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2- Use superposition to find vx(t) in the circuit below. 25 V 2002 www 5A (4 492 www 0.1%,

2- Use superposition to find vx(t) in the circuit below. 25 V 2002 www 5A (4 492 www 0.1%,

Introductory Circuit Analysis (13th Edition)
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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USE SPT THEOREM FIND VX(NEED A NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE)

### Exercise: Using Superposition to Find \( v_x(t) \) #### Problem Statement: Use superposition to find \( v_x(t) \) in the circuit below. #### Circuit Description: The circuit consists of the following components: - A 25 V voltage source. - A 20 Ω resistor. - A 5 A current source. - A 4 Ω resistor. - A dependent current source described as \( 0.1i_x \). The configuration of these components can be described as: 1. The 25 V voltage source is connected in series with a 20 Ω resistor. 2. The node at the end of the 20 Ω resistor branches out into two parallel paths: - The first parallel path contains a 5 A current source. - The second parallel path contains a 4 Ω resistor connected in series with a dependent current source represented as \( 0.1i_x \). 3. The bottom of the dependent current source is connected to the ground, closing the circuit. #### Diagram Explanation: In the given circuit diagram: - The voltage source (+25 V) is located on the left side. - The 20 Ω resistor is situated horizontally and connected to the right of the 25 V voltage source. - After the 20 Ω resistor, the circuit splits into two branches. - The top branch contains the 5 A current source. - The bottom branch contains a 4 Ω resistor and then the dependent current source (\( 0.1i_x \)). - The dependent current source's negative end is connected to the ground. ### Steps for Superposition Analysis: Superposition involves analyzing the circuit by considering one independent source at a time while turning off all other independent sources. When "turning off" a voltage source, you replace it with a short circuit (0 V). When "turning off" a current source, you replace it with an open circuit (0 A). 1. **Analyze with the 25 V Voltage Source Active:** - Replace the 5 A current source with an open circuit. - Determine \( v_x(t) \) using the remaining active source. 2. **Analyze with the 5 A Current Source Active:** - Replace the 25 V voltage source with a short circuit. - Calculate \( v_x(t) \) under these conditions. 3. **Combine the Results:** - Sum the individual contributions of \( v_x(t) \)
Transcribed Image Text:### Exercise: Using Superposition to Find \( v_x(t) \) #### Problem Statement: Use superposition to find \( v_x(t) \) in the circuit below. #### Circuit Description: The circuit consists of the following components: - A 25 V voltage source. - A 20 Ω resistor. - A 5 A current source. - A 4 Ω resistor. - A dependent current source described as \( 0.1i_x \). The configuration of these components can be described as: 1. The 25 V voltage source is connected in series with a 20 Ω resistor. 2. The node at the end of the 20 Ω resistor branches out into two parallel paths: - The first parallel path contains a 5 A current source. - The second parallel path contains a 4 Ω resistor connected in series with a dependent current source represented as \( 0.1i_x \). 3. The bottom of the dependent current source is connected to the ground, closing the circuit. #### Diagram Explanation: In the given circuit diagram: - The voltage source (+25 V) is located on the left side. - The 20 Ω resistor is situated horizontally and connected to the right of the 25 V voltage source. - After the 20 Ω resistor, the circuit splits into two branches. - The top branch contains the 5 A current source. - The bottom branch contains a 4 Ω resistor and then the dependent current source (\( 0.1i_x \)). - The dependent current source's negative end is connected to the ground. ### Steps for Superposition Analysis: Superposition involves analyzing the circuit by considering one independent source at a time while turning off all other independent sources. When "turning off" a voltage source, you replace it with a short circuit (0 V). When "turning off" a current source, you replace it with an open circuit (0 A). 1. **Analyze with the 25 V Voltage Source Active:** - Replace the 5 A current source with an open circuit. - Determine \( v_x(t) \) using the remaining active source. 2. **Analyze with the 5 A Current Source Active:** - Replace the 25 V voltage source with a short circuit. - Calculate \( v_x(t) \) under these conditions. 3. **Combine the Results:** - Sum the individual contributions of \( v_x(t) \)
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