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For the RCL circuit shown in the figure below suppose that R = 1 ohm, L = 1/2H, C = 1/4F, and Vs = 4V. Find i(t) and v(t) for all t. 1Ω ww + t=0 'L m U C R

For the RCL circuit shown in the figure below suppose that R = 1 ohm, L = 1/2H, C = 1/4F, and Vs = 4V. Find i(t) and v(t) for all t. 1Ω ww + t=0 'L m U C R

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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Please solve the following problem showing all details without using Laplace. This is just for practice but I am confused on this. 

**Problem 1** For the RCL circuit shown in the figure below, suppose that \( R = 1 \, \Omega \), \( L = \frac{1}{2} \, \text{H} \), \( C = \frac{1}{4} \, \text{F} \), and \( V_s = 4 \, \text{V} \). Find \( i(t) \) and \( v(t) \) for all \( t \). **Diagram Description:** The circuit diagram includes: 1. A voltage source \( V_s \). 2. A resistor with a resistance of \( 1 \, \Omega \). 3. An inductor \( L \). 4. A capacitor \( C \). 5. A switch is indicating \( t = 0 \). 6. Current \( i(t) \) is shown flowing through the inductor. 7. Voltage across the capacitor is labeled \( v(t) \). The circuit is a series RLC circuit with given component values intended for solving current and voltage functions over time.
Transcribed Image Text:**Problem 1** For the RCL circuit shown in the figure below, suppose that \( R = 1 \, \Omega \), \( L = \frac{1}{2} \, \text{H} \), \( C = \frac{1}{4} \, \text{F} \), and \( V_s = 4 \, \text{V} \). Find \( i(t) \) and \( v(t) \) for all \( t \). **Diagram Description:** The circuit diagram includes: 1. A voltage source \( V_s \). 2. A resistor with a resistance of \( 1 \, \Omega \). 3. An inductor \( L \). 4. A capacitor \( C \). 5. A switch is indicating \( t = 0 \). 6. Current \( i(t) \) is shown flowing through the inductor. 7. Voltage across the capacitor is labeled \( v(t) \). The circuit is a series RLC circuit with given component values intended for solving current and voltage functions over time.
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