Please asap ## Understanding Inductor Behavior in RLC CircuitsThe diagram illustrates a switching RL circuit. Here, we'll analyze the behavior of the inductor current \( i_L \) over time, given different switching conditions.### Problem StatementThe switch in Fig. 03 remained closed for an extended time. 1. **For \( t < 0 \)**: Determine \( i_L \).2. **Just after opening the switch**: Find \( i_L(0^+) \).3. **For \( t \to \infty \)**: Determine \( i_L(\infty) \).4. **Expression for \( i_L(t) \) relative to \( t > 0 \)**: Obtain the expression.### Circuit Description- **Resistors**: 20Ω and 5Ω- **Inductor**: 0.5 H- **Voltage Sources**: Two 100V sources- **Switch Action**: Opens at \( t = 0 \)### Analysis and Solution#### (a) \( i_L \) for \( t < 0 \)When the switch is closed for an extended time, the inductor acts like a short circuit in steady state.- The series combination of resistors forms a voltage divider.- The voltage across the inductor is zero in steady state (short circuit).- The current \( i_L \) can be calculated using the resistors in series.#### (b) \( i_L(0^+) \)Just after the switch opens:- The inductor resists any sudden change in current.- Therefore, \( i_L(0^+) = i_L(0^-) \).#### (c) \( i_L(\infty) \)As \( t \to \infty \):- The inductor will again reach a steady state where it acts like a short circuit.- The current will be determined by the remaining part of the circuit.#### (d) Expression of \( i_L(t) \) for \( t > 0 \)To find \( i_L(t) \) for \( t > 0 \):- Use the natural response of the RL circuit considering the resistor and the inductor.- Write the differential equation governing \( i_L(t) \).- Solve it with initial conditions to find the time-varying current.### Diagram ExplanationThe figure shows:- A switch that opens at \(

Solution:Given Data:=> v=100 v=> R(1)=20 Ohm=> R(2)=5 ohm=> L=0.5 Ht=0 Switch Find :here…

The switch in Fig. 03 remained closed for an extended time. (a) Give iL for t < 0. (b) Just after opening the switch, find iL(0+). (c) Determine iL(∞). after opening the switch, find iL(0+). (c) Determine iL(∞). (d) Obtain the expression of iL(t) relative to t > 0.

The switch in Fig. 03 remained closed for an extended time. (a) Give iL for t < 0. (b) Just after opening the switch, find iL(0+). (c) Determine iL(∞). after opening the switch, find iL(0+). (c) Determine iL(∞). (d) Obtain the expression of iL(t) relative to t > 0.

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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## Understanding Inductor Behavior in RLC Circuits

The diagram illustrates a switching RL circuit. Here, we'll analyze the behavior of the inductor current \( i_L \) over time, given different switching conditions.

### Problem Statement

The switch in Fig. 03 remained closed for an extended time.
1. **For \( t < 0 \)**: Determine \( i_L \).
2. **Just after opening the switch**: Find \( i_L(0^+) \).
3. **For \( t \to \infty \)**: Determine \( i_L(\infty) \).
4. **Expression for \( i_L(t) \) relative to \( t > 0 \)**: Obtain the expression.

### Circuit Description

- **Resistors**: 20Ω and 5Ω
- **Inductor**: 0.5 H
- **Voltage Sources**: Two 100V sources
- **Switch Action**: Opens at \( t = 0 \)

### Analysis and Solution

#### (a) \( i_L \) for \( t < 0 \)

When the switch is closed for an extended time, the inductor acts like a short circuit in steady state.
- The series combination of resistors forms a voltage divider.
- The voltage across the inductor is zero in steady state (short circuit).
- The current \( i_L \) can be calculated using the resistors in series.

#### (b) \( i_L(0^+) \)

Just after the switch opens:
- The inductor resists any sudden change in current.
- Therefore, \( i_L(0^+) = i_L(0^-) \).

#### (c) \( i_L(\infty) \)

As \( t \to \infty \):
- The inductor will again reach a steady state where it acts like a short circuit.
- The current will be determined by the remaining part of the circuit.

#### (d) Expression of \( i_L(t) \) for \( t > 0 \)

To find \( i_L(t) \) for \( t > 0 \):
- Use the natural response of the RL circuit considering the resistor and the inductor.
- Write the differential equation governing \( i_L(t) \).
- Solve it with initial conditions to find the time-varying current.

### Diagram Explanation

The figure shows:
- A switch that opens at \(

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