Practical: Resistance, Inductance and Capacitance - Lab Report Example

Practical: Resistance, Inductance and Capacitance Name: Student No. Introduction Electronic devices cannot function without basic components such as resistors, capacitors and inductors which form the basics of electronics. Each of these components play a different role in electronic circuits. An important characteristic of electronic circuits with these components is the relationship between the current flowing through the components and the voltage across them. The thermal energy dissipated by a resistor, the energy stored in electric field between the plates of a capacitor, and the energy stored in the magnetic field around the solenoid coil of an inductor all limit the amount of current that flows through an electric circuit (Morrison, 2002). Resistance (R) Resistance is a measure of how an electronic component resists the flow of electric current through a material or device. A resistor functions by dissipating energy in the form of heat. Resistance is usually measured in Ohms (). Ohm's law defines resistance as the ratio of applied voltage to current, represented by the equation: There are four main factors that can affect the resistance of flow of electric current through a material. These are: conductivity of the material, the length of the conductor, its cross-section area and the temperature of the conductor. In this experiment, our interest will be on how the length of a conductor affects the resistance of current flow through it, assuming that the conductor material, the cross-sectional area and the temperature all remain constant. The relationship between resistance and these factors is represented by the equation: Where: R – Resistance () – Resistivity () – Length (m) A – Area () Inductance (L) An inductor is an electronic component made of a conductor coil. Current passing through the coil produces a magnetic field which stores energy magnetically. The amount of magnetic energy varies with the amount of current flowing through the coil (Morrison, 2002). Inductance of a coil is measured in Henries (H) or milliHenries (mH). Like resistance, the inductance of a coil is also determined by factors such as the cross-sectional area of the coil, the length of the coil, the number of turns that make up the coil, and the core material of the coil. The core material used determines the magnetic permeability of an inductor. All these factors relate to inductance by the equation below: Where: L – Coil inductance N- Number of turns A – Average cross-sectional area – Length of the solenoid – Permeability of free space (4) – Relative permeability Capacitance (C) A capacitor stores electric current in the form of electric charge across its plates. The ability of a device to store electric charge is termed as capacitance. A capacitor is made of two parallel plates that are separated by a dielectric. Electrical charges are stored on the parallel plates. Capacitance is measured in Farads, but since a farad is too large, micro-Farads are used. Capacitance is defined as the ratio of electric charge, q (in Coulombs) to the voltage supplied across the plates (V). Thus, There are various factors that affect the capacitance of a capacitor. These include; the cross-sectional area of the parallel plates, the distance of separation of the plates, and the type of material used as a dielectric material. The equation that relates capacitance to these factors is as stated below: Where: C – Capacitance A – Area of the plates – Permittivity of free space (8.85 10 -12) – Relative permittivity – the distance between the plats Objectives i. To investigate the equation relating resistance of a pencil lead to its length, cross-sectional area and resistivity. ii. To investigate the equation used to describe the inductance of a long thin solenoid coil. iii. To investigate the equation that describes the capacitance of a parallel plate capacitor. Experimental Methodology Task 1: Resistance and Resistivity Equipment and Materials Needed: Five HB grade pencils of the same length. A pencil sharpener. Crocodile clip connectors and connecting leads. A micrometer or Vernier for measuring the diameter of the pencil leads. A ruler for measuring the length of the pencil leads. A multimeter for measuring the resistance of the pencil leads. Method: Part A: Measuring Resistivity First, all the five pencils were sharpened to expose a suitable length of the leads. Using crocodile clip connectors and leads, the multimeter was connected to the ends of the pencil lead, one at a time, to measure the resistance of current flow through the leads. In order to eliminate random variations in the pencil leads due to variations of clay and graphite, the average length and average resistance of all the three pencils was determined. The diameter of the pencil core was then measured using a micrometer, and then used to calculate the cross-sectional area of the clay-graphite lead conductor. The results obtained in this part were used to calculate the resistivity of the pencil lead conductor. Part B: Variation of resistance with length Three pencils were sharpened at different lengths, and the resistance across their leads measured using a multimeter. The resistance of each lead was recorded against it length to plot the graph of resistance against length on a scatter graph. The graph was then used to examine how resistance varies with conductor length. Task 2: