Find the Thevenin resistance seen at terminals a-b. 20 Ω V Σ10Ω 3 Α 0.5 V
Find the Thevenin resistance seen at terminals a-b. 20 Ω V Σ10Ω 3 Α 0.5 V
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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![### Finding the Thevenin Resistance
#### Problem Statement
**Objective:** Find the Thevenin resistance seen at terminals \( a-b \).
#### Circuit Description:
The circuit consists of:
1. A 20 Ω resistor connected in series.
2. Parallel elements include:
- A 10 Ω resistor
- A 3 A current source
- A dependent current source labeled \( 0.5 V_o \)
Here is the circuit diagram for clarity:
```
+---- 20 Ω ----+
| |
V_o (a)
| |
10 Ω (b)
| |
3 A |
| |
dependent |
current source |
(0.5 V_o) |
| |
+--------------+
```
To find the Thevenin resistance \( R_{th} \), follow these steps:
1. **Turn off all independent sources:**
- Replace the 3 A current source with an open circuit.
2. **Analyze the remaining elements:**
- The 20 Ω resistor and 10 Ω resistor are now in series.
- The dependent current source \( 0.5 V_o \) is also considered.
3. **Combine series resistances:**
- The combination of 20 Ω and 10 Ω resistors gives the equivalent resistance.
#### Additional Notes:
- Remember that while independent sources are turned off (current sources open, voltage sources shorted), dependent sources remain in the analysis.
- Use Ohm's law and Kirchhoff's laws as necessary for detailed calculations.
By following these steps, you can determine the Thevenin equivalent resistance at terminals \( a-b \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff04af373-6616-44d4-9142-5aa7a1930a82%2F3d994f08-780c-421d-9456-3f4b05da6767%2Fl7faawo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Thevenin Resistance
#### Problem Statement
**Objective:** Find the Thevenin resistance seen at terminals \( a-b \).
#### Circuit Description:
The circuit consists of:
1. A 20 Ω resistor connected in series.
2. Parallel elements include:
- A 10 Ω resistor
- A 3 A current source
- A dependent current source labeled \( 0.5 V_o \)
Here is the circuit diagram for clarity:
```
+---- 20 Ω ----+
| |
V_o (a)
| |
10 Ω (b)
| |
3 A |
| |
dependent |
current source |
(0.5 V_o) |
| |
+--------------+
```
To find the Thevenin resistance \( R_{th} \), follow these steps:
1. **Turn off all independent sources:**
- Replace the 3 A current source with an open circuit.
2. **Analyze the remaining elements:**
- The 20 Ω resistor and 10 Ω resistor are now in series.
- The dependent current source \( 0.5 V_o \) is also considered.
3. **Combine series resistances:**
- The combination of 20 Ω and 10 Ω resistors gives the equivalent resistance.
#### Additional Notes:
- Remember that while independent sources are turned off (current sources open, voltage sources shorted), dependent sources remain in the analysis.
- Use Ohm's law and Kirchhoff's laws as necessary for detailed calculations.
By following these steps, you can determine the Thevenin equivalent resistance at terminals \( a-b \).
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