EAT118 Electrical Laboratory Exercises - Lab Report Example

EAT118 Electrical Laboratory Exercises Lab: Resistance, Inductance and Capacitance Name: Student No. Introduction Resistors, capacitors and inductors are the three basic devices used in electronic circuits. Each of these elements have a standard symbol and unit of measurement, and plays an important role in the behavior of electronic circuits. Resistance (denoted by R, measured in Ohm,) is a measurement of how difficult or easy the flow of electric current occurs through a given material or device. Resistance is defined by Ohm’s law which states that: or. Four factors are known to affect the resistance of a conductor material: conductivity of the material, its cross-sectional area, length and temperature. If the temperature remains constant, then the mathematical relationship between resistance and the other three factors is represented using the equation: Where: R – Resistance () – Resistivity () – Length (m) A – Area () Inductance (denoted by L, unit is Henrys) is the magnetic storage of charge in a conductor coil. The magnetic field created when current flows in the coil is uniformly concentrated in the center of the solenoid. The inductance of a coil is determined by factors such as the number of turns, the cross-sectional area of the coil, coil length, and the core material which determines its magnetic permeability (Bhattacharya, 2007). The equation relating inductance to these factors is stated in the equation stated below: Where: L – Coil inductance N- Number of turns A – Average cross-sectional area () – Length of the solenoid (m) – Permeability of free space (4) – Relative permeability A capacitor stores electric charge and its capacitance (denoted by C, unit is Farads) is a measure of the amount of charge stored. It consists of two or more conductive plates that are parallel and not in contact, but separated by air or a dielectric material. The dielectric material prevents the flow of current through the capacitor, allowing voltage to be stored as electrical charge across the plates. The capacitance of a capacitor is defined by the equation: , is charge in Coulombs, and is voltage through the capacitor. Three factors that are known to affect the capacitance of a capacitor are the cross-sectional area of the parallel plates, the nature of the dielectric material, and the separation distance between the plates (Bhattacharya, 2007). The equation for obtaining capacitance, taking into account these factors is as stated below: Where: C – Capacitance (Farads) A – Area of the plates () – Permittivity of free space (8.85 10 -12) – Relative permittivity – the distance between the plats (m) Aims of the Experiments To investigate the equation relating resistance of a pencil lead to its length, cross-sectional area and resistivity (). To investigate the equation used to describe the inductance of a long thin solenoid (). To investigate the equation which describes the capacitance of a parallel plate capacitor (). Experimental Methodology Task 1: Resistance and Resistivity Equipment used The following list of materials were needed to complete this task: Three HB grade pencils of the same length and a pencil sharpener A multimeter or an LCR meter with leads, capable of measuring resistance, inductance and capacitance Crocodile clip connectors A vernier and/or micrometer, and a ruler Method Part A: Measuring Resistivity The pencils were sharpened on both ends to expose the lead. The resistance of each of the three pencils was measured by connecting the multimeter on both ends using leads and crocodile clips. The average resistance and the average length of the three pencils was then determined to eliminate random variations that may occur due to variation of graphite and clay in the leads. Using a micrometer, the diameter of the pencil lead cores was also measured and used to calculate the cross-section area. The results obtained after carrying this procedure were used in determining the resistivity of the pencil lead. Part B: Variation of resistance with length Five pencils of different lengths were sharpened at both ends and a resistance meter used to measure the resistance of each pencil. The results were used to plot a line of best fit on a scatter graph in Excel to determine the relationship between length and resistance. Task 2: Inductance of a Solenoid Equipment and Materials Used The following list of materials were used to investigate the inductance of a solenoid: An iron nail A length of insulated copper wire A ruler A multimeter or an LCR meter for measuring inductance, capacitance and resistance A piece of sand paper that was used to remove the insulation on the copper wire. Method The copper wire was wound around the iron nail to make a coil with 60 turns. After constructing the inductor, a suitable LCR meter was connected to it to measure the inductance of the coil. A ruler was then used to measure the length and diameter of the coil. The diameter was used to calculate the cross-sectional area of the coil. The length of the conductor was then varied by compressing or stretching the wire coil to investigate