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,
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**Title: Circuit Analysis Using Loop Analysis Method** **Objective:** Determine the voltages \( V_1 \), \( V_2 \), \( V_3 \), and \( V_4 \) for the given electrical circuit using loop analysis. **Circuit Description:** The provided circuit contains several components arranged in a loop format, suitable for loop or mesh analysis. **Components:** - **Current Sources:** - \( I_1 = 0.5 \, \text{Adc} \) - \( I_2 = 0.25 \, \text{Adc} \) - **Resistors:** - \( R_1 = 330 \, \Omega \) - \( R_2 = 1.5 \, \text{k}\Omega \) - \( R_3 = 1.2 \, \text{k}\Omega \) - \( R_4 = 2.5 \, \text{k}\Omega \) - \( R_5 = 2 \, \text{k}\Omega \) - \( R_6 = 3 \, \text{k}\Omega \) - \( R_7 = 500 \, \Omega \) **Nodes and Voltage Points:** - \( V_D \) - \( V_C \) - \( V_B \) - \( V_A \) **Diagram Explanation:** - The circuit diagram shows connections among resistors and current sources, forming closed loops. - Each loop can be analyzed to determine the voltage drops across various components using Kirchhoff's Voltage Law (KVL). **Analysis Method:** 1. **Identify independent loops** in the circuit. 2. Apply **Kirchhoff’s Voltage Law (KVL)** to each loop, summing voltages to equate to zero. 3. Solve the system of equations resulting from KVL application to find unknown voltages across the components. **Calculations:** Use Ohm’s Law (\( V = IR \)) in conjunction with KVL to solve for individual voltages \( V_1 \), \( V_2 \), \( V_3 \), and \( V_4 \) in the circuit loops. By properly setting up and solving the equations derived from each loop, the voltages at points \( V_A \), \( V_B \), \( V_C \), and \( V_D \) can
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Transcribed Image Text:**Title: Circuit Analysis Using Loop Analysis Method** **Objective:** Determine the voltages \( V_1 \), \( V_2 \), \( V_3 \), and \( V_4 \) for the given electrical circuit using loop analysis. **Circuit Description:** The provided circuit contains several components arranged in a loop format, suitable for loop or mesh analysis. **Components:** - **Current Sources:** - \( I_1 = 0.5 \, \text{Adc} \) - \( I_2 = 0.25 \, \text{Adc} \) - **Resistors:** - \( R_1 = 330 \, \Omega \) - \( R_2 = 1.5 \, \text{k}\Omega \) - \( R_3 = 1.2 \, \text{k}\Omega \) - \( R_4 = 2.5 \, \text{k}\Omega \) - \( R_5 = 2 \, \text{k}\Omega \) - \( R_6 = 3 \, \text{k}\Omega \) - \( R_7 = 500 \, \Omega \) **Nodes and Voltage Points:** - \( V_D \) - \( V_C \) - \( V_B \) - \( V_A \) **Diagram Explanation:** - The circuit diagram shows connections among resistors and current sources, forming closed loops. - Each loop can be analyzed to determine the voltage drops across various components using Kirchhoff's Voltage Law (KVL). **Analysis Method:** 1. **Identify independent loops** in the circuit. 2. Apply **Kirchhoff’s Voltage Law (KVL)** to each loop, summing voltages to equate to zero. 3. Solve the system of equations resulting from KVL application to find unknown voltages across the components. **Calculations:** Use Ohm’s Law (\( V = IR \)) in conjunction with KVL to solve for individual voltages \( V_1 \), \( V_2 \), \( V_3 \), and \( V_4 \) in the circuit loops. By properly setting up and solving the equations derived from each loop, the voltages at points \( V_A \), \( V_B \), \( V_C \), and \( V_D \) can
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