Inductance of a Solenoid Coil Equipment and Materials Needed Iron nail Insulated copper wire of suitable length A ruler A multimeter A piece of sandpaper (used to remove insulation at the ends of the copper wire) Method To construct a solenoid coil, the copper wire was wound around the nail to make 60 turns. After construction of the coil was completed, the inductance of the coil was measured using a multimeter and recorded. The length of the solenoid coil was measured using a ruler and its diameter measured using a vernier and recorded down. The diameter was used to calculate the cross-sectional area of the coil. In order to investigate the effect of coil length on inductance, the length of the solenoid was varied by stretching or compressing the coil, taking inductance measurements at each length. Task 3: Capacitance of a parallel plate capacitor Equipment and Materials Needed A multimeter Aluminum foil A4 paper (used as a dielectric material) A glue stick A ruler A pair of scissors Method A parallel plate capacitor with a height of 18.7 cm and a width of 14.9 cm was constructed by gluing two aluminum sheets on either sides of the A4 paper. After the capacitor was constructed, its capacitance was measured using the multimeter and recorded. The micrometer was then used to measure the thickness of the foil-glue-paper-glue-foil sandwich and also the paper and foil separately, to obtain the distance of separation (d) between the capacitor plates. The relative permittivity of the paper dielectric was then calculated using the capacitance equation. The results obtained were compared with the expected relative permittivity of paper in literature. Results and Discussion Task 1: Resistance and Resistivity Part A: Measuring Resistivity Table 1: Measurements of resistance of five pencil leads Length of pencil lead (m) Resistance () 0.085 14.6 0.088 15.5 0.090 16.4 0.081 20.6 0.083 15.4 Average 0.0854 16.5 Using the equation: We let the subject of the formula, Diameter of the pencil lead = 2.23 mm. Thus, r = 0.00112 m Cross-section area, Therefore, Resistivity, = = 7.61 m The resistivity value obtained falls in the range of conductor materials. Thus, we can classify a pencil lead as a conductor. Part B: Variation of Resistance with Length Table 2: Measurements of how resistance varied with the length of the pencil leads Length of pencil lead (cm) Resistance () 17.5 33.3 14.5 16.2 11.3 16 Figure 1 below is a plot of resistance against length on a scatter graph with a line of best fit. From this graph, it can be observed that as the length of the pencil lead increases, its resistance to current flow increases. This is because, as the length increases, electrons have more distance to travel and more collisions between the electrons and atoms of the material occur, reducing current flow. Figure 1: Variation of Resistance with Length Task 2: Inductance of a Solenoid Coil N = 75 Length of the solenoid () = 5 cm Diameter of the solenoid = mm, radius = 0.03512 m Cross-section area of the coil Permeability of free space () = 4 Relative permeability of pure iron () = 5000 Assumption: the iron nail is 99.8% pure iron Measured inductance of the coil = 0.069mH Using the equation: Making the subject: = = 0.126 Inductance measures the resistance of change of current flow through the coil. The larger the value of inductance, the lower the rate of current change in a circuit. The results of the measurements of inductance for different lengths of the solenoid coil are as recorded in the table below. Table 3: Inductance measured for different lengths of the solenoid coil Length of the coil (cm) Inductance (mH) 7 0.056 6 0.063 5 0.069 4 0.079 3 0.089 A plot of inductance against the length of the coil is shown in figure 2. From the graph, it can clearly be seen that as the coil length increases, the value of inductance reduces. This is because longer coil length increases the path of magnetic field flux, reducing the field force. Figure 2: A plot of inductance against coil length Task 3: Capacitance of a parallel plate capacitor Capacitance of the parallel plate capacitor = 4.14 F. Height of plate = 187 mm. Width of plate = 149 mm. Area of the plates = mm2 Thickness of foil = 0.007 mm Thickness of paper = 0.09 mm The distance that separates the two plates = 0.104mm. We can rearrange the capacitance equation to make relative permittivity the subject, so that: Relative permittivity, Relative permittivity is dependent on the characteristics of the dielectric. The reference relative permittivity of paper is 3.85. This difference may be brought about by other external factors such as temperature, moisture etc. and the physical characteristics of the paper used. Sources of Experimental Errors i. Internal resistance of the connectors and leads. This could result in inaccurate measurements of resistance of the pencil leads. Also, the resistance of the multimeter is not finite, and is likely to draw some current from the circuit. This is likely to affect the resistance measured across the circuit. The remedy to these errors is to reset and calibrate the multimeter. ii. Measurement errors could also result when measuring the length and diameters of pencil leads and the coil, and also when measuring the height and width of the capacitor. The accuracy of the micrometer screw gauge and Vernier is 0.01 mm. These limits the measurements to 2 decimal places, which may affect the accuracy of the measurements. Reference Read More

