Lab 3

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ELEC-2110 Electric Circuit Analysis FROM: Jonathan Leviner TO: Tanner Grider DATE: September 14, 2020 LAB SECTION: 001 Electrical Measurements: More Practice with DC Measurements

Jonathan Leviner Electrical Measurements: More Practice September 14, 2020 1 of 8 Introduction This lab serves to build on the skills students learned in the previous lab (“EXPERIMENT 2 Electrical Measurements: Breadboarding, NI ELVIS, Multimeter, Lab Reporting”), as well providing new examples and a few more advanced techniques used to solve circuits. Among this, students should continue to familiarize themselves with taking basic measurements in a circuit. The student will also learn to use NI ELVIS’s variable power supply in order to complete each exercise. Exercise 1 Process, Data, and Results: This exercise asks students to set up two different sources that will be used for each exercise. The student should first familiarize themselves with NI ELVIS’s variable power supply. Once it is set up correctly (shown in Figures 2 & 3 of the lab manual), the voltage should be set to produce 7 Volts. This should be verified using a multimeter. The same should be done for a fixed voltage, which will come from the ELVIS board’s 5 Volt power supply. The actual values of both voltages are shown in Table 1. Table 1: Power Supplied from ELVIS Board Fixed Voltage Variable Voltage 4.96 V 7.00 V Exercise 2 Process and Data: In this next exercise, the student is tasked with acquiring seven different resistors, all with a theoretical value of 470 Ω. Once the values have been measured, the student should create a table to record those values. For the purpose of this lab, these values should be used whenever the student makes a hand calculation involving these resistors. Table 2: Actual Values of Resistors Resistor Measured Value R 1 469 Ω R 2 467 Ω R 3 470 Ω R 4 469 Ω R 5 468 Ω R 6 468 Ω R 7 466 Ω

Jonathan Leviner Electrical Measurements: More Practice September 14, 2020 2 of 8 Results: Using a multimeter, the student should measure the values of all seven resistors. Once each resistance has been measured, their values should be recorded in a table, as shown in Table 2. These values will be used later on in the student’s calculations. Exercise 3 Process and Data: In this exercise, the student should recreate a physical circuit using the model shown in Figure 1. Using the ELVIS board and resistors R 1 through R 5 , the student should set up the circuit below, asking for their TA’s assistance if needed. Once they are comfortable with their circuit design, the student should measure the voltages across V A , V B , V C , V D , V AC , and V BD . Once these values are obtained, they should verify Kirchhoff’s Voltage Law (KVL) using V A , V C , and V AC . Then do the same for V B , V D , and V BD . After verifying KVL for those loops, the student should measure the current flowing from Node D to Node C (I DC ). Once the student finds this current, they should use a combination of KVL, KCL, and Ohm’s Law to find the value of I AC . Figure 1: Circuit for Exercise 3 Table 3: Voltage Measurements for Exercise 3 Circuit Voltage Components Value V A 6.99 V V B 5.11 V V C 4.97 V V D 3.36 V V AC 2.03 V V BD 1.76 V

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Jonathan Leviner Electrical Measurements: More Practice September 14, 2020 3 of 8 Table 4: Current Measurements for Exercise 3 Circuit Current Components Value I DC -3.40 mA I AB 4.06 mA 𝑽𝑽 = 𝑰𝑰 × 𝑹𝑹 Equation 1: Ohm’s Law Results: To measure the voltages across each component, the multimeter should be set to the voltage position. For the case of measuring from two nodes, such as V AC and V BD , the multimeter’s probes should be connected in series with each node and then measured. All voltage values have been recorded in Table 3. Next, the currents must be measured so the multimeter should be moved to the current position. To find these values, the circuit must be broken to allow a place for the multimeter to measure. For example, to measure I AB , the circuit is broken between the right side of R 2 and connected back to Node B. These current values are recorded in Table 4. Exercise 4 Process and Data: In the next exercise, the student should create the circuit shown in Figure 2 on the ELVIS board using resistors R 1 through R 3 . The student is reminded to keep track of the position of each node. Once they have correctly created the circuit, they can begin to take their measurements. First, they are asked to measure the voltages at each of the defined nodes (V A , V B , and V C ). These voltages should be verified using nodal analysis. Next, they must measure the currents I BA , I B0 , and I BC , using Kirchhoff’s Current Law (KCL) at Node B to verify their findings. Then by using Ohm’s Law, the student should solve for those same current values using their resistor values and measured node voltages.

