Lab_Report_4

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California Polytechnic State University, Pomona *

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1101L

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Electrical Engineering

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Jan 9, 2024

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P a g e | 1 ECE 1101L – Lab 4 Series and Parallel Circuits Name: Leyi Zhou Group: L 10/04/2023

P a g e | 2 Introduction Background Theory: The Kirchhoff’s Voltage Law (KVL) says that the algebraic sum of all voltages in a loop is 0, ∑Vi = 0. Therefore, in series circuits, the values of current are the same in the loop. Besides, for circuits in series, the equivalent Req = Rtotal = R1 + R2 + R3 + … +Ri. Besides, the Kirchhoff’s Current Law (KCL) says that the algebraic sum of all currents entering a node is 0, ∑Ii = 0, I1 + I2 + I3 + … + Ii = 0. Therefore, in parallel circuits, the values of voltage are the same across parallel branches. Objective: In this experiment, we took measurements and calculated the voltages and the currents in different series circuits and parallel circuits, to verify the KVL and KCL. For Part 1 of this lab, we built a series circuit, measured the node voltages and found branch voltages from node voltages. Then, we calculated the currents through each resistor and verified the values of current were all the same. Furthermore, we verified the KVL from the measurements of branch voltages, and we used the voltage and current measurements to calculate the equivalent resistance of the circuit. Lastly, we used Ohmmeter to measure the total resistance, and compared the result with the equivalent resistance. For Part 2 of this lab, we measured the value of V1 between 2 nodes using the Voltmeter. For Part 3 of this lab, we used Cadence to build a series circuit, and ran the Bias Point Simulation of the circuit in PSpice and found the node voltages. We then calculated the branch voltages and verified that the KVL worked correctly around the loop. For Part 5 of this lab, we build a parallel circuit and measured the voltages across all resistors. Then, we found the values of current through each resistor from voltage measurements, and we wrote KCL at node B of this circuit. After that, we were able to find I in which I = I2 – I3 + I4.

P a g e | 3 Pre-Lab

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P a g e | 4

P a g e | 5

P a g e | 6 Lab

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P a g e | 7

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P a g e | 9 3. Given: (Build the following circuit on Cadence/PSpice) a. Find I ( run Bias Point Simulation ) From the schematic, we could find out the value of I was the same throughout the circuit, which was 701.8 A = 701.8 * 10 ^(-6) A. ɥ b. Measure the branch voltages and check KVL around the loop. KVL around the loop: (-5V) + IR1 + IR2 – 3V +IR3 +IR4 = 0; (-5V) + [701.8 * 10 ^(-6) A] * (1000 Ohm) + [701.8 * 10 ^(-6) A] * (2700 Ohm) -3V + [701.8 * 10 ^(-6) A] * (3000 Ohm) + [701.8 * 10 ^(-6) A] * (4700 Ohm) = 0.00052 V ≈ 0V, so KVL works correctly around the loop.

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1 . Given P a g e | 10 Questions and Problems What is the relation between I1, I2, I3, I4 and I5? Since the circuit is in series, I1 = I2 = I3 = I4 = I5. 2. Given E volts What happens to V2 as R2 increases? As V2 is directly proportional to R2, when R2 increases, V2 also increases.

P a g e | 11 3. Given 10 v Find V if V2 = - 2 volts and V1 = 1 volt. Use KVL: (-10 V) + V1 – 3V –V2 + V = 0; (-10 V) + (1 V) – 3V – (-2 V) + V = 0, -10 V + V = 0, V = 10 V. 4. Given: Find R If voltage source is 12V. 12V = IR + I (1000 Ohm), 12V = (3mA) *R + (3mA) (1000 Ohm), 12V = (3mA) *R + 3V, IR = 9V, R = (9V) / (3mA) = 3000 Ohm = 3 kOhm. R I = 3mA

P a g e | 12 Data Analysis: - For Part 1 of this lab, we built a series circuit with Vin = 5V, R1 = 180 Ohm, R2 = 220 Ohm, R3 = 470 Ohm and R4 = 130 Ohm, and we used the multimeter to measure the node voltages, VA = 3.9760 V, VB = 1.8369 V and VC = 0.8014V. Then, we calculated V1 = 1.024V, V2 = 2.1391V, V3 = 1.0335V and V4 = 0.8014V. Using the values of V1 – V4, we were able to find out the values of I1 – I4, which ranges from 0.185 mA and 0.187 mA. Since the values of I1 – I4 were almost the same, we could find I = I1 = I2 = I3 = I4 = 0.185 mA. After that, we used the values of voltages and current to calculated the Req, which was 27.03 kOhm. Lastly, we measured Req which was 26.819 kOhm. The percentage difference between the calculated and measured values of Req = (27.03 – 26.819) kOhm / 27.03 kOhm * 100% = 0.78%. Since the percent difference between these two values was extremely small (< 1%), we could conclude the measured value of Req was accurate. - For Part 2 of this lab, we measured the value of V1, which was 1.5426 V. For Part 3 of this lab, we used Cadence to build a series circuit, in which Vin = 5V, R1 = 1 kOhm, R2 = 2.7 kOhm, V = 3V, R3 = 3 kOhm and R4 = 4.7 kOhm. We ran the Bias Point Simulation in PSpice and found I = 701.8 A = 701.8 * 10 ^(-6) A. We then calculated V1 – V4, ɥ and were able to verify the KVL for this loop in which (-5V) + IR1 + IR2 – 3V +IR3 +IR4 = 0. - For Part 5 of this lab, we build a parallel circuit in which Vin = 5V, R1 = 4.7 kOhm, R2 = 10 kOhm, R3 = 2.2 kOhm and V = -1.5 V. Using the KCL at node B, we calculated I2 = 0.901 mA, I3 = - 0.436 mA, I4 = 1.284 mA, and I = I2 – I3 + I4 = 2.621 mA. Conclusion In this experiment, I learned that I could build series and parallel circuits to verify the KVL and KCL, by taking measurements of the values of resistors, voltages and currents. I also learned how to build a circuit using Cadence, and how to show the values of the current and the voltage by performing Bias Point Simulation in PSpice. In Part 1 of this lab, we constructed a series circuit with specified resistors and measured node voltages and currents. The negligible difference between calculated and measured values of equivalent resistance (Req) demonstrated the precision of our measurements. In Part 2 of this lab, we further extended our understanding by measuring V1, which provided valuable insights into the voltage distribution within the circuit. Part 3 introduced us to computer-aided simulation using Cadence, and through Bias Point Simulation in PSpice, we verified the KVL and displayed the current I in the circuit. This part emphasized the practicality and effectiveness of simulation

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P a g e | 13 tools in understanding real-world electrical circuits. In Part 5, we delved into parallel circuits, calculating various currents using KCL. The calculations and results improved our ability to analyze and solve complex parallel circuit configurations. Overall, this lab not only enhanced our grasp of circuit theory, but also reinforced the importance of accurate measurements, simulation, and the applicability of fundamental electrical laws in practical situations.

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