CEE310L_Lab Report 3_Catherine Campos_900252200

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CEE310L

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Feb 20, 2024

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Catherine Campos ID: 900252200 January 21, 2024 CEE310L: Thevenin and Norton Equivalent Circuit Report Pre-Lab Our third lab we are going to be applying Thevenin’s circuit by calculating our results, building the circuit in theory using Multisim, and lastly physically building the circuit. Our pre-lab sections provide details on the Thevenin and Norton circuits where, “Thevenin's Theorem states that we can replace entire network by an equivalent circuit that contains only an independent voltage source in series with an impedance (resistor) such that the current-voltage relationship at the load is unchanged. Norton's Theorem is identical to Thevenin's Theorem except that the equivalent circuit is an independent current source in parallel with an impedance (resistor). Pre-lab also provides the steps for the Thevenin’s equivalent circuit as well as Norton’s equivalent circuit. Introduction Part I – Circuit Theory is involved here in the first part where we are given a circuit with R1 = 470 Ω, R2 = 1kΩ, R3 = 2.2k Ω, R4 = 1k Ω, and Vs = 9V. Here the calculations come into play where we need to determine the open-circuit voltage 𝑉 ை஼ that appears at terminals (a,b). We will also determine the short-circuit current 𝐼 ௌ஼ that flows through a wire connecting terminals (a,b) together. The last equation with have us determine the 𝑅 ௧ . Lastly, we will draw the Thevenin equivalent circuit for this circuit. Part II – Multisim Simulations is the second part of our lab where we will build the circuit from part one with the same values, R1 = 470 Ω, R2 = 1kΩ, R3 = 2.2k Ω, R4 = 1k Ω, and Vs = 9V. There are several steps we also need to do such as connect a resistor 𝑅 ௅ as a load between terminals (a; b). We will use interactive analysis and measurement probes to determine the open-circuit voltage. Then use interactive analysis and measurement probes to determine the short-circuit current. We will then compare my results with the theoretical calculation in Part I step 1. Another build is involved here in the lab where on the same schematics the Thevenin equivalent circuit for the circuit as you determined in Part I step 1 of the lab. We need to connect a copy of the same resistor RL as a load between terminals. Select 5 various RL values and measure the voltage across the load resistor and the current passing through for both the original circuit and the Thevenin equivalent circuit. Part III – Circuit Implement and Measurements, here we are physically going to build the circuit with same values, R1 = 470 Ω, R2 = 1kΩ, R3 = 2.2k Ω, R4 = 1k Ω, and Vs = 9V. We would then measure the open-circuit voltage and the short-circuit current between terminals (a;b). We would then select the 5 different RL resistors from your component kit with the same resistances as in Part II step 7. We then need to measure the voltage across the load resistor and the current passing through the load resistor. Once all those measurements are noted we then need to compare our measurements with both simulation results from Part II and the theoretical calculation from Part I of the lab.

Experimental Results Part I – Circuit Theory R1 = 470 Ω, R2 = 1kΩ, R3 = 2.2k Ω, R4 = 1k Ω, and Vs = 9V 𝑉 ை஼ = 𝑉 ௔ − 𝑉 ௕ 𝑉 ை஼ = 1𝑘 1𝑘 + 0.47𝑘 ∗ 9 − 1𝑘 1𝑘 + 2.2𝑘 ∗ 9 𝑉 ை஼ = 3.31𝑉 𝑅 ௧ = (1𝑘‖470) + (2.2𝑘‖1𝑘) 𝑅 ௧ = 1𝑘 ∗ 470 1𝑘 + 470 + 2.2𝑘 ∗ 1𝑘 2.2𝑘 + 1𝑘 𝑅 ௧ = 1007.3Ω 𝐼 ௌ஼ = 3.31 1007.3 = 3.29𝑚𝐴 1,007.3Ω

Part II – Multisim Simulations Open Circuit Voltage ( 𝑉 ை஼ ) : 3.31V Short Circuit Current ( 𝐼 ௌ஼ ): 3.29mA Upon completing the Multisim simulations we can see that the results from the circuit theory are exactly the same. Our calcutions for the 𝑉 ை஼ = 3.31V and the calculations for the 𝐼 ௌ஼ = 3.29mA. With the results being the same we can see that we are on the right track for confirming the Thevenin equivalent.

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Results for 27kΩ Results for 18kΩ Results for 300kΩ

Results for 10Ω Results for 100Ω 𝑅 ௅ Resistance Original Circuit Thevenin Equivalent Voltage across 𝑅 ௅ Current through 𝑅 ௅ Voltage across 𝑅 ௅ Current through 𝑅 ௅ 27kΩ 3.191V 118uA 3.191V 118uA 18kΩ 3.135V 174uA 3.135V 174uA 330kΩ 3.3V 10.0uA 3.3V 174uA 10Ω 32.539mV 3.25mA 32.537mV 3.25mA 100Ω 298.94mV 2.99mA 298.925mV 2.99mA

Part III – Circuit Implementation and Measurements Open-Circuit Voltage Short-Circuit Current

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𝑅 ௅ Resistance Original Circuit Voltage Across 𝑅 ௅ Current Through 𝑅 ௅ 27kΩ 3.02 V 0.01 18kΩ 2.92V 0.01 330kΩ 3.08V 0.01 10Ω 30.7mV 0.02 100Ω .277V 0.02 27kΩ Voltage and Current 18kΩ Voltage and Current

330kΩ Voltage and Current 10Ω Voltage and Current

100Ω Voltage and Current Upon completion of this build and the results here we can see that the voltage is more or less the same when it comes to the theoretical, the simulation, and the physical build. For this particular build I had started out with the same 9V battery from the last two labs which proved to have very little power left. Once I had started to use a fresh 9V battery the results were a little closer to that Multisim simulations that I had created for the resistances that I chose. In my table you can see that I chose 27kΩ, 18kΩ, 330kΩ, 10Ω, and 100Ω. When it came to measuring current, I was unable to verify the theoretical with the physical build. Conclusion For us to complete this lab we needed to find Thevenin’s equivalent circuit which needed us to find the open-circuit voltage ( 𝑉 ை஼ ), the short-circuit current ( 𝐼 ௌ஼ ), and the Thevenin resistance ( 𝑅 ௧ ). I was able to match the calculations portion with that the simulations that I created to help further prove the theoretical notion. Upon completing the physical build, I was to be able physically create the circuit based on the schematic. However, I did run into trouble when it came to measuring the current. A lot of trouble shooting had gone into helping me find the correct measurement but alas I still was unable to recreate that result. The voltage of course was not a problem which helped me to see the proof that the theoretical matched the physical based off the schematic. Still current seems to allude me, even after breaking the circuit at that point and using the multimeter to complete the circuit I did not receive the desired numbers.

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