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Consider the circuit shown. The values of the circuit elements are: E = 12.0 V, R = 10.0, C = 500 nF, L = 2.00 mH. The switch is electronic and can switch from a to b redirecting but not breaking the current flow. Initially, the switch is in position b, no current is flowing, and the capacitor is uncharged. E At t = 0, the switch moves to position a. It will stay there for two time constants. (a) Find the current through the battery at t = 2T. Then, at t = 2T, the switch moves to position b. It will stay there for a long time. Energy will oscillate back and forth between the inductor and capacitor, (b) What is the maximum energy stored in the capacitor? R ele

Consider the circuit shown. The values of the circuit elements are: E = 12.0 V, R = 10.0, C = 500 nF, L = 2.00 mH. The switch is electronic and can switch from a to b redirecting but not breaking the current flow. Initially, the switch is in position b, no current is flowing, and the capacitor is uncharged. E At t = 0, the switch moves to position a. It will stay there for two time constants. (a) Find the current through the battery at t = 2T. Then, at t = 2T, the switch moves to position b. It will stay there for a long time. Energy will oscillate back and forth between the inductor and capacitor, (b) What is the maximum energy stored in the capacitor? R ele

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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### Circuit Analysis Exercise #### Circuit Description: The circuit given includes the following components: - **EMF (ε)**: 12.0 V - **Resistor (R)**: 10.0 Ω - **Capacitor (C)**: 500 nF - **Inductor (L)**: 2.00 mH The circuit features an electronic switch (S) that alternates between positions **a** and **b**, allowing current redirection without interrupting the flow. #### Initial Conditions: - **Switch Position**: Initially in position **b**. - **Current**: No current flows. - **Capacitor**: Uncharged. #### Circuit Operation: 1. **Switch to Position a**: At time \( t = 0 \), the switch moves to position **a** and remains there for two time constants. - **Task (a)**: Determine the current through the battery at \( t = 2\tau \). 2. **Switch to Position b**: At \( t = 2\tau \), the switch moves to position **b** and stays for an extended period, leading to energy oscillation between the inductor and capacitor. - **Task (b)**: Calculate the maximum energy stored in the capacitor. - **Task (c)**: Compute the time needed for the capacitor to reach maximum energy initially. - **Task (d)**: Graph the current through the circuit from \( t = 0 \), illustrating the transition to oscillation. #### Diagram Explanation: The circuit diagram consists of: - A voltage source indicated by \( ε \). - A switch marked **S** that can alternate between contacts **a** and **b**. - A resistor \( R \) in series with the capacitor \( C \). - An inductor \( L \) in the loop, connected across the switch. #### Analysis Goals: - **Understand RC and LC Circuit Dynamics**: Analyze initial charging phase and periodic oscillations. - **Time Constant Calculations**: Determine periods of significant current or energy changes. - **Graphical Representation**: Articulate changes in current over time effectively through a graph. This exercise explores time-dependent behavior in RLC circuits, highlighting crucial calculations and conceptual understanding areas in electrical engineering.
Transcribed Image Text:### Circuit Analysis Exercise #### Circuit Description: The circuit given includes the following components: - **EMF (ε)**: 12.0 V - **Resistor (R)**: 10.0 Ω - **Capacitor (C)**: 500 nF - **Inductor (L)**: 2.00 mH The circuit features an electronic switch (S) that alternates between positions **a** and **b**, allowing current redirection without interrupting the flow. #### Initial Conditions: - **Switch Position**: Initially in position **b**. - **Current**: No current flows. - **Capacitor**: Uncharged. #### Circuit Operation: 1. **Switch to Position a**: At time \( t = 0 \), the switch moves to position **a** and remains there for two time constants. - **Task (a)**: Determine the current through the battery at \( t = 2\tau \). 2. **Switch to Position b**: At \( t = 2\tau \), the switch moves to position **b** and stays for an extended period, leading to energy oscillation between the inductor and capacitor. - **Task (b)**: Calculate the maximum energy stored in the capacitor. - **Task (c)**: Compute the time needed for the capacitor to reach maximum energy initially. - **Task (d)**: Graph the current through the circuit from \( t = 0 \), illustrating the transition to oscillation. #### Diagram Explanation: The circuit diagram consists of: - A voltage source indicated by \( ε \). - A switch marked **S** that can alternate between contacts **a** and **b**. - A resistor \( R \) in series with the capacitor \( C \). - An inductor \( L \) in the loop, connected across the switch. #### Analysis Goals: - **Understand RC and LC Circuit Dynamics**: Analyze initial charging phase and periodic oscillations. - **Time Constant Calculations**: Determine periods of significant current or energy changes. - **Graphical Representation**: Articulate changes in current over time effectively through a graph. This exercise explores time-dependent behavior in RLC circuits, highlighting crucial calculations and conceptual understanding areas in electrical engineering.
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