1 V + Vx 202 ww Find the power received by each of the four elements. 1Ω 2Vx

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Simple circuits techniques
**Educational Content: Analyzing a Circuit**

**Task:**
Find the power received by each of the four elements in the given circuit diagram.

**Diagram Explanation:**

The circuit consists of the following components:

1. **Voltage Source**: 
   - A 1V voltage source on the left side of the circuit.
   
2. **Resistors**:
   - A 2Ω resistor in series with the voltage source.
   - A 1Ω resistor in parallel with the other components on the right side.
   
3. **Voltage-Controlled Current Source**:
   - Labeled as 2Vx, positioned vertically, indicating the current direction is downward.

**Analysis Steps:**

1. **Identify Unknowns**:
   - The voltage across the 2Ω resistor is labeled as Vx. 
   - The current source is labeled with 2Vx, meaning the current depends on Vx.

2. **Calculate Vx**:
   - Use Ohm's law (V = IR) and Kirchhoff’s laws to find the voltage Vx across the 2Ω resistor.

3. **Determine the Currents**:
   - Calculate the currents flowing through each resistor and the current source using the values found.

4. **Calculate Power**:
   - Use the formula P = IV for each element, where P is power, I is current, and V is voltage.

5. **Verify Power Balance**:
   - Ensure the total power delivered equals the total power absorbed, according to the conservation of energy.

By solving these steps, you can find the power received by each element in the circuit to understand the energy distribution within this configuration.
Transcribed Image Text:**Educational Content: Analyzing a Circuit** **Task:** Find the power received by each of the four elements in the given circuit diagram. **Diagram Explanation:** The circuit consists of the following components: 1. **Voltage Source**: - A 1V voltage source on the left side of the circuit. 2. **Resistors**: - A 2Ω resistor in series with the voltage source. - A 1Ω resistor in parallel with the other components on the right side. 3. **Voltage-Controlled Current Source**: - Labeled as 2Vx, positioned vertically, indicating the current direction is downward. **Analysis Steps:** 1. **Identify Unknowns**: - The voltage across the 2Ω resistor is labeled as Vx. - The current source is labeled with 2Vx, meaning the current depends on Vx. 2. **Calculate Vx**: - Use Ohm's law (V = IR) and Kirchhoff’s laws to find the voltage Vx across the 2Ω resistor. 3. **Determine the Currents**: - Calculate the currents flowing through each resistor and the current source using the values found. 4. **Calculate Power**: - Use the formula P = IV for each element, where P is power, I is current, and V is voltage. 5. **Verify Power Balance**: - Ensure the total power delivered equals the total power absorbed, according to the conservation of energy. By solving these steps, you can find the power received by each element in the circuit to understand the energy distribution within this configuration.
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