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In the following 2 circuits, all resistors and inductors are the same. There is no current in the circuits at time t=0. Draw the current in the battery's branch of each circuit as a function of time assuming the switch is thrown at time t=0. Make sure your plots show the correct long term behavior. + 26/R ɛ/R + 2ɛ/R E/R

In the following 2 circuits, all resistors and inductors are the same. There is no current in the circuits at time t=0. Draw the current in the battery's branch of each circuit as a function of time assuming the switch is thrown at time t=0. Make sure your plots show the correct long term behavior. + 26/R ɛ/R + 2ɛ/R E/R

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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**Educational Content on RL Circuits** In the following two circuits, all resistors and inductors are the same. Initially, there is no current in the circuits at time \( t=0 \). Your task is to draw the current in the battery's branch of each circuit as a function of time, assuming the switch is thrown at time \( t=0 \). Ensure your plots depict the correct long-term behavior. ### Circuit Diagrams: #### First Circuit (Top): - The circuit consists of a battery (\( \epsilon \)), a resistor, an inductor, and a switch. - Upon closing the switch at \( t=0 \), the current begins to flow, affected by the resistance and inductance. #### Second Circuit (Bottom): - Similar to the top circuit, this one also includes a battery (\( \epsilon \)), a resistor, an inductor, and a switch. - When the switch is closed at \( t=0 \), the behavior mirrors the first circuit initially, with the current developing over time due to the resistance and inductance present. ### Graphs to Illustrate Current Over Time: For both circuits, the right-hand side contains graphs representing current as a function of time: - **Vertical Axis (Current):** - Points marked at \( \frac{2\epsilon}{R} \) and \( \frac{\epsilon}{R} \). - **Horizontal Axis (Time):** - Time progresses to the right, showing how current stabilizes over time. Both circuits display curves that start from zero current and adjust according to the characteristics of the resistor and inductor, illustrating how the current stabilizes to its final value over time. The graphs should show an exponential rise in current as \( t \) increases, ultimately reaching the steady-state where the inductor behaves like a short circuit. For educational purposes, note how the inductance initially resists changes in current, causing the exponential growth and eventual settling of the current at long-term values.
Transcribed Image Text:**Educational Content on RL Circuits** In the following two circuits, all resistors and inductors are the same. Initially, there is no current in the circuits at time \( t=0 \). Your task is to draw the current in the battery's branch of each circuit as a function of time, assuming the switch is thrown at time \( t=0 \). Ensure your plots depict the correct long-term behavior. ### Circuit Diagrams: #### First Circuit (Top): - The circuit consists of a battery (\( \epsilon \)), a resistor, an inductor, and a switch. - Upon closing the switch at \( t=0 \), the current begins to flow, affected by the resistance and inductance. #### Second Circuit (Bottom): - Similar to the top circuit, this one also includes a battery (\( \epsilon \)), a resistor, an inductor, and a switch. - When the switch is closed at \( t=0 \), the behavior mirrors the first circuit initially, with the current developing over time due to the resistance and inductance present. ### Graphs to Illustrate Current Over Time: For both circuits, the right-hand side contains graphs representing current as a function of time: - **Vertical Axis (Current):** - Points marked at \( \frac{2\epsilon}{R} \) and \( \frac{\epsilon}{R} \). - **Horizontal Axis (Time):** - Time progresses to the right, showing how current stabilizes over time. Both circuits display curves that start from zero current and adjust according to the characteristics of the resistor and inductor, illustrating how the current stabilizes to its final value over time. The graphs should show an exponential rise in current as \( t \) increases, ultimately reaching the steady-state where the inductor behaves like a short circuit. For educational purposes, note how the inductance initially resists changes in current, causing the exponential growth and eventual settling of the current at long-term values.
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