the effect on inductance. Task 3: Capacitance of a parallel plate capacitor Equipment Used: The following materials were used in carrying out this task: Aluminum foil for the plates An A4 paper sheet to be used as a dielectric material A glue stick for fixing the aluminum foil to either side of the dielectric material A pair of scissors and a ruler A multimeter or an LCR meter for measuring capacitance Method A parallel plate capacitor with a height of 17.9 cm and a width of 19.4 cm was made by gluing two sheets of aluminum foil to both sides of a paper. After making the device, its capacitance was measured using a capacitance meter and recorded. A micrometer was then used to measure the thickness of the 5-layer sandwich (i.e. foil-glue-paper-glue-foil), and also the paper and the foil separately. This was done in order to get an estimation of the distance separating the capacitor plates (). The relative permittivity () of the paper dielectric was then obtained by re-arranging the capacitance equation. These results were compared with the expected relative permittivity of the material. Results and Discussion Task 1: Resistance and Resistivity Part A: Measuring Resistivity Table 1: Measurement of resistance of three pencil leads Length of pencil lead (m) Resistance () 0.11 15.2 0.10 15.5 0.095 13 Average 0.102 14.57 From equation 1: Letting the subject of the formula, Diameter of the pencil lead was found to be = 2.02 x 10-3 mm = 2.02 x 10-6 m or radius = 1.01 x 10-6 m Cross-section area, . Using r = 1.01 x 10-6 m, Therefore, Resistivity, = = 4.57 cm With this value of resistivity, the pencil lead can be considered as a conductor. Materials classified as conductors normally have bulk resistivity in the range of 10-8 to 10-4 ohm-cm. Part B: Variation of resistance with length Table 2: Measurement of resistance for different pencil leads Length of pencil lead (m) Resistance () 16 33.3 12 16.2 6.5 16 10.2 14 11.5 15.3 Figure 1: How resistance varies with the length of the conductor In figure 1 above, it is seen that a linear relationship exists between the length of the pencil lead conductor and resistance. The longer the pencil lead, the more current resistance is experienced through the conductor. Resistance is as a result of collisions that occur between atoms of the pencil lead and charge carriers. Therefore, the longer the conductor, the more collisions, resulting in higher resistance. Task 2: Inductance of a Solenoid Number of turns (N) = 60 Length of the solenoid = 40mm = 0.04 m Diameter of the solenoid = m, radius = 2.1 m Cross-section area of the coil . Using r = 2.1 m, A = Relative permeability of pure iron () = 5000 (Assuming the iron nail is made of pure iron -99.8%) Permeability of free space () = 4 Inductance of the coil as measured in the lab = 0.03mH From equation 2, Rearranging this equation to make the subject: = = 19.08 Since, inductance is a measure of the coil’s resistance to change of current through the conductor, the larger the inductance, the lower the rate of current flow through the circuit. Inductance increases with increase in the number of turns, cross-section area and relative permeability of the core material. However, it reduces with increase in length. Table 3 below shows the results of inductance measured for different lengths of coil. Table 3: Measurement of inductance with different coil length Length of the coil (m) Inductance (H) 0.040 47 0.036 53 0.031 58 0.025 66 0.021 73 0.017 80 This is shown in the graph represented in figure 2 below: Figure 2: Variation of Inductance with coil length The graph clearly illustrates that as the length of the coil is increased, coil inductance drops provided that other factors are kept constant. The longer the length, the longer path and opposition of formation of magnetic flux. Task 3: Capacitance of a parallel plate capacitor Measured capacitance of the parallel plate capacitor = 8.21 F. Width of plate = 194 mm, height of plate = 179 mm. Area of the plates = 69452 mm2 Thickness of paper = 0.1 mm Thickness of foil = 0.01 mm Total thickness of the sandwich (foil-glue-paper-glue-foil) = 0.13mm. This is the distance that separates the two plates. Rearranging equation 3 to make relative permittivity the subject, we have, Relative permittivity, The relative permittivity of paper in the literature is 3.85. The difference between the literature value and the value obtained in the practical can be attributed to the specific material used to make the paper, and the material that separates the material with the foil. Sources of Experimental Errors and how they were minimized Sources of errors in this experiment include: i. Measurements – Errors could result from measurements of length of pencil leads, the coil and the capacitor plates. This may be due to reading errors or fault of the measurement equipment. However, this was minimized by being keen in every step of the experiments. ii. Another possible source of error could arise from the multimeter. Dirty lead pins could give invalid measurements of resistance, and the resistance of the connecting cables too is likely to lead to invalid results. Reference Read More

