Only do A-C # Solving Electrical Circuit ProblemsIn this exercise, we will explore how to solve electrical circuit problems using various techniques. We will focus on creating logical solutions in terms of resistances (R), inductance (L), capacitance (C), and specified variables.## Problem Description:### Consider the Circuit:We have a circuit consisting of the following components and configurations:- **Voltage Source**: $ V(t) $- **Resistor** $ R_S $- **Inductor** $ L_1 $- **Capacitor** $ C_1 $- **Resistor** $ R_1 $- **Capacitor** $ C_2 $The circuit has two mesh currents: $ i_1(t) $ and $ i_2(t) $.### Task Breakdown:#### a) Finding the Forced Response $ V(s) $:- **Objective**: Begin with Kirchhoff's Voltage Law (KVL) analysis and derive $ V(t) $ in terms of $ i_1(t) $.- **Steps**: 1. Apply KVL to the circuit loops. 2. Use mesh currents $ i_1 $ and $ i_2 $ to find the solution 3. Calculate the Laplace Transform $ \mathcal{L}\{V(t)\} = V(s) $.#### b) General $ V(s) $ and Specific Current:- **Objective**: After expressing the general $ V(s) $, assume a specific form of current $ i(t) $. $ i(t) = A(u(t) - u(t - T_A)) $. - **Steps**: 1. Substitute the specific current form into the expression for $ V(s) $.#### c) Specific Case for $ V(t) $:- **Objective**: Now assume: \[ V(t) = \int_{\ell \ell}^{u t} e^{-t}\cos (\omega t + \phi) dt \] - **Steps**: 1. Calculate $ i(s) $ for this specific case.#### d) Impedance $ Z(s) $:- **Objective**: Determine $ Z(s) $. - **Part b)**: For the part b assumption. - **Part c)**: If $ Z $ is

Answered: Image /qna-images/answer/94dad452-a9ab-4c07-9d89-04c87c9be80e.jpg

Show all work, equations and how numbers plug into your equations to calculate answers 1) Consider the following: (create logical solutions in equation form in terms of R, L, Cand specified variables) , (t) Vo ww- (a) Rs C1 V(t) C2 (t))R1 (iz(t) a) Find the Forced Response V(s). Begin with KVL analysis and find V(t) in terms of i, (t)... then find L{V(t)} = V(s). Use mesh currents i, iz to create your solution. b) After expressing the general V(s) assume i(t) = A(u(t) – u(t – TĄ)) and find V (s) for the specific current c) Now assume ul V(t) = e-t cos(wt + $) dt and find i(s) for this new specific case d) What is Z(s) for part b), part c) if Z is the impedance looking from node (a) to the right.. with the source disconnected? e) How do you calculate the magnitude of the current in part c) at a frequency of 100 Hz? The angle of i(s) at 100 Hz? Vo(s) f) Find = H(s) in general (i.e. no specific form of V (s)). V(s)

Show all work, equations and how numbers plug into your equations to calculate answers 1) Consider the following: (create logical solutions in equation form in terms of R, L, Cand specified variables) , (t) Vo ww- (a) Rs C1 V(t) C2 (t))R1 (iz(t) a) Find the Forced Response V(s). Begin with KVL analysis and find V(t) in terms of i, (t)... then find L{V(t)} = V(s). Use mesh currents i, iz to create your solution. b) After expressing the general V(s) assume i(t) = A(u(t) – u(t – TĄ)) and find V (s) for the specific current c) Now assume ul V(t) = e-t cos(wt + $) dt and find i(s) for this new specific case d) What is Z(s) for part b), part c) if Z is the impedance looking from node (a) to the right.. with the source disconnected? e) How do you calculate the magnitude of the current in part c) at a frequency of 100 Hz? The angle of i(s) at 100 Hz? Vo(s) f) Find = H(s) in general (i.e. no specific form of V (s)). V(s)

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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Only do A-C

# Solving Electrical Circuit Problems

In this exercise, we will explore how to solve electrical circuit problems using various techniques. We will focus on creating logical solutions in terms of resistances (R), inductance (L), capacitance (C), and specified variables.

## Problem Description:

### Consider the Circuit:

We have a circuit consisting of the following components and configurations:
- **Voltage Source**: $ V(t) $
- **Resistor** $ R_S $
- **Inductor** $ L_1 $
- **Capacitor** $ C_1 $
- **Resistor** $ R_1 $
- **Capacitor** $ C_2 $

The circuit has two mesh currents: $ i_1(t) $ and $ i_2(t) $.

### Task Breakdown:

#### a) Finding the Forced Response $ V(s) $:
- **Objective**: Begin with Kirchhoff's Voltage Law (KVL) analysis and derive $ V(t) $ in terms of $ i_1(t) $.
- **Steps**:
1. Apply KVL to the circuit loops.
2. Use mesh currents $ i_1 $ and $ i_2 $ to find the solution
3. Calculate the Laplace Transform $ \mathcal{L}\{V(t)\} = V(s) $.

#### b) General $ V(s) $ and Specific Current:
- **Objective**: After expressing the general $ V(s) $, assume a specific form of current $ i(t) $.
$ i(t) = A(u(t) - u(t - T_A)) $.

- **Steps**:
1. Substitute the specific current form into the expression for $ V(s) $.

#### c) Specific Case for $ V(t) $:
- **Objective**: Now assume:
\[
V(t) = \int_{\ell \ell}^{u t} e^{-t}\cos (\omega t + \phi) dt
\]

- **Steps**:
1. Calculate $ i(s) $ for this specific case.

#### d) Impedance $ Z(s) $:
- **Objective**: Determine $ Z(s) $.
- **Part b)**: For the part b assumption.
- **Part c)**: If $ Z $ is

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