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The switch in the following Fig. has been closed for a long time, and it opens at t = 0. Find i(t) for t > /=0 30V χ 10Ω wwwww 4Ω i(t) m τ ΕΩ 5Η 8 Ω www 8 Ω

The switch in the following Fig. has been closed for a long time, and it opens at t = 0. Find i(t) for t > /=0 30V χ 10Ω wwwww 4Ω i(t) m τ ΕΩ 5Η 8 Ω www 8 Ω

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 switch in the following figure has been closed for a long time, and it opens at \( t = 0 \). Find \( i(t) \) for \( t \geq 0 \). ### Description of the Circuit: - **Source**: A voltage source of 30V is connected to the circuit. - **Components**: - A 10 Ω resistor connected in series with the switch. - After the switch, a 4 Ω resistor follows in series. - The circuit then connects to a 6 Ω resistor, and in parallel with it are two 8 Ω resistors. - An inductor of 5 H is also present in the circuit, showing the current \( i(t) \) flowing through it. ### Analysis: - The circuit analyzes the behavior of \( i(t) \) when the switch is opened at \( t = 0 \). - Since the switch was closed for a long time, the inductor is assumed to be fully energized at \( t = 0 \). ### Objective: - To find the expression for \( i(t) \) for \( t \geq 0 \), considering the change in circuit conditions when the switch opens. This involves solving a differential equation based on the components and their arrangement.
Transcribed Image Text:The switch in the following figure has been closed for a long time, and it opens at \( t = 0 \). Find \( i(t) \) for \( t \geq 0 \). ### Description of the Circuit: - **Source**: A voltage source of 30V is connected to the circuit. - **Components**: - A 10 Ω resistor connected in series with the switch. - After the switch, a 4 Ω resistor follows in series. - The circuit then connects to a 6 Ω resistor, and in parallel with it are two 8 Ω resistors. - An inductor of 5 H is also present in the circuit, showing the current \( i(t) \) flowing through it. ### Analysis: - The circuit analyzes the behavior of \( i(t) \) when the switch is opened at \( t = 0 \). - Since the switch was closed for a long time, the inductor is assumed to be fully energized at \( t = 0 \). ### Objective: - To find the expression for \( i(t) \) for \( t \geq 0 \), considering the change in circuit conditions when the switch opens. This involves solving a differential equation based on the components and their arrangement.
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