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Lab 4

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Evandro Conceicao

This document reports on an electrical engineering lab experiment involving the superposition principle and Thevenin's theorem. The experiment used resistors, power supplies, and multimeters to measure voltages and currents in circuits. For the superposition principle part, measurements were taken with individual and combined sources and compared. For Thevenin's theorem, voltage and current across a variable load resistor were measured and recorded in a table to determine the equivalent resistance and voltage of the original circuit.

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nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 1 Table of Contents Introduction......................................................................................................................................2 Theory ..............................................................................................................................................2 Figure: 5............................................................................................................................................4 Pre lab ..............................................................................................................................................4 Figure 3 .............................................................................................................................................5 Equipment used ................................................................................................................................6 Proceedures ......................................................................................................................................6 Part: 1 of the report. The superposition principle ...................................................................................6 Part: 2 of the report. Thevenins theorem.............................................................................................7 Figure 4 .............................................................................................................................................7 Results ..............................................................................................................................................7 Part 1 of the lab: the superposition principle. ..................................................................................8 Table 1...............................................................................................................................................8 Part 2 of the lab: Thevenins theory .....................................................................................................8 Table 2...............................................................................................................................................8 Discussions of results ......................................................................... Error! Bookmark not defined. Part 1 of the lab ................................................................................... Error! Bookmark not defined. Part 2 of the lab ................................................................................... Error! Bookmark not defined. Conclusion ........................................................................................................................................9 BIBLIOGRAPHY..................................................................................................................... 10
nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 2 INTRODUCTION Electricity is an essential part of the modern life experience, and as an engineer it is essential to know how it behaves and responds to changes in its trajectory. A very important skill that any person analyzing a circuit must have is the complete understanding of the superposition principle of analyzing circuits. These law states that the value of any variable may be found by the sum of the values of that variable produced by each of the values of that variable produced by each of the excitation sources( power sources) acting separately. Another such important law is the law which lets you reduce a circuit to its resistance thevenin and voltage thevenin. The thevenin`s theorem may be explained as a virus that reduces a complex circuit by its simplest equivalent. Therefore the primary goal of this laboratory experiment is to help students practically prove the concepts of the superposition principle and to prove that an equivalent thevenin circuit has the same Req and Veq as the original circuit before it was reduced. Therefore in addition this lab shall consist of the following major parts namely, table of contents, introduction, theory, pre-lab, equipment used, procedures, results, conclusion, references. THEORY Ohms law states that the resistance across component within a circuit is directly proportional to that components voltage but inversely proportional to its current. Resistance=voltage/current (EQUATION 1) KVL (Kirchhoff`s voltage law) states that the sum of all the voltages around a closed loop is equal to zero. This in addition is in accord with the law of conservation of energy that states that energy cannot be made nor destroyed it can just be changed from one form to another. For ease of understanding lets look at Figure:1 Applying KVL around loop 1 Vs V2 V3 V1 = 0 Loop 1
nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 3 Vs = V1+ V2 + V3 Vs = IsR1 + IsR2 + IsR3 Vs = (R1 + R2 + R3) Is The equivalent resistance for resistors in series may be replaced with a single resistance. This is a direct extension of the Kirchhoffs law therefore Req = R1 + R2 + R3 only for resistors in series. A node of a network is defined as a point where two or more branches are joined. If three or more branches join at a node, then that node is called a principal node or junction. KCL (Kirchhoffs current law) states that the sum of all currents entering a node is equal to the sum of all currents leaving the node. This however also verifies the law of conservation of energy at a node, this law is stated above on the second bullet. For simplicity let us consider the single node circuit illustrated in Figure: 2. IS - I1 - I2 - I3 = 0 IS = I1 + I2 + I3 Equivalent resistance for resistors in parallel is denoted by the following equation REQ = 1 / (1 / R1 + 1 / R2 + 1 / R3). Superposition principle states that the value of any variable may be found as the sum of the values of that variable produced by each of the values of that variable produced by each of the excitation sources acting separately. This is done by Only using one of the sources separately by setting the voltage source to zero and replacing it by a short circuit. Solve for the currents. Insert the voltage source and set the current source to zero by replacing it with an open circuit. Solve for currents` Add the currents since the total current is the algebraic sum of the independent currents provided by each source. From the currents using ohms law (equation 1) other properties may be found like voltage
nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 4 Thevenin`s theorem states that any network consisting of linear resistance and independent sources may be replaced at a given pair of nodes by an equivalent circuit consisting of a single voltage source and a series resistor. This is shown below by figure 5 Thevenin equivalent circuit FIGURE: 5 Figure: 5 shows how the reduction process due to the thevenin principle. From a circuit with 3 resistors to a circuit with 1 equivalent resistor in series with the power source which is the voltage thevenin... PRE LAB For the pre- lab that follows these below are the figures used. Figure :2 was used for question 1
nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 5 FIGURE 3 Figure 3 was used for questions 2, 3, 4 respectivelly.
nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 6 EQUIPMENT USED 2 power supplies 3 digital Multimeters (D.M.M) will serve as both the voltmeter and the ammeter) for the laboratory experiment 2 decade resistor box(s). 1 decade resistor box with a variable resistor to be used as the load during part 2 of the lab. Different conductor cables PROCEEDURES Part: 1 of the report. The superposition principle Construct the circuit illustrated in figure 2. Remember to set the power supplies to the required values of 10V and 5V. Supply voltages should be set prior to connection to the circuit. Measure the value of resistors. R1, ( nominally 1.8 K ), R2 (1.2K) and R3 (1.2K) Note that quantities V1, V2 and VR1, VR2 and VR3 are measured using the Multimeter. Currents IR1, IR2 and IR3 are to be calculated using Ohms Law (equation 1) above.. Repeat this for each of the following conditions: Both sources on. With the 10 V (VS1) source replaced with a short circuit and 5 V on. With the 10 V source on and the 5 V (VS2) source replaced with a short circuit. Measure and record the data as required in Table 1 below Using the values measured for R1, R2, R3, V1, and V2 calculate the theoretical values of VR1, VR2, VR3, IR1, IR2 and IR3. The theoretical values are part of the pre-lab exercise calculated outside the lab. These are provided above. Briefly illustrate that the principle of superposition appears to be valid by comparison.
nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 7 Part: 2 of the report. Thevenins theorem Set up the circuit illustrated in Figure 3. Note that the load resistor is variable; use a decade boxes Set the power supply to 10V Vary the value of the load resistor (Rload) from 0 in intervals of 20 to any large value e.g. infinity. Record the voltage and current readings as indicated in Table 2 below. Note that one can easily take voltage and current measurements with a single Multimeter. Figure 4 shows the same circuit except that the physical location of the ammeter has been relocated. Note that voltage is measured between the top and middle terminals, and current flowing in the bottom and out the middle. Determine the Thevenin equivalent of the circuit illustrated in Figure 3 below.. First disconnect the load resistor and measure the open circuit voltage across load terminals (record the values measured, VOC). Then introduce a short circuit across load terminals (load removed) and measure the short circuit current, ISC. Record all the values in table 2 below in the results section of the report. FIGURE 4 RESULTS
nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 8 Part 1 of the lab: the superposition principle. Actual Measured Values: R1 = 1.84K ; R2 = 1.99K ; and R3 = 1.2K TABLE 1 Part I Part II Part III Theoretical Experimental Theoretical Experimental Theoretical Experimental VS1 10V 10V 0 V 0V 10 V 10V VS2 0 0V 5 V 5V 5 V 5V VR1 7.5V 7.4V 1.875V 1.85V 5.625V 5.56V VR2 2.5V 2.5V 1.875V 1.85V 4.375V 4.38V VR3 2.5V 2.5V 3.125V 3.10V 0.625V 0.57V IR1 4.2mA 4.02mA 1.04mA 1mA 3.125mA 3.02mA IR2 2.08mA 2.01mA 1.56mA 1.55mA 3.65mA 3.68mA IR1 2.08mA 2.08mA 2.6mA 2.6mA 0.52mA 0.47mA The values acquired in the theoretical columns were acquired during the pre-lab by using the various appropriate laws and theories discussed above in the theory section. Part 2 of the lab: Thevenins theory TABLE 2 Original Circuit Thevenin Equivalent Circuit RLOAD ILOAD (mA) VLOAD(mV) ILOAD (mA) VLOAD(mV) 0 4.15 0.1 4.09 0.1 20 4.07 81.7 4.09 80 40 4.00 160.5 3.98 159.1 60 3.95 238 3.86 224 80 3.87 306 3.86 295 99.4 3.79 380 3.79 360
180.00 160.00 140.00 120.00 100.00 80.00 60.00 40.00 20.00 0.00 -20.00 -40.00 nd Vol tage (mV) Qualificat ion (B. Eng., 2 Voltage Vs Current graph original 0.00 0.10 81.70 circuit 160.50 0.00 0.00 0.00 0 1 2 3 4 5 6 7 8 Currents (mA) Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 9 Compare your results with the theoretically calculated values. Explain the why the values are not the same! CONCLUSION In conclusion with all of the above information and all of the theoretical similarities in the results obtained experimentally it is safe to assume that ohms law explains how any circuit operates in terms of voltage, current and resistance. In addition the only thing that changes the results is the problem of internal resistance, this change is so small that it can be considered negligible. Furthermore this knowledge will aid me in my engineering career both theoretically and practically.
nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 10 BIBLIOGRAPHY bird, j. (2003). electrical circuit theory. sidney: newnes. chand, S. (2000). a textbook of electrical technology. singapore: newnes.

