient by the smallest area value. lowest ? =0. 1144? 1. 482? 10-7m2? 1. 70? 10-8? m For the maximum value of resistivity, I took the value of the gradient of the line from the minimum uncertainty in the lowest resistance to the maximum uncertainty of the highest resistance. I did this to obtain the steepest gradient possible from all of the points on the graph. I then multiplied this by the maximum area. maximum ? =0. 1263? (1. 489? 10-7m2)? 1. 88? 10-8? mAfter looking at the average, minimum and maximum values of the resistivity taking into account all of the uncertainties within the calculation one could say that from the investigation conducted, the resistivity of copper wire is 1. 76? 10-81. 2? 10-9. The percentage uncertainty of the resistivity would then be 1. 2? 10-91. 76? 10-8? 100%? 6. 8% Biggest Source of Uncertainty From looking at all of the percentage uncertainties for all my measurements, the resistance produced the most uncertainty. The uncertainty of resistance was worked out by adding up the uncertainty of the voltage and the current measured.It must have been from these two calculations where the uncertainty of the resistance became noticed. From calculating the instrumental errors of the multimeter used as a voltmeter and an ammeter, I would not settle that the vast majority of the error came from the accuracy of the apparatus. I would say that the average resistance I calculated was from the average current which had the biggest difference from its original data, and the average voltage which had the biggest difference from its original data. The average data I had chosen was 0. 2060. 05V and the average data I had chosen for current was 1. 7290. 019A, as they had the biggest uncertainties. Due to this fact I would have produced an u ncertainty which had the biggest difference from the original value, so the maximum possible uncertainty for the resistance. Anomalies and dogmatic Errors I did not have any anomalous results when looking at the average resistance graph. All of the points plotted show strong correlation with the increase in length. Systematic errors may have contributed to some of my resistivity values being high or lower than my overall average.An caseful of this could have been when measuring the diameter of the copper wire. The micrometer did not let me know if both of the sides of the copper wire were jot the micrometer measuring device sufficiently enough or whether or not it was touching both sides of the copper wire more than enough, which would then mean it mash the diameter of the wire resulting in a lower diameter at certain points across the wire, since I took 3 readings and averaged them out. If this was the case, then one of my wires may have had a higher resistance than the others .One other taxonomic error may have come from the stamp battery pack. It may have had a temporary glitch in which less electrical energy was sent through the circuit meaning less current was flowing through the circuit, resulting in a larger resistance than that of the previous record with the same length of wire. This would also turn the final value of the resistivity. Another uncertainty which would be counted as human error could have been the position at which I had placed the crocodile clips at either end of the copper wire.For the same length of wire, the crocodile clip may have been placed further away from the end of the copper wire than the previous measurement, meaning that the length of the wire would have decreased marginally which may have resulted in a lower resistance recording. Also, when I measured the length of the copper wire, I had to straighten out the length of the wire since it was coiled. When doing this I may have accidently pulled the length of the wire increasing its length by a waist-length amount.Having said this, it may have neutered the resistance measured in the wire making it larger than it should have been since the electrons have to travel a longer distance. rating After looking at all of my results, I intend that the method I used and the ways of reducing the uncertainty in my experiment were effective. The instrumental errors were nominal and the overall uncertainty of my final calculation of resistivity was a low value. The resistivity value itself did alter but generally stayed constant throughout the experiment.As I have said, I do not believe this was because of the accuracy of the multimeters I used but due to other factors such as changes in the environment like temperature, or due to systematic errors to do with the battery pack I used. To decrease the uncertainty in my resistance measured, I could use an even lower resolution on my voltmeter (0. 1mV) and ammeter (0. 001mA) to reduce the negative effect of l east Significant Digits (LSD) and to give the most accurate result.This way I could then increase the precision of my results and record a value which is closer to the true value When equivalence my average value of resistivity with the print value of resistivity which is 1. 72? 10-8? m, my average value is very close to the published value which shows the level of accuracy throughout my experiment considering the more precise tools that were used by the professionals to gain the published value. The repeats I did helped me to record a value for the resistivity that was close to the published value by reducing the random uncertainty in my results.To gain even more accuracy I could do more repeats, or I could alter the intervals between each length to 0. 1m to increase my range of data. That way I will reduce even more random error within my data. I could also change the different diameters of the wire or change the material I use to compare these results with those and see how the y differ. One other change I could do next time is to use an Alternating Current (AC) rather than a Direct Current (DC), since AC is more conventional in houses so it would have provided further information as to how skillful copper is in the use of houses.