Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Current Division Method
The generalized current divider formula is given by the following relation below,
Question
**Circuit Analysis Using Node Method** **Objective:** Determine the values of all the resistor voltages using node analysis. **Circuit Description:** In the diagram, we have a complex circuit with the following components and connections: 1. **Voltage Sources:** - **5V DC Source**: On the left side, connected to resistor \( R_1 \). - **9V DC Source**: On the right side, labeled as \( V_1 \). 2. **Resistors:** - \( R_1 \): 220 Ohms, connected between the 5V source and the first node. - \( R_2 \): 1k Ohm, connected in series between Nodes 1 and 2. - \( R_3 \): 100 Ohms, connected in parallel from Node 2 to the \( V_1 \) source. - \( R_4 \): 500 Ohms, connected in parallel from the ground to Node 1. - \( R_5 \): 1k Ohm, connected from Node 2 to Node 3. - \( R_6 \): Not present in the diagram despite typical mention in sequences. - \( R_7 \) and \( R_8 \): Both 10k Ohms, connected in series from Node 1 to Node 2. 3. **Ground Connection:** - Present at the base, providing a common reference point. **Procedure:** Using node analysis, apply the following steps: 1. Identify and label each node. 2. Apply Kirchhoff's Current Law (KCL) to each node (except the reference node). 3. Set up and solve the resulting system of equations to find the node voltages. 4. Use the node voltages to calculate the voltage across each resistor. **Graph/Diagram Explanation:** - The circuit is shown with nodes designated by red dots. The components are connected with straight lines representing wires. - The diagram includes the necessary values for each resistor and voltage source to perform calculations. By following these steps, one can accurately determine the voltage across each resistor, facilitating an understanding of the circuit dynamics through node analysis.
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Transcribed Image Text:**Circuit Analysis Using Node Method** **Objective:** Determine the values of all the resistor voltages using node analysis. **Circuit Description:** In the diagram, we have a complex circuit with the following components and connections: 1. **Voltage Sources:** - **5V DC Source**: On the left side, connected to resistor \( R_1 \). - **9V DC Source**: On the right side, labeled as \( V_1 \). 2. **Resistors:** - \( R_1 \): 220 Ohms, connected between the 5V source and the first node. - \( R_2 \): 1k Ohm, connected in series between Nodes 1 and 2. - \( R_3 \): 100 Ohms, connected in parallel from Node 2 to the \( V_1 \) source. - \( R_4 \): 500 Ohms, connected in parallel from the ground to Node 1. - \( R_5 \): 1k Ohm, connected from Node 2 to Node 3. - \( R_6 \): Not present in the diagram despite typical mention in sequences. - \( R_7 \) and \( R_8 \): Both 10k Ohms, connected in series from Node 1 to Node 2. 3. **Ground Connection:** - Present at the base, providing a common reference point. **Procedure:** Using node analysis, apply the following steps: 1. Identify and label each node. 2. Apply Kirchhoff's Current Law (KCL) to each node (except the reference node). 3. Set up and solve the resulting system of equations to find the node voltages. 4. Use the node voltages to calculate the voltage across each resistor. **Graph/Diagram Explanation:** - The circuit is shown with nodes designated by red dots. The components are connected with straight lines representing wires. - The diagram includes the necessary values for each resistor and voltage source to perform calculations. By following these steps, one can accurately determine the voltage across each resistor, facilitating an understanding of the circuit dynamics through node analysis.
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