Task 3: Capacitance of a parallel plate capacitor Equipment Used: The following materials were used in carrying out this task: Aluminum foil for the plates An A4 paper sheet to be used as a dielectric material A glue stick for fixing the aluminum foil to either side of the dielectric material A pair of scissors and a ruler A multimeter or an LCR meter for measuring capacitance Method A parallel plate capacitor with a height of 17.9 cm and a width of 19.4 cm was made by gluing two sheets of aluminum foil to both sides of a paper.

After making the device, its capacitance was measured using a capacitance meter and recorded. A micrometer was then used to measure the thickness of the 5-layer sandwich (i.e. foil-glue-paper-glue-foil), and also the paper and the foil separately. This was done in order to get an estimation of the distance separating the capacitor plates (). The relative permittivity () of the paper dielectric was then obtained by re-arranging the capacitance equation. These results were compared with the expected relative permittivity of the material.

Results and Discussion Task 1: Resistance and Resistivity Part A: Measuring Resistivity Table 1: Measurement of resistance of three pencil leads Length of pencil lead (m) Resistance () 0.11 15.2 0.10 15.5 0.095 13 Average 0.102 14.57 From equation 1: Letting the subject of the formula, Diameter of the pencil lead was found to be = 2.02 x 10-3 mm = 2.02 x 10-6 m or radius = 1.01 x 10-6 m Cross-section area, . Using r = 1.01 x 10-6 m, Therefore, Resistivity, = = 4.57 cm With this value of resistivity, the pencil lead can be considered as a conductor.

Materials classified as conductors normally have bulk resistivity in the range of 10-8 to 10-4 ohm-cm. Part B: Variation of resistance with length Table 2: Measurement of resistance for different pencil leads Length of pencil lead (m) Resistance () 16 33.3 12 16.2 6.5 16 10.2 14 11.5 15.3 Figure 1: How resistance varies with the length of the conductor In figure 1 above, it is seen that a linear relationship exists between the length of the pencil lead conductor and resistance.

The longer the pencil lead, the more current resistance is experienced through the conductor. Resistance is as a result of collisions that occur between atoms of the pencil lead and charge carriers. Therefore, the longer the conductor, the more collisions, resulting in higher resistance. Task 2: Inductance of a Solenoid Number of turns (N) = 60 Length of the solenoid = 40mm = 0.04 m Diameter of the solenoid = m, radius = 2.1 m Cross-section area of the coil . Using r = 2.1 m, A = Relative permeability of pure iron () = 5000 (Assuming the iron nail is made of pure iron -99.8%) Permeability of free space () = 4 Inductance of the coil as measured in the lab = 0.

03mH From equation 2, Rearranging this equation to make the subject: = = 19.08 Since, inductance is a measure of the coil’s resistance to change of current through the conductor, the larger the inductance, the lower the rate of current flow through the circuit. Inductance increases with increase in the number of turns, cross-section area and relative permeability of the core material. However, it reduces with increase in length. Table 3 below shows the results of inductance measured for different lengths of coil.

Table 3: Measurement of inductance with different coil length Length of the coil (m) Inductance (H) 0.040 47 0.036 53 0.031 58 0.025 66 0.021 73 0.017 80 This is shown in the graph represented in figure 2 below: Figure 2: Variation of Inductance with coil length The graph clearly illustrates that as the length of the coil is increased, coil inductance drops provided that other factors are kept constant. The longer the length, the longer path and opposition of formation of magnetic flux.

Task 3: Capacitance of a parallel plate capacitor Measured capacitance of the parallel plate capacitor = 8.21 F.

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