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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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 \( V_1 \).
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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