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Find the currents I₁, I2, I3 in the circuit for the following network. B MM W I' R₁-30 92 A in F R₂-10 92 с R₂=592 E₁-30 V 1 R₁ =492 M E₂=60 V E R₁-10 22 С E₂=120 V D

Find the currents I₁, I2, I3 in the circuit for the following network. B MM W I' R₁-30 92 A in F R₂-10 92 с R₂=592 E₁-30 V 1 R₁ =492 M E₂=60 V E R₁-10 22 С E₂=120 V D

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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**Find the currents \( I_1, I_2, I_3 \) in the circuit for the following network.** ### Circuit Diagram Explanation This circuit diagram depicts a complex electric network with three power sources and multiple resistors. The goal is to find the currents \( I_1, I_2, \) and \( I_3 \) flowing through different parts of the circuit. - **Resistors:** - \( R_1 = 4 \, \Omega \) - \( R_2 = 5 \, \Omega \) - \( R_3 = 10 \, \Omega \) - \( R_4 = 30 \, \Omega \) - \( R_5 = 10 \, \Omega \) - **Voltage sources:** - \( E_1 = 30 \, V \) - \( E_2 = 120 \, V \) - \( E_3 = 60 \, V \) ### Analysis of the Circuit The network is divided into loops designated by points A, B, C, D, E, and F: - **Loop 1 (A, F, E, B):** - Contains \( R_2, R_3, R_5 \) - Contains voltage sources \( E_1 \) and \( E_3 \) - Current \( I_1 \) flows through \( R_2 \) - Current \( I_2 \) flows through \( R_3 \) and \( R_5 \) - **Loop 2 (B, C, D, E):** - Contains \( R_4 \) - Contains voltage source \( E_2 \) - Current \( I_3 \) flows through \( R_4 \) ### Kirchhoff's Voltage Law (KVL) To solve for the currents \( I_1, I_2, I_3 \), we can apply Kirchhoff's Voltage Law (KVL) to each loop. - **Loop 1 (A, F, E, B):** - \( E_1 - I_1 R_2 - I_2 R_3 - (I_2 - I_1) R_5 + E_3 = 0 \) - **Loop 2 (B, C, D, E):**
Transcribed Image Text:**Find the currents \( I_1, I_2, I_3 \) in the circuit for the following network.** ### Circuit Diagram Explanation This circuit diagram depicts a complex electric network with three power sources and multiple resistors. The goal is to find the currents \( I_1, I_2, \) and \( I_3 \) flowing through different parts of the circuit. - **Resistors:** - \( R_1 = 4 \, \Omega \) - \( R_2 = 5 \, \Omega \) - \( R_3 = 10 \, \Omega \) - \( R_4 = 30 \, \Omega \) - \( R_5 = 10 \, \Omega \) - **Voltage sources:** - \( E_1 = 30 \, V \) - \( E_2 = 120 \, V \) - \( E_3 = 60 \, V \) ### Analysis of the Circuit The network is divided into loops designated by points A, B, C, D, E, and F: - **Loop 1 (A, F, E, B):** - Contains \( R_2, R_3, R_5 \) - Contains voltage sources \( E_1 \) and \( E_3 \) - Current \( I_1 \) flows through \( R_2 \) - Current \( I_2 \) flows through \( R_3 \) and \( R_5 \) - **Loop 2 (B, C, D, E):** - Contains \( R_4 \) - Contains voltage source \( E_2 \) - Current \( I_3 \) flows through \( R_4 \) ### Kirchhoff's Voltage Law (KVL) To solve for the currents \( I_1, I_2, I_3 \), we can apply Kirchhoff's Voltage Law (KVL) to each loop. - **Loop 1 (A, F, E, B):** - \( E_1 - I_1 R_2 - I_2 R_3 - (I_2 - I_1) R_5 + E_3 = 0 \) - **Loop 2 (B, C, D, E):**
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