11. In the figure below, use node-voltage analysis to solve for all unknown values of voltage and current. 28 V R1=40 C www www FE R3=202 D R2=202 7 V
11. In the figure below, use node-voltage analysis to solve for all unknown values of voltage and current. 28 V R1=40 C www www FE R3=202 D R2=202 7 V
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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**Exercise on Node-Voltage Analysis**
**Problem Statement:**
11. In the figure below, use node-voltage analysis to solve for all unknown values of voltage and current.
**Diagram Explanation:**
- The diagram consists of a circuit with three nodes labeled A, C, and D.
- There are three resistors:
- \( R1 = 4 \, \Omega \) between nodes A and C
- \( R2 = 2 \, \Omega \) between nodes C and E
- \( R3 = 2 \, \Omega \) between nodes C and D
- There is a voltage source of 28 V between node A (positive terminal) and node B (negative terminal).
- There is another voltage source of 7 V between node E (positive terminal) and node F (negative terminal).
**Diagram Key Points:**
- **Nodes**:
- \( A \), \( C \), and \( E \) are the key nodes for voltage analysis.
- **Voltage Sources**:
- 28 V source connected between nodes A and B.
- 7 V source connected between nodes E and F.
- **Resistors**:
- \( R1 \) (4 \( \Omega \)) between nodes A and C.
- \( R2 \) (2 \( \Omega \)) between nodes C and E.
- \( R3 \) (2 \( \Omega \)) between nodes C and D.
**Analytical Approach:**
To solve for the node voltages and then the branch currents, you can follow these steps:
1. **Identify Reference Node**: Set node B (or any other node) as the reference ground (0V).
2. **Apply Kirchhoff's Current Law (KCL) at each non-reference node**:
- For node \( A \)
- For node \( C \)
- For node \( E \)
3. **Write Equations**:
- Write the KCL equation for each node in terms of node voltages.
- Solve the simultaneous equations to find node voltages.
4. **Calculate Currents**:
- Use Ohm's Law (\(I = \frac{V}{R}\)) to find currents through each resistor.
Using these steps, you can solve for all unknown voltages and currents in the given circuit.
---
This exercise will help in"
Transcribed Image Text:---
**Exercise on Node-Voltage Analysis**
**Problem Statement:**
11. In the figure below, use node-voltage analysis to solve for all unknown values of voltage and current.
**Diagram Explanation:**
- The diagram consists of a circuit with three nodes labeled A, C, and D.
- There are three resistors:
- \( R1 = 4 \, \Omega \) between nodes A and C
- \( R2 = 2 \, \Omega \) between nodes C and E
- \( R3 = 2 \, \Omega \) between nodes C and D
- There is a voltage source of 28 V between node A (positive terminal) and node B (negative terminal).
- There is another voltage source of 7 V between node E (positive terminal) and node F (negative terminal).
**Diagram Key Points:**
- **Nodes**:
- \( A \), \( C \), and \( E \) are the key nodes for voltage analysis.
- **Voltage Sources**:
- 28 V source connected between nodes A and B.
- 7 V source connected between nodes E and F.
- **Resistors**:
- \( R1 \) (4 \( \Omega \)) between nodes A and C.
- \( R2 \) (2 \( \Omega \)) between nodes C and E.
- \( R3 \) (2 \( \Omega \)) between nodes C and D.
**Analytical Approach:**
To solve for the node voltages and then the branch currents, you can follow these steps:
1. **Identify Reference Node**: Set node B (or any other node) as the reference ground (0V).
2. **Apply Kirchhoff's Current Law (KCL) at each non-reference node**:
- For node \( A \)
- For node \( C \)
- For node \( E \)
3. **Write Equations**:
- Write the KCL equation for each node in terms of node voltages.
- Solve the simultaneous equations to find node voltages.
4. **Calculate Currents**:
- Use Ohm's Law (\(I = \frac{V}{R}\)) to find currents through each resistor.
Using these steps, you can solve for all unknown voltages and currents in the given circuit.
---
This exercise will help in
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