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The circuit below is the problem we did in class for R=300 2 (overdamped) and 200 2 (critically damped). Compute a, Mn and for R=100 N (the underdamped case) and determine Ve(t). You should obtain v.(t) = 10 – 10e-at cos(@nt) – 5.77e-at sin(@nt)

The circuit below is the problem we did in class for R=300 2 (overdamped) and 200 2 (critically damped). Compute a, Mn and for R=100 N (the underdamped case) and determine Ve(t). You should obtain v.(t) = 10 – 10e-at cos(@nt) – 5.77e-at sin(@nt)

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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The circuit below is the problem we did in class for \( R = 300 \, \Omega \) (overdamped) and 200 \(\Omega\) (critically damped). Compute \( \alpha \), \( \omega_n \), and \( \zeta \) for \( R = 100 \, \Omega \) (the underdamped case) and determine \( v_c(t) \). You should obtain \[ v_c(t) = 10 - 10e^{-\alpha t} \cos(\omega_n t) - 5.77e^{-\alpha t} \sin(\omega_n t) \] **Circuit Diagram Explanation:** - **Voltage Source:** A 10 V DC source is connected at the left. - **Switch (SW1):** A switch is positioned directly after the voltage source. - **Inductor (L1):** A 10 mH inductor is connected in series after the switch. - **Resistor:** A resistor (unspecified resistance) follows the inductor and is connected in series. - **Capacitor (C1):** A 1 µF capacitor is connected in parallel to the resistor and inductor, and the voltage across it is marked as \( v_c \). - **Ground Connection:** The circuit is completed back to the ground from the voltage source. The task involves analyzing the damping behavior of the circuit for different resistance values and computing the response of the voltage across the capacitor.
Transcribed Image Text:The circuit below is the problem we did in class for \( R = 300 \, \Omega \) (overdamped) and 200 \(\Omega\) (critically damped). Compute \( \alpha \), \( \omega_n \), and \( \zeta \) for \( R = 100 \, \Omega \) (the underdamped case) and determine \( v_c(t) \). You should obtain \[ v_c(t) = 10 - 10e^{-\alpha t} \cos(\omega_n t) - 5.77e^{-\alpha t} \sin(\omega_n t) \] **Circuit Diagram Explanation:** - **Voltage Source:** A 10 V DC source is connected at the left. - **Switch (SW1):** A switch is positioned directly after the voltage source. - **Inductor (L1):** A 10 mH inductor is connected in series after the switch. - **Resistor:** A resistor (unspecified resistance) follows the inductor and is connected in series. - **Capacitor (C1):** A 1 µF capacitor is connected in parallel to the resistor and inductor, and the voltage across it is marked as \( v_c \). - **Ground Connection:** The circuit is completed back to the ground from the voltage source. The task involves analyzing the damping behavior of the circuit for different resistance values and computing the response of the voltage across the capacitor.
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