In the circuit given below, R = 20 Ω. Find vo using mesh analysis. 6Ω 11 www 60 V +201 www vo 4Ω 12 R + 20 Ω + 5%

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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**Circuit Analysis Problem Using Mesh Analysis**

In the circuit given below, \( R = 20 \, \Omega \). Find \( v_o \) using mesh analysis.

**Diagram Explanation**

- The circuit contains two loops which are labeled for mesh currents \( i_1 \) and \( i_2 \).
- The left loop consists of:
  - A 4 Ω resistor connected to a voltage source \( v_o \).
  - A 60 V independent voltage source.
  - A 20 Ω resistor in the middle shared with the right loop.

- The right loop consists of:
  - A resistor \( R \) with a value of 20 Ω.
  - A dependent voltage source represented by \( 5v_o \).

**Component Connections**

- The left loop's mesh current \( i_1 \) passes through the 6 Ω resistor, the 60 V source, and the 20 Ω resistor.
- The right loop's mesh current \( i_2 \) flows through the resistor \( R \) and the dependent source \( 5v_o \).

**Purpose**

- Use mesh analysis to determine the value of \( v_o \), the output voltage across the 4 Ω resistor on the left side of the circuit.

**Note**

- When performing mesh analysis, apply Kirchhoff's Voltage Law (KVL) to each loop to establish equations for \( i_1 \) and \( i_2 \), then solve these equations to find \( v_o \).
Transcribed Image Text:**Circuit Analysis Problem Using Mesh Analysis** In the circuit given below, \( R = 20 \, \Omega \). Find \( v_o \) using mesh analysis. **Diagram Explanation** - The circuit contains two loops which are labeled for mesh currents \( i_1 \) and \( i_2 \). - The left loop consists of: - A 4 Ω resistor connected to a voltage source \( v_o \). - A 60 V independent voltage source. - A 20 Ω resistor in the middle shared with the right loop. - The right loop consists of: - A resistor \( R \) with a value of 20 Ω. - A dependent voltage source represented by \( 5v_o \). **Component Connections** - The left loop's mesh current \( i_1 \) passes through the 6 Ω resistor, the 60 V source, and the 20 Ω resistor. - The right loop's mesh current \( i_2 \) flows through the resistor \( R \) and the dependent source \( 5v_o \). **Purpose** - Use mesh analysis to determine the value of \( v_o \), the output voltage across the 4 Ω resistor on the left side of the circuit. **Note** - When performing mesh analysis, apply Kirchhoff's Voltage Law (KVL) to each loop to establish equations for \( i_1 \) and \( i_2 \), then solve these equations to find \( v_o \).
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