48V + 20k ww + 2Vx + I + V₂ 10k 10k www + 12V Determine V₁
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Question
Determine V1
![### Circuit Analysis Problem: Determine \( V_1 \)
#### Description
The given circuit consists of different components connected in a loop. The components include:
1. A 48V DC voltage source on the left side of the circuit.
2. A 12V DC voltage source on the right side of the circuit.
3. Three resistors:
- 20kΩ resistor (between the 48V source and the dependent voltage source)
- 10kΩ resistor (between the dependent voltage source and the 12V voltage source)
- 10kΩ resistor (in the lower branch, between the bottom two nodes)
4. A dependent voltage source with a value of \( 2V_x \) where \( V_x \) is the voltage across the 10kΩ resistor in the lower branch.
#### Objective
The goal is to determine the voltage \( V_1 \), which is the voltage across the dependent voltage source.
#### Steps to Solve
To find \( V_1 \), follow these steps:
1. **Calculate \( V_x \):**
- \( V_x \) is the voltage across the 10kΩ resistor in the lower branch.
- This calculation involves the voltage division rule or other circuit analysis techniques such as node voltage method, mesh current method, etc.
2. **Determine the value of the dependent voltage source \( 2V_x \):**
- Multiply \( V_x \) by 2 to find the voltage provided by the dependent source.
3. **Apply Kirchhoff’s Voltage Law (KVL) or Node Voltage Method:**
- Sum the voltages around the loops of the circuit to relate \( V_1 \), \( 2V_x \), and other voltage drops in the circuit.
4. **Solve for \( V_1 \):**
- Using the calculated \( V_x \) and voltage laws, solve for the value of \( V_1 \).
#### Detailed Diagram Explanation
The circuit diagram is divided into two loops:
1. The main loop contains the 48V source, 20kΩ resistor, 10kΩ resistor, and the 12V source across one side.
2. The dependent voltage source \( 2V_x \) and the 10kΩ resistors create a path for analyzing \( V_x \).
#### Conclusion
By following the above steps, we can determine the voltage \( V_1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5f3e4ce-f46c-48a5-a74c-9a62ffe7be87%2F5eb2728d-83b3-4117-8fd7-6b251fe8ae2b%2Flmp7v2_processed.png&w=3840&q=75)
Transcribed Image Text:### Circuit Analysis Problem: Determine \( V_1 \)
#### Description
The given circuit consists of different components connected in a loop. The components include:
1. A 48V DC voltage source on the left side of the circuit.
2. A 12V DC voltage source on the right side of the circuit.
3. Three resistors:
- 20kΩ resistor (between the 48V source and the dependent voltage source)
- 10kΩ resistor (between the dependent voltage source and the 12V voltage source)
- 10kΩ resistor (in the lower branch, between the bottom two nodes)
4. A dependent voltage source with a value of \( 2V_x \) where \( V_x \) is the voltage across the 10kΩ resistor in the lower branch.
#### Objective
The goal is to determine the voltage \( V_1 \), which is the voltage across the dependent voltage source.
#### Steps to Solve
To find \( V_1 \), follow these steps:
1. **Calculate \( V_x \):**
- \( V_x \) is the voltage across the 10kΩ resistor in the lower branch.
- This calculation involves the voltage division rule or other circuit analysis techniques such as node voltage method, mesh current method, etc.
2. **Determine the value of the dependent voltage source \( 2V_x \):**
- Multiply \( V_x \) by 2 to find the voltage provided by the dependent source.
3. **Apply Kirchhoff’s Voltage Law (KVL) or Node Voltage Method:**
- Sum the voltages around the loops of the circuit to relate \( V_1 \), \( 2V_x \), and other voltage drops in the circuit.
4. **Solve for \( V_1 \):**
- Using the calculated \( V_x \) and voltage laws, solve for the value of \( V_1 \).
#### Detailed Diagram Explanation
The circuit diagram is divided into two loops:
1. The main loop contains the 48V source, 20kΩ resistor, 10kΩ resistor, and the 12V source across one side.
2. The dependent voltage source \( 2V_x \) and the 10kΩ resistors create a path for analyzing \( V_x \).
#### Conclusion
By following the above steps, we can determine the voltage \( V_1 \).
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