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Use mesh current method to determine the voltages labeled below. 10Ω 20 + + -j42 12020 j42

Use mesh current method to determine the voltages labeled below. 10Ω 20 + + -j42 12020 j42

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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**Title: Using Mesh Current Method to Determine Voltages in an AC Circuit** **Objective:** To determine the voltages across various components in a given AC circuit using the mesh current method. **Circuit Description:** The circuit consists of an AC voltage source and a series of impedances arranged in a particular diamond-shaped configuration. The components and their respective impedances are as follows: - **Voltage Source:** 120∠0° (AC source) - **Resistors and Reactors:** - 10 Ω resistor - 2 Ω resistor - -j4 Ω inductor - j4 Ω capacitor **Mesh Currents:** - \( i_1 \), \( i_2 \), \( i_3 \) are the mesh currents flowing in the counter-clockwise direction. **Voltage Labels:** - \( v_1, v_2, v_3, v_4, v_5 \) are the voltages across various components in the circuit. **Circuit Analysis:** 1. **Identify Loops:** - **Loop 1:** Includes the voltage source and the 10 Ω resistor. - **Loop 2:** Includes the 10 Ω resistor, -j4 Ω inductor, and 2 Ω resistor. - **Loop 3:** Includes the j4 Ω capacitor, 2 Ω resistor, and an overlapping part of Loop 2. 2. **Apply Kirchhoff’s Voltage Law (KVL) to Each Loop:** - **Loop 1 Equation:** \[ 120∠0° = 10Ω(i_1 - i_2) + v_1 \] - **Loop 2 Equation:** \[ v_2 = 2Ω(i_2 - i_3) - j4Ω(i_2) \] - **Loop 3 Equation:** \[ j4Ω(i_3 - i_1) + 2Ω(i_3) + v_5 = 0 \] 3. **Solve the Simultaneous Equations:** - Calculate the mesh currents (\( i_1, i_2, i_3 \)). - Use these currents to find the voltages (\( v_1, v_2, v_3, v_4, v_5 \)). **
Transcribed Image Text:**Title: Using Mesh Current Method to Determine Voltages in an AC Circuit** **Objective:** To determine the voltages across various components in a given AC circuit using the mesh current method. **Circuit Description:** The circuit consists of an AC voltage source and a series of impedances arranged in a particular diamond-shaped configuration. The components and their respective impedances are as follows: - **Voltage Source:** 120∠0° (AC source) - **Resistors and Reactors:** - 10 Ω resistor - 2 Ω resistor - -j4 Ω inductor - j4 Ω capacitor **Mesh Currents:** - \( i_1 \), \( i_2 \), \( i_3 \) are the mesh currents flowing in the counter-clockwise direction. **Voltage Labels:** - \( v_1, v_2, v_3, v_4, v_5 \) are the voltages across various components in the circuit. **Circuit Analysis:** 1. **Identify Loops:** - **Loop 1:** Includes the voltage source and the 10 Ω resistor. - **Loop 2:** Includes the 10 Ω resistor, -j4 Ω inductor, and 2 Ω resistor. - **Loop 3:** Includes the j4 Ω capacitor, 2 Ω resistor, and an overlapping part of Loop 2. 2. **Apply Kirchhoff’s Voltage Law (KVL) to Each Loop:** - **Loop 1 Equation:** \[ 120∠0° = 10Ω(i_1 - i_2) + v_1 \] - **Loop 2 Equation:** \[ v_2 = 2Ω(i_2 - i_3) - j4Ω(i_2) \] - **Loop 3 Equation:** \[ j4Ω(i_3 - i_1) + 2Ω(i_3) + v_5 = 0 \] 3. **Solve the Simultaneous Equations:** - Calculate the mesh currents (\( i_1, i_2, i_3 \)). - Use these currents to find the voltages (\( v_1, v_2, v_3, v_4, v_5 \)). **
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