Electrical Laboratory Exercises-Inductance and Capacitance - Lab Report Example

Electrical laboratory exercises-inductance and Capacitance Introduction This report involves laboratory exercises that allows exploration of resistors , inductors and capacitors. Theory Resistance and resistivity The relationship between resistance of a material, the length and resistivity is given by Where R= resistance () =resistivity () L=length (m) A=Area (m2) The experiment involves measurement of electrical resistance of pencil lead for a set HB pencils with the results used in calculation of resistivity of the graphite based core of the pencil and this will enable classification of materials are conductor, semiconductor or insulator. There will be also investigation on whether the resistance of pencil core varies linearly with length of pencil. Equipment required The following are the materials required A set of HB grade pencils and pencil sharpener A multimeter with capability of measuring inductance, resistance and capacitance (LCR mete) with leads and crocodile clip connectors A ruler, vernier and/or micrometer Procedure 1 A group of pencils with the same length were obtained, were sharpened at both ends. Using a resistance meter the resistance of each of the pencils were obtained. As a measure of reducing effect of random variation in the graphite/clay mixture used in making the pencil it was necessary a number of pencils, three in this case. The resistance and the length of the pencils were as shown in table 1 below Table 1 PEN RESISTANCE LENGTH Pen 1 19.8 9.2 Pen 2 17.5 8.6 Pen 3 14.5 8.1 Using a vernier the diameter of the pencil lead core was obtained. Caution was taken to ensure that the diameter was the maximum and had not been reduced as a result of sharpening. The diameter of lead core d=0.00223m Calculation Average length = (9.2+8.6+8.1)/3=8.63=0.0863m Average resistance= (19.8+17.5+14.5)/3=17.27 Area of lead A= ==0.0000039 Average resistivity = Task 1 =Part B (Variation of resistance with length) The resistance different length of pencils were measure using a resistance meter. All the pencils had the same lead core diameter d= The resistance and length of the pencils were as shown in table 2 Table 2 PEN RESISTANCE LENGTH Pen 1 39.2 0.174m Pen 2 24.2 0.143 Pen 3 18.3 0.136 Pen 4 20.2 0.117 Pen 5 18 0.107 Pen 6 14.5 0.085 Figure 1 From the graph it can be seen that there is a linear relationship between length and resistance of pencil. The gradient of the graph represent resistivity/Area. The graph is represented by equation Y=268.9x-10.45 Also we know that  Therefore =268.9 We have seen that the calculated resistivity is  while graphical resistivity is . The graph show close to a linear relationship between resistance and length. Though the results are close to what would be expected the fact that there is some discrepancy between calculated values and graphical values. Also from the equation of the graph it is seen that the graph does not pass through the origin as would be expected. This is because at o length it means short circuit and thus there should be no resistance. The sources of errors can be attributed to non-uniformity of resistance in the lead cores, ie materials for pencils used are different. Task 2: Inductance of a solenoid The objective is investigation of the equation which describes the inductance of along thin solenoid: Where N is number of turns, A =average cross sectional area (m2), l= length (m), = permeability of free space ( and = relative permeability. Equipment required inductance experiment The following materials were used 1. An iron nail 2. A length of enameled (insulated) copper wire 3. A multimeter capable of measuring inductances, resistance and capacitance (LCR meter) 4. A ruler 5. A small piece of sandpaper (to remove enamel insulation) Procedure A wire was wrapped around a while carefully counting the number of turns. The number of turns was established using the last digit of student number. LCR meter was connected with the coil and inductance was measured. A rular was used in the measurement of the length of the coil (l) and the average diameter (d) Results of measurements were as follows Inductance=  Length of coil l= Average diameter d= Method and Analysis Calculations Area A =  From  Rearranging we have Substituting relevant values we have =  Graphical solution The inductance at various length were as in table Table 3 Length (cm) Inductance 9 0.058 8 0.065 7 0.073 6 0.084 5 0.103 Figure 2 The graph is represented by equation Y=0.005x+0.002 The gradient of graph = 0.005= The calculated values are quite close to graphical value and the small difference can be attributed to experimental error. The errors could be attributed to the fact that in measurements of diameter it is assumed that the diameter was uniform in the entire length of the coil but in true sense there could have been variation. Generally the experiment was a success as there was a linear relation between inductance and inverse of length. Task 3-Capacitance of a parallel plate capacitor The objective was investigating the equation which describes the capacitance of a parallel plate capacitor. For a capacitor we have the relationship Where C is the capacitance (F), A is he area of the plates (m2) ,  is permittivity of free space,  is the relative permittivity and d is the distance between plates. Equipment required The material required were 1. Aluminium foil for conducting plates 2. Dielectric material 3. A glue stick, used to fix the aluminium foil to either side of the sheet of paper 4. An LCR meter or multimeter capable of measuring capacitance 5. A ruler and a pair of scissors Capacitor construction A simple parallel plate capacitor was made by gluing two sheets of aluminium foil to either side of a sheet of paper. The dimension were established using the student number according to the direction given A capacitance meter was used in measuring the resulting capacitance and the information recorded. Using a micrometer screw gauge the thickness of the five layer sandwich was measured and also there was separate measurement of paper and foil separately and from this the distance d between the capacitor plates. Experimental method and analysis Height =15.6 Width=10.6 Capacitor thickness=0.11mm Paper thickness =0.09mm Thickness of foil =0.007mm Distance between plates =0.09mm Capacitance =16.30Mf Area=height x width=16.536x10-3 Graphical solution Capacitance for various areas is as shown below Area) Capacitance 0.0165 1.63x 0.0209 2.131x 0.0201 1.96x 0.0204 1.967x Figure 3 The graph is represented by equation Y=0.001x+0.0000007 The gradient of graph = 0.001=  From the results it can be seen that the calculated = and the graphical . These values are close but not exactly the same. The difference can be attributed to the errors in measurements. In measurement of capacitance the difference can be attributed to the fact that the distance d between the plates is likely to vary for each case. Application of the sticking glue could also be non-uniform resulting to the difference. Generally it c an be concluded that the objective of this experiment was achieved as there was a linear relationship between capacitance and area (A) and also calculated values were close to graphical values. Read More