Lab4

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EET310

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Dec 6, 2023

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Lab 4 - Node voltage analysis Please download the Multisim Lab file. Download Multisim Lab file. Solve for node voltages and then connect your measuring instruments to verify your calculations. Objective: Solve the circuit in the lab using Node Voltage Analysis following the below steps:  Identify the number of nodes There are two nodes B and C.  Assign each node a voltage notation. V B and V C I 2 I 1 I L I 4 I 3 I 3

 Write the characteristic equations for each node by applying KCL and assuming all currents are leaving the node. At node “C”: I 2 + I L = I 4 At node “B”: I 1 – I L – I 2 I 1 = (12V – V B ) / 0.330 I 2 = (V B – 0) / 0.300 I 3 = (12V – V C ) / 0.360 I 4 = (V C – 0) / 0.390 I L = (V B – V C ) / 1  Solve the simultaneous equations to calculate the node voltages. And then calculate the current in each resistor. I 3 + I L = I 4 (12V – V C ) / 0.360 + (V B – V C ) / 1 = (V C – 0) / 0.390 = 0 (12V / 0.360) – (V C / 0.360) + V B – V C – (V C /0.390) = 0 (12V / 0.360) + V B – V C (1 / 0.360 + 1 + 1 / 0.390) = 0 33.33 + V B – V C (2.78 + 1 + 2.56) = 0 33.33 + V B – V C (6.34) = 0 33.33 + V B – 6.34V C = 0 – 33.33 = V B – 6.34V C I 1 = I 2 – I L (12V – V B ) / 0.330 = (V B – 0) / 0.300 – (V B – V C ) / 1 (12V / 0.330) – (V B / 0.330) – (V B /0.300) – V B + V C = 0 36.36 – V B (1 / 0.330 – 1 / 0.300) – V B + V C = 0 36.36 – V B (3.03 + 3.33 + 1) + V C = 0 36.36 – V B (7.36) + V C = 0 36.36 = 7.36V B – V C – 33.33 = V B – 6.34V C 36.36 = 7.36V B – V C [ 1 − 6.34 7 . 36 − 1 ] [ v B v C ] = [ − 33.33 36.36 ] Matrix A Matrix B 1 -6.34 -33.33 7.36 -1 36.36 INV of A sol of X -0.0219 0.13885 5.7783 - 0.16118 0.0219 6.1685

VB = 5.78V VC = 6.17V I 1 = (12V – V B ) / 0.330 I 1 = (12V – 5.78V) / 0.330 I 1 = 6.22 / 0.330 I 1 = 18.9 mA I 2 = (V B – 0) / 0.300 I 2 = (5.78V – 0) / 0.300 I 2 = 5.78V / 0.300 I 2 = 19.3 mA I 3 = (12V – V C ) / 0.360 I 3 = (12V – 6.17V) / 0.360 I 3 = 5.83 / 0.360 I 3 = 16.2 mA I 4 = (V C – 0) / 0.390 I 4 = (6.17V – 0) / 0.390 I 4 = 6.17V / 0.390 I 4 = 15.8 mA I L = (V B – V C ) / 1000 I L = (5.78V – 6.17V) / 1 I L = – 0.39 / 1000 I L = – 0.39 µA

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 You will need to connect your measuring instruments to measure the node voltage and verify your calculations. Multisim Screenshot of Verified Voltage and Current Values

 Conclusion Conclusion: The Node Voltage Analysis method allows us to solve for any unknown voltages in a circuit using Kirchhoff’s current and voltage laws (KCL and KVL). Cramer’s rule is also used once equations have been made to find the voltages. The determinant, or function of the entire equation, is used to then find the individual variables, which in this instance is the individual resistor voltages.

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