The factors affecting the resistance of a metalic conductor Essay Example for Free

The factors affecting the resistance of a metalic conductor Essay I1 12 As I have found from my experiments, the results I obtained show that the factors I predicted of affecting the resistance of a wire have proved true. Firstly, the factor of length increasing and resulting in an increase of resistance of the wire held true, because, as I varied the lengths of the wire form 50cm to 200cm the resistance increased from approximately 5 to 20. Secondly, the factor of the cross sectional area increasing and resulting in a decrease of the resistance of the wire also held true, because as I varied the cross sectional areas of the wire from 0. 4mm to 0. 91 mm, the resistance went from approximately 5. 4 to 0. 9. The above-mentioned results occur due to the fact of how many free electrons are being conducted through the wires of different lengths and areas.   In the case of length; the resistance increases as the length increases because a wire with a shorter distance will have a smaller amount of atoms for the free electrons to hit. Whereas a wire with a longer distance will have more atoms for the electrons to hit and the resistance gradually increases as a result.   In the case of the cross-sectional area; a wire with a greater area allows more electrons to flow through it as well as having more channels for the electrons to flow through it. As a result the resistance decreases, because current can flow without any restrictions. Whereas a wire with a smaller area all a smaller number of electrons to flow through it resulting in diminished flow of current through the wire. Thus the resistance increases because the current is flowing with restrictions. From the graphs on the following pages, I have illustrated my results obtained from my experiments and done so with the relationship between the current [I] and the voltage [V]. As predicted earlier, the graphs explain how, as the length of the wire increases, the resistance also increases, as shown in the graph I. As well as explaining how, as the cross sectional area of the wire increases, the resistance decreases, as seen in graph II. I have also plotted a graph to the effect on the resistance of the wire when a specific type of circuit is being used. A series circuit effect is seen in graph III and a parallel circuit effect is seen in graph IV. GRAPH I:   Length as a factor affecting the resistance of a wire: From the graph, we can see that the shorter the wire, the steeper the slope. Each line represents the wires I used that were of lengths ranging from 50cm to 200cm. The 50cm wire line has the steepest slope, thus we say it has the lowest resistance, while the 200cm wire has the least steep slope and we say it has the highest resistance. However to verify this fact I calculated R from the graph and found: For the length of the wire: 50 cm GradientÃ'Ž Therefore; R =1/0. 05 = 20 Below is my observation table that compares the value of R from my tabular calculations and the value of R from my graphical results: Length [cm] Calculated value of R [] Graphical value of R [] R/L [] 50 5. 06 5 100 9. 83 10 150 14. 63 13 200 19. 87 20 This graph shows, that the length of the wire is directly proportional to the resistance. GRAPH II: * Cross sectional area as a factor affecting resistance of a wire: From the graph, we can see that the thicker the wire the steeper the slope. Each slope represents the various thickness of wires I used ranging from 0.4mm to 0. 91mm. The 0. 4mm wire has the least steep slope, and we say that it has highest resistance, whereas the 0. 91mm wire line has the steepest slope and thus we say it has the lowest resistance. However I must verify these facts form my graph and calculate the value of R from the graph. Therefore; R = 1/0. 54 = 1. 8 0. 91mm Gradient = 1. 03 0. 81/ 1. 0 0. 8 = 0. 22/0. 2 = 1. 1 Therefore; R = 1/1. 1 = 0. 9 Below is my observation table that compares the value of R from my tabular calculations and the value of R from my graphical results: Area [m ] Calculated value of R [] Graphical value of R [] R x A [] 0. 12 5. 49 4. 8 0. 25 2. 86 3 0. 39 1. 62 1. 8 0. 65 0. 97 0. 9 This graph shows that the cross sectional area of the wire is inversely proportional to the resistance of the wire. GRAPH III: * A series circuit as a factor affecting the resistance of a wire: From the graph, we can see that when we use a wire of length 50cm, and pass current through it, via a series circuit the resistance is slightly less, than when we pass current through two wires of lengths 20cm and 30 cm and connect them with a series connection then the resistance is slightly higher. This is because were doubling the length of the resistor, thus we say that the resistance increases with the total length of the resistors. To verify my findings   Below is my observation table that compares the value of R from my tabular calculations and the value of R from my graphical results: Length [cm] Calculated value of R [] Graphical value of R [] 2030 6. 04 6. 8 50 5. 06 6. 2 GRAPH IV:   A parallel circuit as a factor affecting the resistance of a wire: From the graph, we can see that when we use a wire with a smaller cross sectional area and pass current through it via a parallel circuit, the resistance is slightly higher than when using a normal circuit. This is because placing resistors in parallel is equivalent to increasing the cross-sectional area A through which current can flow. In my graph I have used a wire of thickness 0. 4mm and passed current through it using a parallel circuit, and the resistance is lower. The resistance for the 0. 56mm wire when passing current through it using a normal circuit is higher. However to verify my findings, I calculated the value of R from my graph and found: 0. 4mm Gradient =Therefore; 35 Therefore; R =1/0. 35 = 2. 8 Below is my observation table that compares the value of R from my tabular calculations and the value of R from my graphical results: Area [m ] Calculated value of R [] Graphical value of R [] 0. 12 2. 62 3. 33 0. 25 2. 86 2. 