Answered: 4.) For the circuit below, the input Vi… | bartleby

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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**Problem 4: Circuit Analysis**

For the circuit shown, the input \( V_i \) is a 10V pulse that lasts for 1 second. The components have the following values:
- \( R = 106 \, \Omega \)
- \( C = 44.4 \, nF \)
- \( L = 1 \, mH \)

Assume all initial conditions are zero.

**Tasks:**

a.) Find the equation for \( V_i(t) \).

b.) Determine \( V_i(s) \), the Laplace Transform of \( V_i(t) \).

c.) Derive the s-domain equation for the voltage across the capacitor, \( V_o(s) \). Also, find the voltage across the capacitor, \( v_o(t) \).

**Circuit Description:**

The circuit diagram features a voltage source \( V_i \) connected in series with an inductor \( L \), a resistor \( R \), and a capacitor \( C \). The capacitor is positioned parallel to the output voltage terminals \( V_o \).

**Diagram Explanation:**

- **Voltage Source (Vi):** Provides a 10V pulse.
- **Inductor (L):** A coil storing energy in a magnetic field; value is 1 mH.
- **Resistor (R):** Opposes the flow of electric current; value is 106 Ω.
- **Capacitor (C):** Stores energy in an electric field; value is 44.4 nF.
- **Output (Vo):** The voltage across the capacitor.

This setup requires analysis of the input and output responses in both the time domain and the frequency domain (Laplace Transform), accounting for the initial zero-state of the system.

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