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Determine il , i2 , and i3 , use Mesh Analysis iz 2Ω 6 V 4Ω 3 A 8Ω ww (+1)

Determine il , i2 , and i3 , use Mesh Analysis iz 2Ω 6 V 4Ω 3 A 8Ω ww (+1)

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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How can i solve this exercise? its about electric circuits

**Mesh Analysis Problem** **Objective:** Determine \( i_1 \), \( i_2 \), and \( i_3 \) using Mesh Analysis. **Circuit Description:** - The circuit consists of: - A 6V voltage source. - Three meshes with currents \( i_1 \), \( i_2 \), and \( i_3 \). - A 2Ω resistor in series with \( i_3 \) and \( i_1 \). - A 4Ω resistor shared between meshes \( i_2 \) and \( i_3 \). - An 8Ω resistor in series with \( i_2 \) and \( i_3 \). - A 1Ω resistor in the loop with \( i_1 \) and \( i_2 \). - A 3A current source in series with the 1Ω resistor affecting \( i_1 \) and \( i_2 \). **Mesh Currents:** - \( i_1 \) flows through the 6V source, the 2Ω resistor, and shares the 1Ω resistor and the 3A source with \( i_2 \). - \( i_2 \) flows through the 4Ω resistor and 8Ω resistor, sharing the 1Ω resistor and 3A source with \( i_1 \). - \( i_3 \) flows through the 2Ω resistor and the 4Ω resistor, sharing the latter with \( i_2 \). **Analysis:** Use mesh analysis to create equations based on Kirchhoff's Voltage Law (KVL) to determine the unknown mesh currents \( i_1 \), \( i_2 \), and \( i_3 \). 1. **Mesh 1 (i_1)**: - Include resistances and voltage source in the loop with any shared components with \( i_2 \). 2. **Mesh 2 (i_2)**: - Consider the 4Ω and 8Ω resistors, noting shared elements with \( i_3 \) and the impact of the 3A source. 3. **Mesh 3 (i_3)**: - Involves the 2Ω and 4Ω resistors, factoring the influence of shared components with \( i_2 \). Apply the mesh analysis technique to solve for each current by: - Setting the sum of
Transcribed Image Text:**Mesh Analysis Problem** **Objective:** Determine \( i_1 \), \( i_2 \), and \( i_3 \) using Mesh Analysis. **Circuit Description:** - The circuit consists of: - A 6V voltage source. - Three meshes with currents \( i_1 \), \( i_2 \), and \( i_3 \). - A 2Ω resistor in series with \( i_3 \) and \( i_1 \). - A 4Ω resistor shared between meshes \( i_2 \) and \( i_3 \). - An 8Ω resistor in series with \( i_2 \) and \( i_3 \). - A 1Ω resistor in the loop with \( i_1 \) and \( i_2 \). - A 3A current source in series with the 1Ω resistor affecting \( i_1 \) and \( i_2 \). **Mesh Currents:** - \( i_1 \) flows through the 6V source, the 2Ω resistor, and shares the 1Ω resistor and the 3A source with \( i_2 \). - \( i_2 \) flows through the 4Ω resistor and 8Ω resistor, sharing the 1Ω resistor and 3A source with \( i_1 \). - \( i_3 \) flows through the 2Ω resistor and the 4Ω resistor, sharing the latter with \( i_2 \). **Analysis:** Use mesh analysis to create equations based on Kirchhoff's Voltage Law (KVL) to determine the unknown mesh currents \( i_1 \), \( i_2 \), and \( i_3 \). 1. **Mesh 1 (i_1)**: - Include resistances and voltage source in the loop with any shared components with \( i_2 \). 2. **Mesh 2 (i_2)**: - Consider the 4Ω and 8Ω resistors, noting shared elements with \( i_3 \) and the impact of the 3A source. 3. **Mesh 3 (i_3)**: - Involves the 2Ω and 4Ω resistors, factoring the influence of shared components with \( i_2 \). Apply the mesh analysis technique to solve for each current by: - Setting the sum of
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