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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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**RLC Circuit Analysis** **Problem Statement:** Find \( v(t) \) in the RLC circuit given in the figure. The source voltage is given by: \[ V_s(t) = 10 \cos(t) \, \text{V} \] **Circuit Description:** - The circuit is powered by an AC voltage source \( V_s(t) \). - The following components are included in the circuit: - A resistor with a resistance of \( 1 \, \Omega \) in series. - An inductor with an inductance of \( 1 \, \text{H} \). - A parallel branch that includes: - A resistor with a resistance of \( 1 \, \Omega \). - A capacitor with a capacitance of \( 1 \, \text{F} \). - The output voltage across the parallel branch is \( v(t) \). **Task:** Determine \( v(t) \) in the form: \[ v(t) = A \, \cos(t + \phi^\circ) \, \text{V} \] **Solution Format:** The value of \( v(t) \) is given as \( \boxed{\,} \cos(t + (\, \boxed{\,} \,)^\circ) \, \text{V} \). **Explanation of Diagram:** The diagram shows a circuit with the following layout: - A voltage source labeled \( V_s(t) \) on the left, with the positive terminal marked in red. - A horizontal component line going from the voltage source through a \( 1 \, \Omega \) resistor. - This line splits into two paths: 1. One branch goes through a \( 1 \, \Omega \) resistor and rejoins the main circuit. 2. The second branch contains a \( 1 \, \text{F} \) capacitor and connects back to the main line to form a closed loop. - An inductor of \( 1 \, \text{H} \) is placed in series directly with the voltage source and the other components, encircling the entire circuit. - The voltage across the parallel capacitor and resistor branch is marked as \( v(t) \).
Transcribed Image Text:**RLC Circuit Analysis** **Problem Statement:** Find \( v(t) \) in the RLC circuit given in the figure. The source voltage is given by: \[ V_s(t) = 10 \cos(t) \, \text{V} \] **Circuit Description:** - The circuit is powered by an AC voltage source \( V_s(t) \). - The following components are included in the circuit: - A resistor with a resistance of \( 1 \, \Omega \) in series. - An inductor with an inductance of \( 1 \, \text{H} \). - A parallel branch that includes: - A resistor with a resistance of \( 1 \, \Omega \). - A capacitor with a capacitance of \( 1 \, \text{F} \). - The output voltage across the parallel branch is \( v(t) \). **Task:** Determine \( v(t) \) in the form: \[ v(t) = A \, \cos(t + \phi^\circ) \, \text{V} \] **Solution Format:** The value of \( v(t) \) is given as \( \boxed{\,} \cos(t + (\, \boxed{\,} \,)^\circ) \, \text{V} \). **Explanation of Diagram:** The diagram shows a circuit with the following layout: - A voltage source labeled \( V_s(t) \) on the left, with the positive terminal marked in red. - A horizontal component line going from the voltage source through a \( 1 \, \Omega \) resistor. - This line splits into two paths: 1. One branch goes through a \( 1 \, \Omega \) resistor and rejoins the main circuit. 2. The second branch contains a \( 1 \, \text{F} \) capacitor and connects back to the main line to form a closed loop. - An inductor of \( 1 \, \text{H} \) is placed in series directly with the voltage source and the other components, encircling the entire circuit. - The voltage across the parallel capacitor and resistor branch is marked as \( v(t) \).
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