EET310_Lab1_Charles Haskett

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EET310

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Dec 6, 2023

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EET310 Circuit Analysis Instructor: Neeta Tivare Lab 1 Superposition Theorem Student Name: Charles Haskett Honor Pledge: I pledge to support the Honor System of ECPI. I will refrain from any form of academic dishonesty or deception, such as cheating or plagiarism. I am aware that as a member of the academic community, it is my responsibility to turn in all suspected violators of the honor code. I understand that any failure on my part to support the Honor System will be turned over to a Judicial Review Board for determination. I will report to the Judicial Review Board hearing if summoned.

2 Charles Haskett Date:

3 Table of Contents ABSTRACT ................................................................................................................................................ 3 INTRODUCTION ....................................................................................................................................... 3 PROCEDURE ............................................................................................................................................. 4 Part I: Design a multisource circuit in Multisim ....................................................................................... 4 Part II: Remove Vs2 from the circuit” ....................................................................................................... 4 Part III: Multisource Circuit with 10 V source removed ........................................................................... 5 ANALYSIS & RESULTS ............................................................................................................................ 6 Calculations ............................................................................................................................................. 6 Tables ....................................................................................................................................................... 7 Figures ..................................................................................................................................................... 7 CONCLUSION ......................................................................................................................................... 12 REFERENCES .......................................................................................................................................... 13

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4 ABSTRACT In this lab the student will use the Multisim software to verify their calculations of a multisource circuit. The student will use the superposition theorem to analysis a circuit. The student will use various formulas to calculate the total resistance and the current through a component. This will reinforce the students learning of the superposition theorem. I NTRODUCTION Superposition theorem is a circuit analysis theorem used to solve a network where there are two or more sources present and connected. The superposition theorem states that in any circuit having multiple independent sources, the response of an element in the circuit will be equal to the algebraic sum of the responses of that element by considering one source at a time. There are four steps in using the superposition theorem. The first step is to select one of the multiple sources that are present in the circuit. Except for the selected source, all other sources must be replaced by their internal impedance. Then evaluate the current flowing through or the voltage drop across a particular element within the circuit. Considering a single source is repeated for all the other sources in the circuit. Upon obtaining the respective response for the individual source, perform the summation of all the responses to get the overall voltage drop or current through the circuit element.

5 PROCEDURE Components needed: 1. Multisim Part I: Design a multisource circuit in Multisim 1. Construct the circuit show in Figure1. This circuit has two voltage sources connected to a common reference ground. Figure 1: Multisource Circuit Part II: Remove Vs2 from the circuit” 1. Remove the 5V source and place a jumper between the points C and D, as shown in Figure2. This jumper represents the internal resistance of the 5 V power supply. Figure 2: Multisource Circuit with V S2 Removed 2. Compute the total resistance, R T , as seen by the +10V source. (R T : between points A/B) Temporarily remove the +10V source and measure the resistance between points A and B using a multimeter DMM (disconnect ground while measuring resistance) to confirm the calculation. Record the computed and measured values in Table 1.

6 3. Use the source voltage, V S1 , and the total resistance to compute the total current, I T , from the +10.0 V source. I T = V S1 / R T 4. This current is through R 1 , so record it as I 1 in Table 2. Use the current divider rule to determine the currents in R 2 and R 3 . The current divider rule for I 2 and I 3 is: I 2 = I T (R 3 / (R 2 + R 3 )) Part III: Multisource Circuit with 10 V source removed 1. Reinstate the 5 V source and remove the 10 V source (by placing a short between points A and B). As shown in Figure 3. Figure 3: Multisource Circuit with V S1 Removed 2. Compute the RT between points C and D. Measure the resistance to confirm the calculation. Record the computed and measured resistance in Table 1. 3. Use the 5V source voltage, V S2 , and the total resistance to compute the total current, I T , from the +10.0 V source. This current is through R 1 , so record it as I 1 in Table 2. I T = V S1 / R T 4. Use the current divider rule to determine the currents in R 2 and R 3 . The current divider rule for I 2 and I 3 is: I 2 = I T (R 1 / (R 1 + R 2 )) 5. Then connect the +10 V source as illustrated in Figure 1, compute the algebraic sum of currents and voltage listed in Table2. Then measure and record the respective currents and voltage. The measured voltages should agree with the algebraic sum. Record the measurements in Table 2.

