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3Ω + Vx 4Α t=0 18 Ω For the circuit, Determine the value of VouT(t) for t > 0. 12 Ω 0.5.Vx + + VOUT 200 μΗ m Μ 6Ω

3Ω + Vx 4Α t=0 18 Ω For the circuit, Determine the value of VouT(t) for t > 0. 12 Ω 0.5.Vx + + VOUT 200 μΗ m Μ 6Ω

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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### Circuit Analysis The circuit diagram presented features several components including resistors, a current source, an inductor, and a dependent voltage source. #### Components: 1. **Resistors:** - A 3-ohm resistor in series with the voltage \( V_x \). - An 18-ohm resistor connected in series with the 200 µH inductor. - A 12-ohm resistor in parallel with the output voltage \( V_{OUT} \). - A 6-ohm resistor connected in series with the dependent voltage source. 2. **Current Source:** - A 4 A current source is connected which provides current through the circuit. 3. **Inductor:** - 200 microhenries (µH) inductor connected following the 18-ohm resistor. 4. **Dependent Voltage Source:** - A voltage source controlled by the voltage across the 3-ohm resistor (\( V_x \)), defined as \( 0.5 \times V_x \). #### Objective: - Determine the value of \( V_{OUT}(t) \) for \( t > 0 \). ### Explanation: - **Initial Conditions:** - The circuit operates with a switch action at \( t = 0 \). - **Analysis Approach:** - The circuit's behavior for \( t > 0 \) can be evaluated using Kirchhoff’s laws, considering the inductive and resistive components. - The dependent voltage source will affect \( V_{OUT} \), as it relies on the voltage \( V_x \). ### Study Points: - Understand how to set up and solve differential equations for RL circuits, particularly for \( t > 0 \). - Grasp the role of dependent sources in modifying circuit behavior based on other circuit parameters. By solving this circuit for \( t > 0 \), students will enhance their understanding of transient responses and the impact of dependent sources in electrical circuits.
Transcribed Image Text:### Circuit Analysis The circuit diagram presented features several components including resistors, a current source, an inductor, and a dependent voltage source. #### Components: 1. **Resistors:** - A 3-ohm resistor in series with the voltage \( V_x \). - An 18-ohm resistor connected in series with the 200 µH inductor. - A 12-ohm resistor in parallel with the output voltage \( V_{OUT} \). - A 6-ohm resistor connected in series with the dependent voltage source. 2. **Current Source:** - A 4 A current source is connected which provides current through the circuit. 3. **Inductor:** - 200 microhenries (µH) inductor connected following the 18-ohm resistor. 4. **Dependent Voltage Source:** - A voltage source controlled by the voltage across the 3-ohm resistor (\( V_x \)), defined as \( 0.5 \times V_x \). #### Objective: - Determine the value of \( V_{OUT}(t) \) for \( t > 0 \). ### Explanation: - **Initial Conditions:** - The circuit operates with a switch action at \( t = 0 \). - **Analysis Approach:** - The circuit's behavior for \( t > 0 \) can be evaluated using Kirchhoff’s laws, considering the inductive and resistive components. - The dependent voltage source will affect \( V_{OUT} \), as it relies on the voltage \( V_x \). ### Study Points: - Understand how to set up and solve differential equations for RL circuits, particularly for \( t > 0 \). - Grasp the role of dependent sources in modifying circuit behavior based on other circuit parameters. By solving this circuit for \( t > 0 \), students will enhance their understanding of transient responses and the impact of dependent sources in electrical circuits.
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