### 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 \( a-b \).

it is asked to find the thevenin resistance seen at terminals

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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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Concept explainers

Thevenin Theorem

Any linear circuit, no matter how complex, maybe simplified to an equivalent circuit utilizing only a single voltage source and series resistance coupled to a load, according to Thevenin's Theorem. The superposition principle says that all foundational equations must be linear, and the notion of "linear" is still the same (i.e., there should not be any exponentials or roots). This is particularly the case when operating with passive elements like resistors, inductors, and capacitors. However, some components (particularly some gaseous and semiconductor devices like tunnel diode, Schottky diode, transistors like BJT, MOSFET) are nonlinear, meaning their current resistance fluctuates with voltage and current. As a result, circuits made up of these parts are known as nonlinear circuits.

Question

### 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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