LAB6EE

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University of Nevada, Reno *

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220L

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Electrical Engineering

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Feb 20, 2024

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EE 220L, Section #1003 Lab #7: Thevenin ’ s and Norton ’ s Equivalent Circuits 10/18/2023 Javier Correa-Martinez Nicholas Hong

2 Objective: The purpose of this lab is to demonstrate Thevenin ’ s and Norton ’ s equivalent circuit theorems. Equipment Used: 180𝛺 resistor ± 5% 470𝛺 resistor ± 5% 2?𝛺 resistor ± 5% 614𝛺 resistor ± 5% 510𝛺 resistor ± 10% 560𝛺 resistor ± 5% 620𝛺 resistor ± 10% 680𝛺 resistor ± 5% 750𝛺 resistor ± 10% Breadboard Multimeter Power Supply Multism Software Theory (Javier Correa-Martinez): Thevenin ’ s theorem is used to replace multiple element circuit with a single voltage source and resistor while Norton’s theorem is used to replace a multiple element circuit with a single current source and resistor. This allows the calculations to be simplified when analyzing circuits Theory Nicholas Hong: Thevenin ’ s theorem states that any circuit is equivalent to a circuit of a voltage source connected in series to a resistor. Norton ’ s theorem staters that any circuit is equivalent to a circuit of a current source connected in parallel to a resistor. By utilizing these theorems in circuit analyses to create a simplified equivalent circuit, it makes the calculations easier. Procedure:

3 1. Thevenin ’ s and Nortons Equivalent Circuits In the first part of the lab we found the Thevenin ’ s equivalent of Circuit 1 then we built circuit 1. We then measured the short circuit current and the Thevenin ’ s resistance and compared it to the calculated values from the first step. Next we built the Thevenin ’ s equivalent circuit using the corresponding ? 𝑇𝐻 and 𝑅 𝑇𝐻 values and measured the short circuit current, open circuit voltage, and the Thevenin ’ s resistance. Finally we measured the current through a 510 𝛺 resistor placed across the A and B terminals. Figure 1: Circuit 1

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4 Figure 2: Final Circuit Table 1: Circuit 1 Values Calculated Simulated Measured %Error Calculated Simulated Measured %Error ? ?? (V) 9.12 9.12 9.25 1.43 ?, ?? (V) 9.12 9.12 10 9.65 𝐼 ?? (mA) 14.4 14.4 14.5 0.69 𝐼, ?? (mA) 14.4 14.4 16.2 12.5 𝑅 𝑇𝐻 ( Ω ) 635 635 636 0.16 𝑅, 𝑇𝐻 ( Ω ) 635 635 614 3.31 𝐼 510Ω (mA) 7.86 7.86 8.09 2.93 𝐼, 510Ω (mA) 7.86 7.86 9.03 2.93 Calculations:

5 1. 𝑅 𝑇𝐻 = (180 ∥ 2𝐾) + 470 = 635Ω 2. 𝐼 = ? 𝑅 = 10 2000 + 180 = 45?𝐴 3. ? 𝑇𝐻 = 2000 ∗ 4.5 ∗ 10 −3 = 9? 4. 2?𝐼 2 = 470𝐼 1 180𝐼 3 + 470𝐼 1 = 10 𝐼 3 = 𝐼 1 + 𝐼 2 𝐼 1 = 14.44?𝐴 = 𝐼 𝑁 Questions: With the 510 Ω resistor in place, how much power does the entire Thevenin ’ s equivalent circuit consume? The Thevenin ’ s equivalent circuit consumes 33.1 mW of power. 2. Maximum Power Transfer In the second part of the lab we used different load resistances and measured the voltage and current across the load resistance. Then we calculated the power dissipated by each load resistance. Table 2: Maximum Power Load Resistance ( 𝑅 𝐿 ) 𝑅 𝐿 ????𝑎𝑔𝑒 (V) 𝑅 𝐿 𝐶?𝑟𝑟𝑒?? ( mA ) 𝑅 𝐿 𝑃?𝑤𝑒𝑟 ( ?? ) 510 Ω 4.56 9.03 41.18 560 Ω 4.81 8.61 41.41 620 Ω 5.05 8.23 41.56

6 680 Ω 5.29 7.84 41.47 750 Ω 5.51 7.48 41.21 Simulations Circuit 1: Shorted Circuit:

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7 Shorted Voltage: Thevenin ’ s Equivalent Circuit: Shorted Thevenin ’ s Circuit:

8 636 Ω Resistor Circuit: Power Consumed by Thevinin ’ s Circuit:

9 Conclusion Javier Correa-Martinez: In this lab we verified that Thevenin ’ s and Norton ’ s equivalency allows a DC circuit to be modeled, with respect to its terminals, as either and independent voltage source in series with a resistor – or – an independent current source in parallel with a resistor. Our calculated results and simulated results were consistent with the measure results from the physical circuit. Some minor discrepancies can be explained due to potential faults in the equipment used along with resistors with values that were not exactly the same as the ones used in the calculations. Conclusion Nicholas Hong: In conclusion of this lab, we successfully used Thevenin’s and Norton’s theorems to accurately analyze circuits and create equivalent circuits to each respective theorem. The results from the Multisim schematics and our physical circuits were very similar to the calculated values. By then creating and taking measurements of an equivalent circuit that follows the Thevenin and Norton theorems, we were able to prove that it allowed an easier time to calculate voltages and currents. Due to the high accuracy of our experiments, the few likely sources of error would be from potential faults in lab equipment and resistor tolerances

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