Ohm's Law and Direct Current - Lab Report Example

LAB 2: OHM’S LAW AND DIRECT CURRENT by: Presented to: Course/ Class: University: City and state: Due date: Abstract The first task revolved around Ohms law for 1kΩ resistor. To ascertain its resistance, digital multimeter and AVO is employed in measuring voltage and current. The results are then plotted on voltage vs current graph. This graph will give line of best fit whose gradient represents resistance of a resistor. It is also apparent that as more voltage is applied in the circuit, the current also increases in the same direction. This observation affirms Ohms law where voltage varies directly with current. The reading of resistor colour code gives the upper and lower tolerance limits of the resistor. The result obtained in the measure i.e.  lies within the tolerance limits obtained by reading the colour code i.e. 1.05 kΩ and 0.950 kΩ. The second task is estimation of unknown resistor R2. During the experiment, voltage ranging from 0 to 15V was applied then the corresponding current recorded. The result is plotted on a graph of voltage vs current and gradient obtained to illustrate resistance of the unknown resistor. Introduction This paper is a report following an experiment covering electric power and Ohm’s law in addition to connections in series and parallel. In the experiment, the first task will involve Ohms law for the resistor. This will be followed by the second task that will entail estimation of resistance of an unknown resistor R2. Before conducting the experiment, it is imperative to understand the basics of the experiment i.e. Ohms law, electrical power, series and parallel connection of resistors. Theory Ohms Law Georg Ohm was a great German physicist who came up with Ohms law. According to him, electrical current passing through a resistor varies directly with voltage applied and inversely with resistance under the condition that the temperature is constant (Schagrin, 1963). This is the basic principle of Ohms Law, which can be summarized in the following relationship. Electrical Power Electrical power, P, represents the amount of energy in a circuit that has been produced or absorbed (Forbes, 2006). It is apparent that when voltage is supplied in a circuit, it produces power while the load within the circuit absorbs that power. According to Forbes, the formula for electrical power is as follows: ) Series resistors When resistors are connected in series, the equivalent resistance, Req is obtained as follows:  (Smith, 1966) Series connection is shown by the diagram: There is no doubt that the same current passes through all resistors whereas voltage dropped in each resistor is given by: Parallel Resistors This connection is shown by the figure below: The equivalent resistance, Req is obtained by the formulae:  (Williams, 2005) In such a connection; And; Task 1: Ohm’s Law for the Resistor  Method The steps followed were as follows: 1. The circuit was connected 2. Values for resistor voltage from 0 to 15v were injected and the corresponding current recorded. Voltage drop and Current was then recorded in tabular form. 3. Graph of voltage vs current was plotted 4. Gradient of the line of best fit obtained 5. Using DMM, the resistor was measured directly 6. Relationship between DMM and measured resistance compared 7. Resistor colour coding also obtained to ascertain tolerance limits 8. Maximum voltage that can be applied without exceeding power rating is confirmed through calculations. Results and discussions After setting up the circuit according to instructions, values for voltage between 0 and 15V and the corresponding currents are recorded as follows: I (A) V (volts) 0.01 0.017 0.001 0.95 0.0019 1.894 0.0027 2.878 0.0039 3.81 0.0049 4.77 0.0059 5.69 0.0069 6.69 0.0076 7.9 0.0089 8.55 0.01 9.97 0.011 10.93 0.012 11.99 0.013 12.92 0.014 13.91 Graph of Voltage vs. Electric Current From the graph, the equation is:  This means that the gradient is 991.7, which represent resistance in the circuit. Therefore, the resistor is  Ohm () Using the DMM to measure directly the resistance of the resistor, the value obtained is …………. How the measured gradient and the DMM value relate. In the process of estimating resistance using the Resistor Coding table, the first step is to note the colour codes, which are Brown, black, red and gold. The resistance is therefore  The tolerance band is as follows: Lower band:  Upper band:  According to the measurement, resistance is. This value is within the tolerance limit of resistor used. When 10V is applied, power dissipated in the resistor is given by: From the equation,  Hence, when Y is 10V, 0.010084 Using the power equation, power when 10V is applied is given by: Maximum voltage that can be applied to the resistor such that power rating is not exceeded is as follows: Task 2: Estimating the resistance of an unknown resistor R2 Method Steps followed were as follows 1. The circuit was connected 2. Values for resistor voltage from 0 to 15v were injected and the corresponding current recorded. Voltage drop and Current was then recorded in tabular form. 3. Graph of voltage vs current was plotted 4. Gradient of the line of best fit obtained 5. Using DMM, the resistor was measured directly 6. Relationship between DMM and measured resistance compared 7. Maximum voltage that can be applied without exceeding power rating is confirmed through calculations. Results and discussions The readings during the experiment are as follows I (A) V (Volts) 0.01 0.0052 3.6 0.77 7.6 1.637 13 2.876 18 3.897 23 4.85 28 5.82 33 6.77 38 7.8 Plotting Voltage vs Current The equation of the straight line is From the equation, gradient is 0.208, which represents resistance i.e.  Using the DMM to measure directly the resistance of the resistor, the value obtained is …………. How the measured gradient and the DMM value relate ……………… Whether the measured gradient and DMM value lie within the tolerance band of the resistor being used …………………. The maximum voltage that can be applied such that power rating of the resistor is not exceeded is calculated as follows: Conclusion The experiment carried out clearly demonstrates how resistance can be obtained by plotting graphically values of current in A and correspond voltage in volts. The gradient from this graph of Voltage vs Current represents the resistance. This value is correct given that it lies within the tolerance limit of a resistor that is obtained through a colour code reading. Reference List Forbes TB 2006, Engineering System Dynamics: A Unified Graph Centered Approach, CRC Press, Boca Raton. Schagrin, ML 1963, "Resistance to Ohm's Law", American Journal of Physics, Vol. 31, no. 7, pp. 536–47. Smith, RJ 1966, Circuits, Devices and Systems, Wiley International Edition, New York. Williams, T 2005, The Circuit Designer's Companion, Butterworth-Heinemann, Oxford. Read More