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The switch shown in the circuit below has been closed for a long time prior to t= 0. Then, it opens at t = 0 and closes again at t= 1 s. Find iz (t) for all t. 21(0)1 2 H -0000 2Ω www 4Ω ww 17A

The switch shown in the circuit below has been closed for a long time prior to t= 0. Then, it opens at t = 0 and closes again at t= 1 s. Find iz (t) for all t. 21(0)1 2 H -0000 2Ω www 4Ω ww 17A

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 Statement:** The switch shown in the circuit below has been closed for a long time prior to \( t = 0 \). Then, it opens at \( t = 0 \) and closes again at \( t = 1 \, \text{s} \). Find \( i_L(t) \) for all \( t \). **Circuit Diagram:** - The circuit consists of the following components connected in a series-parallel arrangement: - An inductor with an inductance of \( 2 \, \text{H} \), and the current through the inductor is denoted as \( i_L(t) \). - A \( 2 \, \Omega \) resistor. - A \( 4 \, \Omega \) resistor. - A switch, represented as open or closed at different times. - An independent current source supplying \( 7 \, \text{A} \). **Explanation:** 1. **Initial Conditions:** - The switch has been closed for a long time before \( t = 0 \), indicating a steady state has been reached. 2. **At \( t = 0 \):** - The switch opens, affecting the circuit's behavior and the inductor's current. 3. **At \( t = 1 \, \text{s} \):** - The switch closes again, changing the circuit conditions once more. To solve for \( i_L(t) \), analyze the circuit for \( t < 0\), \( 0 \leq t < 1 \), and \( t \geq 1 \). Use the principles of circuit analysis, such as Kirchhoff’s laws, and the properties of inductors in DC circuits. Consider the transient and steady-state responses of the inductor current due to the operation of the switch.
Transcribed Image Text:**Problem Statement:** The switch shown in the circuit below has been closed for a long time prior to \( t = 0 \). Then, it opens at \( t = 0 \) and closes again at \( t = 1 \, \text{s} \). Find \( i_L(t) \) for all \( t \). **Circuit Diagram:** - The circuit consists of the following components connected in a series-parallel arrangement: - An inductor with an inductance of \( 2 \, \text{H} \), and the current through the inductor is denoted as \( i_L(t) \). - A \( 2 \, \Omega \) resistor. - A \( 4 \, \Omega \) resistor. - A switch, represented as open or closed at different times. - An independent current source supplying \( 7 \, \text{A} \). **Explanation:** 1. **Initial Conditions:** - The switch has been closed for a long time before \( t = 0 \), indicating a steady state has been reached. 2. **At \( t = 0 \):** - The switch opens, affecting the circuit's behavior and the inductor's current. 3. **At \( t = 1 \, \text{s} \):** - The switch closes again, changing the circuit conditions once more. To solve for \( i_L(t) \), analyze the circuit for \( t < 0\), \( 0 \leq t < 1 \), and \( t \geq 1 \). Use the principles of circuit analysis, such as Kirchhoff’s laws, and the properties of inductors in DC circuits. Consider the transient and steady-state responses of the inductor current due to the operation of the switch.
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