8 MATHEMATICAL DEDUCTIONS TO FURTHER PROVE MY RESULTS: Consider a wire of length l Where; A = cross -sectional area / number density of electrons n = electron density =number of free electrons per unit volume If voltage V, is applied to the wire, the electrons will drift to the positive terminal with a velocity, v. Volume of the wire = AlÃ'Ž Number of free electrons in conductor = n x A x l = nAl Total charge that is free to move = n x A x l x e =nAle Current = charge/time = Q/t Time required for all electrons to emerge out of the end of the conductor = l/v Therefore; I = Q/t = nAle/l/v = nAve Drift velocity (from battery cell) is the EMF, Therefore; Force = mass x acceleration (force to move current) Acceleration = velocity/time L = m x v / t Work is done by voltage in moving electrons i. e. acceleration: Work done = Force x Distance Distance = l Therefore; work done/electronic charge = w/e Work done per unit charge = V = w/e = lÃ'Ž Therefore; V = l x m x v/et R = V/I therefore; V = l x m x v/et = l x m x et I = nAve nAe From my analysis I can conclude that as the length of a wire increases, so does the resistance. This is because there is a larger amount of wire to travel up and therefore there will be more factors to increase resistance I can now sat that I believe my experiments were quite accurate as I performed them fairly and properly, this is demonstrated in the good results I have obtained. My measurements were accurate enough as I used digital ammeters and voltmeters, making them more reliable. In doing so I also avoided the possibility of parallax errors as well as zero errors. Were my results accurate to draw a conclusion? I was able to draw a valid conclusion for the measurements of current and voltage, as they were more or less what I expected to attain. I managed to prove that resistance is proportional to length as length increases, the resistance of the wire increases and that resistance is inversely proportional to the cross sectional area as cross sectional area increases, the resistance of the wire decreases. As well as that, for 2 wires connected via a series circuit combination, the resistance pattern will be the same as that when length of a wire is varied. Whereas for 2 wires connected via a parallel circuit combination, the resistance pattern will be the same as that for when area of the wire is varied. My results did not agree fully with my heat theory as they showed slight variations, such as a 14. 63 result instead of a result close to 13 for a wire of length 150cm. And a 19. 87 result instead of a result close to 18 for a wire of length 200cm. These were my anomalous results. This was probably due to the temperature variation of the wire. However these anomalous results were not big enough to change my final reading. I believe my results allowed me to cover a wide range of factors affecting the resistance of a wire, because I took a total of 4 lengths and eight readings for each length, giving me enough to analyse. I performed the experiment once, but I did take the reading of the current twice. Once in an ascending order, then in a descending order, thus I had two sets of results, which improved my accuracy. I also did a fair test because I followed the precaution of using the same equipment each time the experiment had to be carried out. Thus I can regard my results as being reliable values, as when compared to actual values, such as getting a 5 resistance for the 50cm wire as compared to supposedly having to get a 4. 5 resistance, or a 9. 83 resistance for a 100cm wire as compared to having to obtain a 9 resistance. I dont have any outstanding anomalous values that showed up on my graphs, only a few points did not quite fit on my line of best fit, which were quite close to it anyway. As I mentioned earlier these could have been caused by the heating effect of the equipment which resulted in slight variations of my readings. OTHER EXPERIMENTS TO MEASURE A CURRENT VOLTAGE RELATIONSHIP: Testing a silicon diode: I could connect a battery, a lamp, and a diode in series. Then connect the narrow end of the diode nearest to the negative terminal of the battery. Using an analog VOM type meter, I would set the meter to one of the lower ohms scales, say 0-2K, and measure the resistance of the diode both ways. If I get zero both ways, the diode is shorted. If I get INFINITY both ways, the diode is open. If I get INFINITY one way but some reading the other way (the value is not important) then the diode is good and I can measure the current and the voltage. As the graph shows, almost no current flows if the voltage applied is in the reverse direction. Testing the transistor: Testing a unijunction transistor (UJT) is a relatively easy task if you view the UJT as being a diode connected to the junction of two resistors, as shown in figure 4-21. With an ohmmeter, measure the resistance between base 1 and base 2; then reverse the ohmmeter leads and take another reading. Both readings should show the same high resistance regardless of the meter lead polarity. Connect the ohmmeters negative lead to the UJTs emitter. Using the positive lead, measure the resistance from the emitter to base 1, and then from the emitter to base 2. Both readings should indicate high resistances approximately equal to each other. Disconnect the negative lead from the emitter and connect the positive lead to it. Using the negative lead, measure the resistance from the emitter to base. From my mathematical deductions (to further prove my investigation) in my analysis section I calculated the value for resistivity for a nichrome wire and compared the calculated value with the actual standard value of rho. That is; LENGTH [cm] R from my experimental results R from my graphical results. REA [m] R from my experimental results [] R from my graphical results therefore; Material Length [m] Area [m ] Resistance [] Calculated [m] Standard [m] NichromeNichrome Nichrome NichromeÃ'Ž Thus we see that my results were not so different from the actual standard value of resistivity, and this is mainly because of the temperature variations that occurred during my experiment. This evidence does support a firm conclusion that if someone was to repeat the same investigation I would expect the to receive the same results. Show preview only The above preview is unformatted text This student written piece of work is one of many that can be found in our GCSE Electricity and Magnetism section.