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)
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 (\( v_1, v_2, v_3, v_4, v_5 \)).
**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9b91490-7014-4990-b9a4-62583a5b405c%2F44760b3d-00ed-496b-8b38-b8673c1d2048%2F5ghgk9_processed.jpeg&w=3840&q=75)
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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