Jonathan Leviner Electrical Measurements: More Practice September 14, 2020 4 of 8 Figure 2: Circuit for Exercise 4 Table 5: Voltage Measurements for Exercise 4 Circuit Measured Components Value V A 6.99 V V B 3.99 V V C 4.96 V Table 6: Current Measurements for Exercise 4 Circuit Measured Components Value I BA -6.34 mA I B0 8.43 mA I BC -2.05 mA Results: In this new circuit (Figure 2), the student needs to find the voltages at Nodes A, B, and C. These values were found using a multimeter and recorded in Table 5. Next, the currents (seen in Table 6) should be found and measured with respect to Node B. The student should notice that I BA and I BC are negative. This is because of how the current flows in this circuit. Loop AB0 flows clockwise while Loop CB0 flows counterclockwise, meaning I BA and I BC are being measured in opposition to the current flow, hence why they are negative. To verify that the currents are correct, the student should use the voltages in Table 5 and the corresponding resistances from Table 2 to calculate Ohm’s Law (Equation 1). The calculated values should be close to the ones in Table 6.

Jonathan Leviner Electrical Measurements: More Practice September 14, 2020 5 of 8 Exercise 5 Process and Data: In this final exercise, the student must create another circuit (Figure 3) and find the values of multiple components. It is crucial that their circuit design is correct for this exercise, otherwise there is risk of invalid results and possibly a blown fuse. For starters, the student should find the voltages V AC , V AB , V AD , V B , V C , V CE , V D , V DE , and V E . After recording those values in a table, they should measure the currents I AC , I AB , I AD , I C0 , I CE , I D0 , I DE , and I E0 . Once the student is done measuring those components, they should begin to calculate the power absorbed by each element in the circuit. Figure 3: Circuit for Exercise 5 Table 7: Voltage Measurements from Exercise 5 Circuit Voltage Components Value V A 4.80 V V AC -0.16 V V AB -2.18 V V AD 2.38 V V B 7.00 V V C 4.97 V V CE 2.50 V V D 2.51 V V DE -0.03 V V E 2.58 V

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Jonathan Leviner Electrical Measurements: More Practice September 14, 2020 6 of 8 Table 8: Current Measurements from Exercise 5 Circuit Current Components Value I AC -0.34 mA I AB -4.66 mA I AD 5.06 mA I C0 5.60 mA I CE 5.31 mA I D0 5.14 mA I DE -0.09 mA I E0 5.21 mA Table 9: Power Absorbed by Each Element in Exercise 5 Circuit Element Power Absorbed R 1 0.054 W R 2 13.17 W R 3 -12.76 W R 4 12.01 W R 5 -3.79E-3 W R 6 -12.36 W R 7 -10.12 W V 1 0.105 W V 2 -0.028 W 𝑷𝑷 = 𝑰𝑰𝑽𝑽 = 𝑰𝑰 𝟐𝟐 𝑹𝑹 = 𝑽𝑽 𝟐𝟐 𝑹𝑹 Equation 2: Power Rule Results: In the final exercise, the student should replicate the circuit in Figure 3 while being careful to keep track of each node. After creating their circuit, the next task is to find the voltage at and across multiple nodes. These values have been recorded in Table 7. The student should now measure the current through some of the same nodes. The student should also remember to break the circuit where it is needed in order to accommodate for the multimeter. The values for each of those currents are shown in Table 8. Next, the student must find the power absorbed by every element in the circuit. To solve for this, the student must use Equation 2 by plugging in resistance values from Table 2 and the current values from Table 8. The result for each component is shown in Table 9. To find the power absorbed by all the elements combined, sum all the values from Table 9 together. The resultant value should be equal or close to 0 Watts due to the power balancing rule.

Jonathan Leviner Electrical Measurements: More Practice September 14, 2020 7 of 8 Conclusion The purpose of this lab was to continue to build on the knowledge students have gained about measuring and calculating the values of components within a circuit. However, in this lab the student had to deal with two voltage sources rather than just the fixed source on the ELVIS board. The student was also shown more advance ways of verifying measurements by using combinations of Ohm’s Law, KVL, and KCL. Using these techniques will help them be able to solve more technical circuits.

Jonathan Leviner Electrical Measurements: More Practice September 14, 2020 8 of 8 References / Bibliography 1. Joel Killingsworth, Brandon Eidson, Elizabeth Devore, Tanner Grider. “EXPERIMENT 2 Electrical Measurements: Breadboarding, NI ELVIS, Multimeter, Lab Reporting”. In: (May 2016). URL: ftp://ftp.eng.auburn.edu/pub/irwinjd/lab_manuals/Lab%202_Electrical%20Measurements _Breadboarding,%20NI%20ELVIS,%20etc.pdf . 2. Brandon Eidson, Elizabeth Devore, Austin Taylor. “EXPERIMENT 3 Electrical Measurements: More Practice with DC Measurements”. In: (January 2020). URL: ftp://ftp.eng.auburn.edu/pub/irwinjd/lab_manuals/Lab%203_Electrical%20Measurements _More%20Practice%20with%20DC.pdf .

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