Wednesday, December 11, 2019
Resistivity Essay Example For Students
Resistivity Essay Aim:To investigate the physical and electrical properties of a wire in order to find the resistance using Ohms law and from this to find the Resistivity of the wire at room temperature. Hypothesis:Electricity is the flow of charged particles around a complete circuit; a circuit consists of three main factors, voltage, current and resistance. Ohms Law states that at a constant room temperature these factors can be related by the equation,V = IRWhere, V = Voltage (V)I = Current (A)R = Resistance (?)Therefore, we can say that at a constant room temperature resistance is relative to the value of the voltage and of the current, this can be expressed by the equation,By altering the values of voltage and current the value of resistance can be altered at any given point in a circuit. In addition to the relationship stated in Ohms Law, resistance is related to length and cross sectional area. By saying that resistance is due to collisions between electrons we can deduce that resistance is proportional to length because by doubling the length of a wire we double the chance of a charged particle colliding (resistance), therefore,R ? LAlso, if we double the area it will consequently double the number of charged particles flowing at a given point and thus double the current and halving the resistance. Therefore,By combining these equations we can produce,Where, = Resistivity (?/m) (material constant)R = Resistance (?)a = Cross Sectional Area (mm)L = Length (m)Resistivity is a constant of a wire, it is the resistance of a standard size wire of a material with 1 unit length and 1 unit cross sectional area, so 1m long with a cross sectional area of 1m. I intend to investigate the constancy of resistivity; if resistivity is indeed a constant then it will be the same at every point along a chosen wire. The standard deviation of the results can be calculated by using this equation,By using the standard deviation of the results I predict that at every point tested along the chosen wire the resistivity will be within 2 standard deviations of the mean resistivity of the wire. Approximately 97% of a sample will lie within 2 standard deviations of the mean, and approximately 99% of a sample lie within 3 standard deviations of the mean. Providing that all the results lie within 2 standard deviations of the mean, then it can be taken that resistivity is a constant. Experimental VariablesThe variables identified in this experiment are as follows,VoltageCurrentResistanceLengthCross Sectional AreaTemperatureThroughout the experiment it will be assumed that there are no other variables present, and that temperature is constant at room temperature. All the variables will be kept as close to constant as possible, barring length which will be the experimental variable and thus will be altered. Experimental Procedure TheoryIn order to calculate resistivity the voltage and current will be taken at a designated point along a wire, these values will then be used to calculate resistance using Ohms Law as shown,This can then be combined with,This will produce the equation,The values used will be recorded and then this process repeated at a decided interval along a 1m length of wire. Prior to this, the wire to use and the interval regularity must first be deiced, and safety precautions taken into account. Preliminary ExperimentAn array of wires were made available that varied in type and SWG (Standard Wire Gauge) values. Copper SWG 30Constanton SWG 28SWG 30Nickel Chrome SWG 18SWG 22SWG 30In order to determine the appropriate wire for experimentation, a preliminary experiment was performed testing each wires resistive properties at 50cm length and 100cm length while using a power supply stated as being 6V with a supplied current of 1A. Charles De Secondat, Baron De La Brede Et De Montesquieu Was Born In 1 EssayThis is shown in the graph above, where it can be clearly seen that the as the length of the wire increases, the voltage will sharply increase until it levels out at 40cm. The current however, decreases at an almost uniform rate as the length increases. In the graph above it can be seen that the resistance increases steadily as the length increases. From the raw data collected the resistivity can be calculated by taking calculating resistivity at each point along the wire and then taking an average value for the wire as a whole. First however the cross sectional area of the wire must be calculated, using the standard wire gauge values (SWG) of diameter, it can be calculated using pi that the cross sectional area is 0.08mm and so is 0.0008m. This value for cross sectional area can now be used in the equation to work out resistivity,This formula was used to calculate the resistivity at each point along the wire,Length (cm)Resistance (?)Resistivity ( )101.16202.34303.54404.58505.71607.36708.02809.979010.4110011.14In order to prove or disprove the hypothesis the standard deviation must be calculated using the equation,We know that,Also,And,Using the equation, we can determine that standard deviation is equal too,It is known that about 97% of the data lies within 2 standard deviations of the mean, therefore, providing all the data lies within 2 standard deviations of the mean then it can be considered to be a constant. The highest value calculated was 9.9710-4 and the minimum was 8.9110-4 The mean equals,The upper limit equals,The lower limit equals,This shows that,Maximum Upper LimitMinimum Higher LimitTherefore, the data all lies within 2 standard deviations of the mean and allowing for variances in the experimental conditions, resistivity can be considered a constant value for Constanton and shall be taken as being 9.2810-6?/mSources of Random and Methodological ErrorIdentified sources include a natural variance in the power supply, which due to conditions out the control of the experiment cause a fluctuation in the power supply and consequently it isnt a constant 230V supply, causing the outputted voltage of 6V to vary, along with the outputted current. Also another possible source of random error is natural impurities in the wire which could cause the flow of current to be affected thus effecting the collected data. The most major source of error will be down to human error, such as inaccurate measurement of current and voltage during the experimental process, and inaccurate measurement of lengths, and placing of connections to the experimental wire from the power supply. The use of standard deviation allows for these errors by giving a tolerance level of 2 standard deviations from the mean of the data collected.