85 10 -12) – Relative permittivity – the distance between the plats Objectives i. To investigate the equation relating resistance of a pencil lead to its length, cross-sectional area and resistivity. ii. To investigate the equation used to describe the inductance of a long thin solenoid coil. iii. To investigate the equation that describes the capacitance of a parallel plate capacitor. Experimental Methodology Task 1: Resistance and Resistivity Equipment and Materials Needed: Five HB grade pencils of the same length.

A pencil sharpener. Crocodile clip connectors and connecting leads. A micrometer or Vernier for measuring the diameter of the pencil leads. A ruler for measuring the length of the pencil leads. A multimeter for measuring the resistance of the pencil leads. Method: Part A: Measuring Resistivity First, all the five pencils were sharpened to expose a suitable length of the leads. Using crocodile clip connectors and leads, the multimeter was connected to the ends of the pencil lead, one at a time, to measure the resistance of current flow through the leads.

In order to eliminate random variations in the pencil leads due to variations of clay and graphite, the average length and average resistance of all the three pencils was determined. The diameter of the pencil core was then measured using a micrometer, and then used to calculate the cross-sectional area of the clay-graphite lead conductor. The results obtained in this part were used to calculate the resistivity of the pencil lead conductor. Part B: Variation of resistance with length Three pencils were sharpened at different lengths, and the resistance across their leads measured using a multimeter.

The resistance of each lead was recorded against it length to plot the graph of resistance against length on a scatter graph. The graph was then used to examine how resistance varies with conductor length. Task 2: Inductance of a Solenoid Coil Equipment and Materials Needed Iron nail Insulated copper wire of suitable length A ruler A multimeter A piece of sandpaper (used to remove insulation at the ends of the copper wire) Method To construct a solenoid coil, the copper wire was wound around the nail to make 60 turns.

After construction of the coil was completed, the inductance of the coil was measured using a multimeter and recorded. The length of the solenoid coil was measured using a ruler and its diameter measured using a vernier and recorded down. The diameter was used to calculate the cross-sectional area of the coil. In order to investigate the effect of coil length on inductance, the length of the solenoid was varied by stretching or compressing the coil, taking inductance measurements at each length.

Task 3: Capacitance of a parallel plate capacitor Equipment and Materials Needed A multimeter Aluminum foil A4 paper (used as a dielectric material) A glue stick A ruler A pair of scissors Method A parallel plate capacitor with a height of 18.7 cm and a width of 14.9 cm was constructed by gluing two aluminum sheets on either sides of the A4 paper. After the capacitor was constructed, its capacitance was measured using the multimeter and recorded. The micrometer was then used to measure the thickness of the foil-glue-paper-glue-foil sandwich and also the paper and foil separately, to obtain the distance of separation (d) between the capacitor plates.

The relative permittivity of the paper dielectric was then calculated using the capacitance equation. The results obtained were compared with the expected relative permittivity of paper in literature. Results and Discussion Task 1: Resistance and Resistivity Part A: Measuring Resistivity Table 1: Measurements of resistance of five pencil leads Length of pencil lead (m) Resistance () 0.085 14.6 0.088 15.5 0.090 16.4 0.081 20.6 0.083 15.4 Average 0.0854 16.5 Using the equation: We let the subject of the formula, Diameter of the pencil lead = 2.23 mm. Thus, r = 0.

00112 m Cross-section area, Therefore, Resistivity, = = 7.

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