Experiment 2 Report

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Apr 3, 2024

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ECE 110L Winter 24’ Instructor: Mesghali, Farid Exp. 2: Kirchhoff’s Laws and Equivalent Source Transformation Om Patel, 605518179 Experiment Introduction and Theory This set of labs in this experiment aims to become more familiar with two main concepts: Kirchoff’s Law and Thevenin/Norton Equivalence Theorems. Kirchoff’s law is broken down into the Voltage Law (KVL) and the Current Law (KCL). KVL states that the sum of the voltages in a loop of a circuit must sum to zero. KCL states that the total current going into a node must equal the total current leaving the node. Source Transformations are a method of simplifying existing circuits for easier analysis. A Thevenin equivalent transformation changes the circuit to have only a single voltage source with a load and equivalent resistor. A Norton equivalent transformation changes the circuit to have only a single current source with a load and equivalent resistor. During this transformation, one thing to remember is that a circuit consisting of a voltage source of value IR in series with a resistor R always equals a current source V/R in parallel with a resistor R. In the process of doing this transformation, the equivalent resistance can be found by replacing voltage sources with a short circuit and the current sources with an open circuit. Lab1: Kirchhoff’s Laws Analysis of Circuits Introduction: In this part of the experiment, we built a circuit with 100, 470, 680, 2200, and 22 ohm resistors in the below configuration. Using KVL and KCL the theoretical values of the voltage and current across each resistor were found. After measuring these same values across each resistor, they were compared to their theoretical values. Figure 1: Wire diagram for Lab 1 Figure 2: Constructed Circuit for Lab 1

Measured Data: Measured Resistance (ohms) Theoretical Voltage (V) Measured Voltage (V) Theoretical Current (mA) Measured Current (mA) Resistor 1 98.8 0.462 0.458 4.68 4.66 Resistor 2 460 2.15 2.15 4.68 4.66 Resistor 3 666 2.39 2.38 3.58 3.56 Resistor 4 2150 2.51 2.36 1.17 1.06 Resistor 5 22.2 0.0259 0.0239 1.17 1.06 Table 1: Voltage and Current Data from Lab 1 Discussion: 1. Measured voltage and current values to agree with the theoretical values calculated with the measured resistor values. There is more error in the voltage drop across resistor 4 and hence carried onto the error in the current through resistor 4/5. I suspect this to be the case since that resistor did have the highest percent deviation from the theoretical resistance value. Other than those values, everything else did agree with very close margins. a. Kirchoff’s Voltage Law i. Loop 1: R1, R2, R3 𝑉 𝑠 − 𝑉 1 − 𝑉 2 − 𝑉 3 = 0 5 − 0. 458 − 2. 15 − 2. 38 = 0. 012 𝑉 ≈ 0 𝑉 ii. Loop 2: R1, R2, R4, R5 𝑉 𝑠 − 𝑉 1 − 𝑉 2 − 𝑉 4 − 𝑉 5 = 0 5 − 0. 458 − 2. 15 − 2. 36 − 0. 0239 = 0. 0081 𝑉 ≈ 0 𝑉 b. Kirchoff’s Current Law i. Top Node 𝐼 12 − 𝐼 3 − 𝐼 45 = 0 4. 66 − 3. 56 − 1. 06 = 0. 04 𝑚𝐴 ≈ 0 𝑚𝐴

Lab 2: Thevenin/Norton Equivalent Introduction: In this part of the experiment, we will be using two voltage sources and 4 resistors of values: 5.6k, 1.2k, 4.7k, and 10k ohms. From this lab, we will be finding the Thevenin equivalent voltage, Norton equivalent current, and Thevenin resistance. Additionally, the open circuit voltage and short circuit current are measured. Figure 3: Wire diagram for Lab 2 Figure 4: Complete Constructed Circuit for Lab 2 Figure 5: Setup without R L for Lab 2 Figure 6: Thevenin Equivalent Circuit for Lab 2

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Measured Data: Theoretical Value Measured Value Resistor 1 (ohms) 5600 5520 Resistor 2 (ohms) 1200 1179 Resistor 3 (ohms) 4700 4670 Resistor L (ohms) 10000 9930 R eq (ohms) 5642 5640 I L (mA) 0.208 0.200 V L (V) 2.07 2.07 V th (V) 3.24 3.24 I N (mA) 0.574 0.560 Thevenin Equivalent Circuit V L (V) 2.07 2.04 I L (mA) 0.208 0.190 Table 2: Data from the original circuit and Thevenin equivalent circuit for Lab 2 Discussion: 1. The voltage across the load resistor with the original circuit (2.07 V) is very close to the voltage across the load resistor in the Thevenin equivalent circuit (2.04 V). These results support the concept of source transformation since those circuits are theoretically equal. 2. If our goal is to maximize power dissipation across the load resistor, the R L must be equal to R eq or R th . This can be shown using the power equation accounting for both resistors and the derivative to find the maximum value of R L . For this lab, we would use a load of 5640. a. → → → 𝑃 = 𝐼𝑉 𝑃 = 𝑉 2 𝑅 𝑃 = 𝑉 2 1 1 𝑅 ?𝑞 + 1 𝑅 𝐿 𝑃 = 𝑉 2 𝑅 𝐿 (𝑅 ?𝑞 +𝑅 𝐿 ) 2 → ?𝑃 ?𝑅 𝐿 = (𝑅 ?𝑞 +𝑅 𝐿 ) 2 −2𝑅 𝐿 (𝑅 𝐿 +𝑅 ?𝑞 ) (𝑅 ?𝑞 +𝑅 𝐿 ) 2 = 0 𝑅 ?𝑞 = 𝑅 𝐿 Signature of Professor:

Prelab: Lab 1: Voltages and currents of all resistors. Lab 2: Voltage and current of RL, Thevenin voltage, Norton current, Thevenin resistance