
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Transcribed Image Text:### Circuit Analysis Problem
#### Circuit Diagram
The given circuit consists of:
- A resistor \( R = 40 \, \Omega \)
- A voltage source \( \epsilon = 12 \, V \)
- Two capacitors with capacitances \( 2 \, \mu F \) and \( 1 \, \mu F \)
- An inductor \( 1 \, mH \)
- A switch \( S \)
The capacitors are initially uncharged, and the switch \( S \) is closed at \( t = 0 \).
#### Problem Statement
a) In the circuit, both capacitors are initially uncharged. The switch \( S \) is closed at \( t = 0 \). Calculate \( i_R \), \( i_L \) at \( t = 0 \).
b) When the current in the circuit reaches steady state, calculate the energy stored in the \( 2 \, \mu F \) capacitor and in the inductor.
c) After the current reached steady state, \( S \) is opened and time is reset to \( t = 0 \). Calculate the maximum charge the \( 2 \mu F \) capacitor can get.
#### Explanation of Diagram:
The provided circuit diagram shows a series-parallel arrangement where:
- The resistor \( R \) and voltage source \( \epsilon \) are in series with the switch \( S \).
- The \( 2 \, \mu F \) capacitor is in parallel with the series combination of the \( 1 \, mH \) inductor and the \(1 \, \mu F \) capacitor.
For the calculations:
1. **At \( t = 0 \):**
- \( i_R \): Current through the resistor immediately after the switch is closed.
- \( i_L \): Current through the inductor immediately after the switch is closed.
2. **At Steady State:**
- Calculate the energy stored in the \( 2 \, \mu F \) capacitor.
- Calculate the energy stored in the inductor.
3. **Reset to \( t = 0 \) after Steady State:**
- Determine the maximum charge that can be stored in the \( 2 \, \mu F \) capacitor when switch \( S \) is reopened and the circuit time is reset to \( t = 0 \).
This diagram and the given
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