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Lab 4

  • 1. nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 1 Table of Contents Introduction......................................................................................................................................2 Theory ..............................................................................................................................................2 Figure: 5............................................................................................................................................4 Pre lab ..............................................................................................................................................4 Figure 3 .............................................................................................................................................5 Equipment used ................................................................................................................................6 Proceedures ......................................................................................................................................6 Part: 1 of the report. The superposition principle ...................................................................................6 Part: 2 of the report. Thevenins theorem.............................................................................................7 Figure 4 .............................................................................................................................................7 Results ..............................................................................................................................................7 Part 1 of the lab: the superposition principle. ..................................................................................8 Table 1...............................................................................................................................................8 Part 2 of the lab: Thevenins theory .....................................................................................................8 Table 2...............................................................................................................................................8 Discussions of results ......................................................................... Error! Bookmark not defined. Part 1 of the lab ................................................................................... Error! Bookmark not defined. Part 2 of the lab ................................................................................... Error! Bookmark not defined. Conclusion ........................................................................................................................................9 BIBLIOGRAPHY..................................................................................................................... 10
  • 2. nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 2 INTRODUCTION Electricity is an essential part of the modern life experience, and as an engineer it is essential to know how it behaves and responds to changes in its trajectory. A very important skill that any person analyzing a circuit must have is the complete understanding of the superposition principle of analyzing circuits. These law states that the value of any variable may be found by the sum of the values of that variable produced by each of the values of that variable produced by each of the excitation sources( power sources) acting separately. Another such important law is the law which lets you reduce a circuit to its resistance thevenin and voltage thevenin. The thevenin`s theorem may be explained as a virus that reduces a complex circuit by its simplest equivalent. Therefore the primary goal of this laboratory experiment is to help students practically prove the concepts of the superposition principle and to prove that an equivalent thevenin circuit has the same Req and Veq as the original circuit before it was reduced. Therefore in addition this lab shall consist of the following major parts namely, table of contents, introduction, theory, pre-lab, equipment used, procedures, results, conclusion, references. THEORY Ohms law states that the resistance across component within a circuit is directly proportional to that components voltage but inversely proportional to its current. Resistance=voltage/current (EQUATION 1) KVL (Kirchhoff`s voltage law) states that the sum of all the voltages around a closed loop is equal to zero. This in addition is in accord with the law of conservation of energy that states that energy cannot be made nor destroyed it can just be changed from one form to another. For ease of understanding lets look at Figure:1 Applying KVL around loop 1 Vs V2 V3 V1 = 0 Loop 1
  • 3. nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 3 Vs = V1+ V2 + V3 Vs = IsR1 + IsR2 + IsR3 Vs = (R1 + R2 + R3) Is The equivalent resistance for resistors in series may be replaced with a single resistance. This is a direct extension of the Kirchhoffs law therefore Req = R1 + R2 + R3 only for resistors in series. A node of a network is defined as a point where two or more branches are joined. If three or more branches join at a node, then that node is called a principal node or junction. KCL (Kirchhoffs current law) states that the sum of all currents entering a node is equal to the sum of all currents leaving the node. This however also verifies the law of conservation of energy at a node, this law is stated above on the second bullet. For simplicity let us consider the single node circuit illustrated in Figure: 2. IS - I1 - I2 - I3 = 0 IS = I1 + I2 + I3 Equivalent resistance for resistors in parallel is denoted by the following equation REQ = 1 / (1 / R1 + 1 / R2 + 1 / R3). Superposition principle states that the value of any variable may be found as the sum of the values of that variable produced by each of the values of that variable produced by each of the excitation sources acting separately. This is done by Only using one of the sources separately by setting the voltage source to zero and replacing it by a short circuit. Solve for the currents. Insert the voltage source and set the current source to zero by replacing it with an open circuit. Solve for currents` Add the currents since the total current is the algebraic sum of the independent currents provided by each source. From the currents using ohms law (equation 1) other properties may be found like voltage
  • 4. nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 4 Thevenin`s theorem states that any network consisting of linear resistance and independent sources may be replaced at a given pair of nodes by an equivalent circuit consisting of a single voltage source and a series resistor. This is shown below by figure 5 Thevenin equivalent circuit FIGURE: 5 Figure: 5 shows how the reduction process due to the thevenin principle. From a circuit with 3 resistors to a circuit with 1 equivalent resistor in series with the power source which is the voltage thevenin... PRE LAB For the pre- lab that follows these below are the figures used. Figure :2 was used for question 1
  • 5. nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 5 FIGURE 3 Figure 3 was used for questions 2, 3, 4 respectivelly.