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7 ANALYSIS & RESULTS Calculations R T = R 1 || (R 2 + R 3 ) R T = 100 Ω || (100 Ω + 100 Ω) R T = 100 Ω || 1 / (1/100 Ω + 1/100 Ω) R T = 100 Ω || 1 / (0.01 + 0.01) R T = 100 Ω || 1 / 0.02 R T = 100 Ω + 50 R T = 150 Ω I T = V S1 / R T I T = 10 V / 150 Ω I T = 0.066 A = 66 mA I 2 = I T (R 3 / (R 2 + R 3 )) I 2 = (66 mA) (100 Ω / (100 Ω + 100 Ω)) I 2 = (66 mA) (100 Ω / 200 Ω) I 2 = (66 mA) (0.5 Ω) I 2 = 0.033 A = 33 mA R T = (R 1 + R 2 ) || R 3 R T = (100 Ω + 100 Ω) || 100 Ω R T = 1 / (1/100 Ω + 1/100 Ω) || 100 Ω R T = 1 / (0.01 + 0.01) || 100 Ω R T = 1 / 0.02 || 100 Ω R T = 50 Ω + 100 Ω R T = 150 Ω I 2 = I T (R 1 / (R 1 + R 1 )) I 2 = (33 mA) (100 Ω / (100 Ω + 100 Ω)) I 2 = (33 mA) (100 Ω / 200 Ω) I 2 = (33 mA) (0.5 Ω) I 2 = 16.7 mA V 2 = (I 2 ) (R 2 ) V 2 = (33 mA) (100 Ω) V 2 = 3.3 V V 2 = (I 2 ) (R 2 ) V 2 = (16.7 mA) (100 Ω) V 2 = 1.67 V

Tables Quantity Computed Measured Step 3 RT (VS1 operating alone) 150 Ω 150 Ω Step 5 RT (VS2 operating alone) 150 Ω 150 Ω Table 1: Calculated and Measured Resistances I 1 I 2 V 2 = (I 2 ) (R 2 ) Computed Measured Computed Measured Computed Measured Step 4 66 mA 66.7 mA 33 mA 33.3 mA 3.3 V 3.333 V Step 6 16.7 mA 16.7 mA 16.7 mA 16.7 mA 1.67 V 1.667 V Step 7 (Total) 50 mA 50 mA 50 mA 50 mA 5 V 5V Table 2: Computed and Measured Current and Voltage Figures Figure #: Measured R T of 10V Source

9 Figure #: Measured I 1 of 10 V Source Figure #: Measured I 2 of 10 V Source

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10 Figure #: Measured V 2 of 10 V Source Figure #: Measured R T of 5 V Source

11 Figure #: Measured I 1 and I 2 of 5 V Source Figure #: Measured V 2 of 5 V Source

12 Figure #: Part III Step 5 Measured of Calculations

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13 CONCLUSION In this lab I analyzed the circuit using the superposition theorem. I started by removing the five volt source by shorting that source out. I then used the series-parallel formulas to calculate the resistance in the circuit using the R T = R || (R + R) formula. After I had the total resistance I used the Ohm’s Law to calculate the total current with the following formula; I T = V/R T . Then to find the current across the R 2 I used the current divider formula I 2 = (I T ) (R / (R + R). Once I had all the information for the ten volt source, I shorted the ten volt source and reintroduced the five volt source and repeated the calculations for the five volt source that I used for the ten volt source. After I calculated all of the requirements for the five volt source, I than used the superposition theorem to impose the two currents and voltages together to find the total current and voltage through R 2 .

14 REFERENCES Floyd, T. L. Principles of Electric Circuits. [VitalSource Bookshelf]. Retrieved from https://bookshelf.vitalsource.com/#/books/9780134880068/ (2017) National Instruments Multisim (V 14.1) [Windows]. Retrieved from http://www.ni.com/multisim/