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4 mH. C is initially Problem 2: E = 8 V, R1 = 6N, R2 = 5N, R3 uncharged, there is no current going through L initially, and the switch S is initially open. The switch S is closed at t = 0. (a) I1 is defined as the current going through R1, I2 is defined as the current going through R2, and Iz is defined as the current going through R3. Find I1, I2, and I3 at t = 0, immediately after the switch is closed. (b) Find I, I2, and Iz a long time after the switch is closed. (c) Find the charge on C a long time after the switch is closed. 20 N, C = 3 µF, and L = || R1 lell R3. S L R2- C

4 mH. C is initially Problem 2: E = 8 V, R1 = 6N, R2 = 5N, R3 uncharged, there is no current going through L initially, and the switch S is initially open. The switch S is closed at t = 0. (a) I1 is defined as the current going through R1, I2 is defined as the current going through R2, and Iz is defined as the current going through R3. Find I1, I2, and I3 at t = 0, immediately after the switch is closed. (b) Find I, I2, and Iz a long time after the switch is closed. (c) Find the charge on C a long time after the switch is closed. 20 N, C = 3 µF, and L = || R1 lell R3. S L R2- C

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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## Problem 2: - \( \mathcal{E} = 8 \, \text{V} \) - \( R_1 = 6\, \Omega \) - \( R_2 = 5\, \Omega \) - \( R_3 = 20\, \Omega \) - \( C = 3\, \mu\text{F} \) - \( L = 4\, \text{mH} \) The capacitor \( C \) is initially uncharged, and initially, there is no current going through the inductor \( L \). The switch \( S \) is initially open and is closed at \( t = 0 \). ### Tasks: - (a) Determine \( I_1 \), \( I_2 \), and \( I_3 \) at \( t = 0 \), immediately after the switch is closed. Where: - \( I_1 \) is the current through \( R_1 \). - \( I_2 \) is the current through \( R_2 \). - \( I_3 \) is the current through \( R_3 \). - (b) Find \( I_1 \), \( I_2 \), and \( I_3 \) a long time after the switch is closed. - (c) Calculate the charge on \( C \) a long time after the switch is closed. ### Diagram Explanation: This circuit diagram includes: 1. A voltage source \( \mathcal{E} \). 2. A switch \( S \) controlling the circuit. 3. An inductor \( L \) connected in series with a resistor \( R_1 \). 4. Two resistors \( R_2 \) and \( R_3 \) connected in parallel with the inductor and \( R_1 \). 5. A capacitor \( C \) connected in parallel with \( R_3 \). Initially, the capacitor is uncharged, and there is no current, indicating a transient analysis problem where the switch's closure initiates the flow of current.
Transcribed Image Text:## Problem 2: - \( \mathcal{E} = 8 \, \text{V} \) - \( R_1 = 6\, \Omega \) - \( R_2 = 5\, \Omega \) - \( R_3 = 20\, \Omega \) - \( C = 3\, \mu\text{F} \) - \( L = 4\, \text{mH} \) The capacitor \( C \) is initially uncharged, and initially, there is no current going through the inductor \( L \). The switch \( S \) is initially open and is closed at \( t = 0 \). ### Tasks: - (a) Determine \( I_1 \), \( I_2 \), and \( I_3 \) at \( t = 0 \), immediately after the switch is closed. Where: - \( I_1 \) is the current through \( R_1 \). - \( I_2 \) is the current through \( R_2 \). - \( I_3 \) is the current through \( R_3 \). - (b) Find \( I_1 \), \( I_2 \), and \( I_3 \) a long time after the switch is closed. - (c) Calculate the charge on \( C \) a long time after the switch is closed. ### Diagram Explanation: This circuit diagram includes: 1. A voltage source \( \mathcal{E} \). 2. A switch \( S \) controlling the circuit. 3. An inductor \( L \) connected in series with a resistor \( R_1 \). 4. Two resistors \( R_2 \) and \( R_3 \) connected in parallel with the inductor and \( R_1 \). 5. A capacitor \( C \) connected in parallel with \( R_3 \). Initially, the capacitor is uncharged, and there is no current, indicating a transient analysis problem where the switch's closure initiates the flow of current.
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