Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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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 \( v(t) \).](https://content.bartleby.com/qna-images/question/2302c526-9755-4035-b569-0a02cd47add7/5e919655-d4a9-4519-8db6-c7c5668112a4/0l2xydf_processed.png)
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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