Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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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.
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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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