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After a long time, the switch S₂ is opened and the switch S₁ is closed at t = 0. Find v(0). 2. Find v(t) for t > 0. 3. Find the instantaneous power dissipated by the circuit for all t> 0. v(t) 30 V 12 Ω S1 mu 6 Ω + 100 mF - 6 Ω S2 . 3 Ω 44 A

After a long time, the switch S₂ is opened and the switch S₁ is closed at t = 0. Find v(0). 2. Find v(t) for t > 0. 3. Find the instantaneous power dissipated by the circuit for all t> 0. v(t) 30 V 12 Ω S1 mu 6 Ω + 100 mF - 6 Ω S2 . 3 Ω 44 A

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
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### Problem Description: After a long time, the switch \( S_2 \) is opened and the switch \( S_1 \) is closed at \( t = 0 \). 1. **Find \( v(0) \).** 2. **Find \( v(t) \) for \( t > 0 \).** 3. **Find the instantaneous power dissipated by the circuit for all \( t > 0 \).** ### Circuit Diagram: - **Components:** - **Voltage Source:** 30 V - **Resistors:** - \( 12 \, \Omega \) connected to the voltage source - Two \( 6 \, \Omega \) resistors in parallel to the \( 100 \, \text{mF} \) capacitor - \( 3 \, \Omega \) resistor in series with the \( 6 \, \Omega \) resistors - **Current Source:** 4 A - **Capacitor:** \( 100 \, \text{mF} \) (Millifarads) - **Switches:** - \( S_1 \): Initially open, closes at \( t = 0 \) - \( S_2 \): Initially closed, opens at \( t = 0 \) - **Connections:** - The \( 30 \, \text{V} \) source is connected to the first \( 12 \, \Omega \) resistor, followed by switch \( S_1 \). - The \( 100 \, \text{mF} \) capacitor is between the two parallel \( 6 \, \Omega \) resistors. - The \( 3 \, \Omega \) resistor connects in series to the \( 4 \, \text{A} \) current source. This setup describes the initial and transient behaviors of a simple RLC circuit as switches alter the circuit configuration at time \( t = 0 \).
Transcribed Image Text:### Problem Description: After a long time, the switch \( S_2 \) is opened and the switch \( S_1 \) is closed at \( t = 0 \). 1. **Find \( v(0) \).** 2. **Find \( v(t) \) for \( t > 0 \).** 3. **Find the instantaneous power dissipated by the circuit for all \( t > 0 \).** ### Circuit Diagram: - **Components:** - **Voltage Source:** 30 V - **Resistors:** - \( 12 \, \Omega \) connected to the voltage source - Two \( 6 \, \Omega \) resistors in parallel to the \( 100 \, \text{mF} \) capacitor - \( 3 \, \Omega \) resistor in series with the \( 6 \, \Omega \) resistors - **Current Source:** 4 A - **Capacitor:** \( 100 \, \text{mF} \) (Millifarads) - **Switches:** - \( S_1 \): Initially open, closes at \( t = 0 \) - \( S_2 \): Initially closed, opens at \( t = 0 \) - **Connections:** - The \( 30 \, \text{V} \) source is connected to the first \( 12 \, \Omega \) resistor, followed by switch \( S_1 \). - The \( 100 \, \text{mF} \) capacitor is between the two parallel \( 6 \, \Omega \) resistors. - The \( 3 \, \Omega \) resistor connects in series to the \( 4 \, \text{A} \) current source. This setup describes the initial and transient behaviors of a simple RLC circuit as switches alter the circuit configuration at time \( t = 0 \).
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