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

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
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Publisher:Robert L. Boylestad
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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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