Find Vo in the circuit below using Thevenin Theorem 12V R + 2 ΚΩ X 2V 2000 2 ΚΩ R + Vx32KΩ ΚΩ 2 ΚΩ + V.

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### Thevenin's Theorem Application to Circuit Analysis

In this educational module, we will explore the application of Thevenin’s Theorem to simplify the analysis of an electrical circuit. The objective is to determine the output voltage \( V_0 \) in the given circuit.

#### Given Circuit:

- **Voltage Source:** 12V
- **Resistors:**
  - \( R_1 = 2 \text{ k}\Omega \)
  - \( R_2 = 2 \text{ k}\Omega \)
  - \( R_3 = 2 \text{ k}\Omega \)
  - \( R_4 = 2 \text{ k}\Omega \)
- **Current Source:** \( \frac{2V_x}{2000} \)

#### Diagram Explanation:

The circuit consists of:

1. A 12V voltage source connected in series with a 2 kΩ resistor (\( R_1 \)).
2. This is followed by a node that branches into:
   - A series combination of two 2 kΩ resistors (\( R_2 \) and \( R_3 \)).
   - A dependent current source defined by \( \frac{2V_x}{2000} \).
3. The output voltage (\( V_0 \)) is measured across resistor \( R_4 \) (2 kΩ), which is placed in parallel to \( R_3 \).

#### Step-by-Step Approach:

1. **Identify \( V_x \) Voltage:**
   - \( V_x \) is the voltage across \( R_1 \).

2. **Determine Open Circuit Voltage (Thevenin Voltage, \( V_{th} \)):**
   - Deactivate all independent sources (replace the voltage source with a short circuit).
   - Calculate the voltage across the open terminals where \( V_0 \) is to be found.

3. **Find Equivalent Resistance (Thevenin Resistance, \( R_{th} \)):**
   - With independent sources deactivated, calculate the resistance seen from the open terminals.

4. **Form Thevenin Equivalent Circuit:**
   - Simplify the circuit to a single voltage source \( V_{th} \) in series with \( R_{th} \), across which \( V_0 \) is calculated.

By applying Thevenin’s theorem, we reduce the complexity of the circuit and systematically determine the output voltage \( V_
Transcribed Image Text:### Thevenin's Theorem Application to Circuit Analysis In this educational module, we will explore the application of Thevenin’s Theorem to simplify the analysis of an electrical circuit. The objective is to determine the output voltage \( V_0 \) in the given circuit. #### Given Circuit: - **Voltage Source:** 12V - **Resistors:** - \( R_1 = 2 \text{ k}\Omega \) - \( R_2 = 2 \text{ k}\Omega \) - \( R_3 = 2 \text{ k}\Omega \) - \( R_4 = 2 \text{ k}\Omega \) - **Current Source:** \( \frac{2V_x}{2000} \) #### Diagram Explanation: The circuit consists of: 1. A 12V voltage source connected in series with a 2 kΩ resistor (\( R_1 \)). 2. This is followed by a node that branches into: - A series combination of two 2 kΩ resistors (\( R_2 \) and \( R_3 \)). - A dependent current source defined by \( \frac{2V_x}{2000} \). 3. The output voltage (\( V_0 \)) is measured across resistor \( R_4 \) (2 kΩ), which is placed in parallel to \( R_3 \). #### Step-by-Step Approach: 1. **Identify \( V_x \) Voltage:** - \( V_x \) is the voltage across \( R_1 \). 2. **Determine Open Circuit Voltage (Thevenin Voltage, \( V_{th} \)):** - Deactivate all independent sources (replace the voltage source with a short circuit). - Calculate the voltage across the open terminals where \( V_0 \) is to be found. 3. **Find Equivalent Resistance (Thevenin Resistance, \( R_{th} \)):** - With independent sources deactivated, calculate the resistance seen from the open terminals. 4. **Form Thevenin Equivalent Circuit:** - Simplify the circuit to a single voltage source \( V_{th} \) in series with \( R_{th} \), across which \( V_0 \) is calculated. By applying Thevenin’s theorem, we reduce the complexity of the circuit and systematically determine the output voltage \( V_
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