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Problem 4.23 (Node-Voltage Method) Find io 800 Ω www Το 50 V (+ 80 Ω V 40 Ω 50 Ω 500 C Yż Ο 4 )750 mA 200 Ω

Problem 4.23 (Node-Voltage Method) Find io 800 Ω www Το 50 V (+ 80 Ω V 40 Ω 50 Ω 500 C Yż Ο 4 )750 mA 200 Ω

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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4.23
### Problem 4.23 (Node-Voltage Method) **Objective:** Find \( i_0 \) **Circuit Description:** The circuit includes: - A voltage source of 50 V connected to the left side. - An 80 Ω resistor in series with \( i_0 \), the current to be found. - An 800 Ω resistor above \( i_0 \). - An 80 Ω resistor to the left of \( V_1 \), which is a node in the circuit. - A 40 Ω resistor between \( V_1 \) and \( V_2 \). - A 50 Ω resistor and a 200 Ω resistor forming a path through \( V_1 \) and \( V_2 \). - A current source of 750 mA directed towards the node \( V_2 \). **Diagram Explanation:** The circuit diagram illustrates the configuration required to apply the node-voltage method. Key components are labeled clearly, and the targeted current (\( i_0 \)) to be determined is shown passing through the 800 Ω resistor. The nodes \( V_1 \) and \( V_2 \) help in setting up equations based on Kirchhoff’s laws to solve for the unknowns in the circuit. **Approach:** 1. **Identify Nodes:** Label all nodes (particularly \( V_1 \) and \( V_2 \)) in the circuit to set up node equations. 2. **Apply Kirchhoff’s Current Law (KCL):** At each node, write the sum of currents coming in and out considering the passive sign convention. 3. **Solve Equations:** Use the equations derived from KCL to find \( V_1 \), \( V_2 \), and subsequently \( i_0 \). This approach leverages the node-voltage method to determine the current flowing through the specified part of the circuit.
Transcribed Image Text:### Problem 4.23 (Node-Voltage Method) **Objective:** Find \( i_0 \) **Circuit Description:** The circuit includes: - A voltage source of 50 V connected to the left side. - An 80 Ω resistor in series with \( i_0 \), the current to be found. - An 800 Ω resistor above \( i_0 \). - An 80 Ω resistor to the left of \( V_1 \), which is a node in the circuit. - A 40 Ω resistor between \( V_1 \) and \( V_2 \). - A 50 Ω resistor and a 200 Ω resistor forming a path through \( V_1 \) and \( V_2 \). - A current source of 750 mA directed towards the node \( V_2 \). **Diagram Explanation:** The circuit diagram illustrates the configuration required to apply the node-voltage method. Key components are labeled clearly, and the targeted current (\( i_0 \)) to be determined is shown passing through the 800 Ω resistor. The nodes \( V_1 \) and \( V_2 \) help in setting up equations based on Kirchhoff’s laws to solve for the unknowns in the circuit. **Approach:** 1. **Identify Nodes:** Label all nodes (particularly \( V_1 \) and \( V_2 \)) in the circuit to set up node equations. 2. **Apply Kirchhoff’s Current Law (KCL):** At each node, write the sum of currents coming in and out considering the passive sign convention. 3. **Solve Equations:** Use the equations derived from KCL to find \( V_1 \), \( V_2 \), and subsequently \( i_0 \). This approach leverages the node-voltage method to determine the current flowing through the specified part of the circuit.
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