Neupane_Suyog_Lab5_EquivalentCircuits_Spring2024

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University of Texas, Arlington *

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1106

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Electrical Engineering

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Apr 3, 2024

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V1 V2 R3 R1 R5 R2 R4 V3 R6 EE1106 Lab Experiment Network Theorems – Equivalent Circuits Pre-Lab assignment  Read Wiki entry on Thevenin’s theorems o https://en.wikipedia.org/wiki/Th%C3%A9venin%27s_theorem  Review Chapters 8-10 of the online text below Vol I - Direct Current (DC) o http://www.allaboutcircuits.com/textbook/ o Special attention to the Chapter 10 section on Thevenin and Norton Equivalence  See the lab handout starting on the next page o Work ahead on the Multisim circuit simulations. You must have calculated values BEFORE coming to class.  For the circuit below, draw the circuit in your lab notebook and answers the following set of questions in your lab notebook. We will go over solution during the live lecture  How many terminal characteristics are in the circuit?  How many terminal characteristics are unknown?  Identify and label all nodes in the circuit. o How many nodes are there? o How many valid KCL equations can be written?  Write a set of valid KCL equations  How many mesh loops are there in the circuit? o How many valid KVL equations can be written?  Write a set of valid KVL equations  How many Ohm’s Law equations can be written  Write a set of Ohm’s Law equations  How does the number of unknowns compare to the number of valid equations?

EE1106 Lab Experiment Network Theorems – Equivalent Circuits Introduction The goal of this lab will be to cover a third theoretical concept needed to complete your understanding of DC resistive networks. This concept is called equivalency. To summarize these labs, we have covered the following theoretical circuits concepts:  Terminal Characteristics and Basic Theory (Ohm’s Law/KVL/KCL)  Superposition (Linearity)  Circuit Equivalency (Thevenin/Norton circuits) Required Materials It is assumed that you have the required materials for EE1106. Experiment Procedures As always, work ahead through the entire lab to simulate using Multisim before coming to class to build and measure the circuit. It is important that you have an ‘expected’ value before ever attempting your physical measurement. Record the values obtained from Multisim as your ‘calculated’ values. 𝑉𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛(%) = 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 − 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 ∙100% Thevenin Equivalency The purpose of this part of the lab is to gain familiarity with a new Electrical Engineering theorem. The experiments performed in this lab involve the following concepts –  Thevenin’s theorem The theory and equations associated with these experiments are covered in your pre-lab reading material. Your job here is to investigate and apply the above theorems on resistive networks to provide a hands-on experience to the theory covered in the lectures on these topics. Imagine the circuit given below is in a box and the only terminals that can be accessed externally are the terminals A and B. In the procedure below, any reference to the Thevenin terminals is referring to the terminals A and B. So, V TH is referring to the voltage across the terminals A and B. 1) Measure individual resistor values for the circuit below and record in your lab notebook. 2) Build the circuit in Multisim. 3) From the Multisim analysis: a. Using Fig 2, calculate the open circuit voltage across A and B, and the short circuit current through A and B using the specified values of the components and record in lab notebook b. repeat this for the measured values of the components and record in lab notebook c. You may optionally use Fig 1 and calculate Rth directly with an Ohm meter 4) Build the Figure 1 circuit on your breadboard a. Take a resistance measurement on the Fig 1 circuit and verify that it matches your Multisim value 5) Now connect the power supplies as shown in Figure 2 ( TAKE CARE TO NEVER SHORT POWER SUPPLIES )

15kΩ A 30kΩ B 15kΩ 30kΩ 12V V2 9V V1 a. Measure the values of the voltage sources at the circuit (not at the supply), and record in your lab notebook. b. apply the DMM to measure values for open circuit voltage and short circuit current and record. c. calculate the difference in percent (%) between values measured from the network and those calculated with specified resistor values, and record 6) Calculate the Thevenin resistance from your measured Voc and Isc and verify that it matches the value measured in Step 4 7) Build the equivalent circuit in Multisim (the one with just Vth and Rth). Place a 7.5kOhm resistor between A and B. Measure V AB . Now place a 7.5kOhm resistor on the breadboard between A and B. Measure V AB and verify that it matches Multisim. 8) Choose two other resistors (greater than 1kOhm and not 7.5kOhm) and repeat step 7. Verify that the circuits are still equivalent with these resistors 9) Provide comments on the accuracy and convenience of Thevenin’s equivalency. 30kΩ 15kΩ Figure 5 - Circuit with supplies “off” to measure Rth directly 30kΩ 15kΩ Figure 2 - Circuit with supplies “on” to measure Voc and Isc

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Figure 3- Equivalent circuit in Multisim Component Values Component Specified Measured V 1 12V 12 V 2 9V 9 R 1 15k 14.98k R 2 30k 30.21k R 3 8.25k 8.22k R 4 2.61k 2.61k R L 5.1KOhm 5.09k V AB (open circuit) 10.751V 10.7438 I AB (short circuit) 0.000792118A 0.0007917 Calculated Measured R TH 13.573k 13.570k Calculate using Multisim twice. Once with the specified resistor values and again with the actual measured values. The percent variation should be between the ‘Calculated with Specified values and the Measured values’ Thevenin Equivalent Component Calculated from Specified R values Calculated from measured R values Measured Variation% V AB (open circuit) 10.751 10.757 10.7438 -0.066 I AB (short circuit) 0.00079211 0.00079146 0.0007917 0.0821 V AB (w 5.1kΩ) 2.936 2.935 2.933 0.034 V AB (w 820Ω) 0.612074 0.611826 0.61184 0.0382 V AB (w 110k Ω) 9.574 9.561 9.555 0.1988