  • 6. nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 6 EQUIPMENT USED 2 power supplies 3 digital Multimeters (D.M.M) will serve as both the voltmeter and the ammeter) for the laboratory experiment 2 decade resistor box(s). 1 decade resistor box with a variable resistor to be used as the load during part 2 of the lab. Different conductor cables PROCEEDURES Part: 1 of the report. The superposition principle Construct the circuit illustrated in figure 2. Remember to set the power supplies to the required values of 10V and 5V. Supply voltages should be set prior to connection to the circuit. Measure the value of resistors. R1, ( nominally 1.8 K ), R2 (1.2K) and R3 (1.2K) Note that quantities V1, V2 and VR1, VR2 and VR3 are measured using the Multimeter. Currents IR1, IR2 and IR3 are to be calculated using Ohms Law (equation 1) above.. Repeat this for each of the following conditions: Both sources on. With the 10 V (VS1) source replaced with a short circuit and 5 V on. With the 10 V source on and the 5 V (VS2) source replaced with a short circuit. Measure and record the data as required in Table 1 below Using the values measured for R1, R2, R3, V1, and V2 calculate the theoretical values of VR1, VR2, VR3, IR1, IR2 and IR3. The theoretical values are part of the pre-lab exercise calculated outside the lab. These are provided above. Briefly illustrate that the principle of superposition appears to be valid by comparison.
  • 7. nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 7 Part: 2 of the report. Thevenins theorem Set up the circuit illustrated in Figure 3. Note that the load resistor is variable; use a decade boxes Set the power supply to 10V Vary the value of the load resistor (Rload) from 0 in intervals of 20 to any large value e.g. infinity. Record the voltage and current readings as indicated in Table 2 below. Note that one can easily take voltage and current measurements with a single Multimeter. Figure 4 shows the same circuit except that the physical location of the ammeter has been relocated. Note that voltage is measured between the top and middle terminals, and current flowing in the bottom and out the middle. Determine the Thevenin equivalent of the circuit illustrated in Figure 3 below.. First disconnect the load resistor and measure the open circuit voltage across load terminals (record the values measured, VOC). Then introduce a short circuit across load terminals (load removed) and measure the short circuit current, ISC. Record all the values in table 2 below in the results section of the report. FIGURE 4 RESULTS
  • 8. nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 8 Part 1 of the lab: the superposition principle. Actual Measured Values: R1 = 1.84K ; R2 = 1.99K ; and R3 = 1.2K TABLE 1 Part I Part II Part III Theoretical Experimental Theoretical Experimental Theoretical Experimental VS1 10V 10V 0 V 0V 10 V 10V VS2 0 0V 5 V 5V 5 V 5V VR1 7.5V 7.4V 1.875V 1.85V 5.625V 5.56V VR2 2.5V 2.5V 1.875V 1.85V 4.375V 4.38V VR3 2.5V 2.5V 3.125V 3.10V 0.625V 0.57V IR1 4.2mA 4.02mA 1.04mA 1mA 3.125mA 3.02mA IR2 2.08mA 2.01mA 1.56mA 1.55mA 3.65mA 3.68mA IR1 2.08mA 2.08mA 2.6mA 2.6mA 0.52mA 0.47mA The values acquired in the theoretical columns were acquired during the pre-lab by using the various appropriate laws and theories discussed above in the theory section. Part 2 of the lab: Thevenins theory TABLE 2 Original Circuit Thevenin Equivalent Circuit RLOAD ILOAD (mA) VLOAD(mV) ILOAD (mA) VLOAD(mV) 0 4.15 0.1 4.09 0.1 20 4.07 81.7 4.09 80 40 4.00 160.5 3.98 159.1 60 3.95 238 3.86 224 80 3.87 306 3.86 295 99.4 3.79 380 3.79 360
  • 9. 180.00 160.00 140.00 120.00 100.00 80.00 60.00 40.00 20.00 0.00 -20.00 -40.00 nd Vol tage (mV) Qualificat ion (B. Eng., 2 Voltage Vs Current graph original 0.00 0.10 81.70 circuit 160.50 0.00 0.00 0.00 0 1 2 3 4 5 6 7 8 Currents (mA) Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 9 Compare your results with the theoretically calculated values. Explain the why the values are not the same! CONCLUSION In conclusion with all of the above information and all of the theoretical similarities in the results obtained experimentally it is safe to assume that ohms law explains how any circuit operates in terms of voltage, current and resistance. In addition the only thing that changes the results is the problem of internal resistance, this change is so small that it can be considered negligible. Furthermore this knowledge will aid me in my engineering career both theoretically and practically.
  • 10. nd Qualificat ion (B. Eng., 2 Yea r) ELC 520S ELECTRICAL PRINCIPLES 124 Report 4 10 BIBLIOGRAPHY bird, j. (2003). electrical circuit theory. sidney: newnes. chand, S. (2000). a textbook of electrical technology. singapore: newnes.