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The circuit given is at steady-state when the switch closes at time t= 0. Determine v(t) for t≥ 0. Use the 4-step approach, listing each step and then showing the work clearly. Box final answer and make sure to write the units and state for what time is the solution valid. 60 24 V 60 1=0 120 ਰਣ 20 mFv(0

The circuit given is at steady-state when the switch closes at time t= 0. Determine v(t) for t≥ 0. Use the 4-step approach, listing each step and then showing the work clearly. Box final answer and make sure to write the units and state for what time is the solution valid. 60 24 V 60 1=0 120 ਰਣ 20 mFv(0

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 Description: The circuit given is at steady-state when the switch closes at time \( t = 0 \). Determine \( v(t) \) for \( t \geq 0 \). **Instructions:** - Use the 4-step approach, listing each step and then showing the work clearly. - Box the final answer and make sure to write the units. - State for what time the solution is valid. ### Circuit Diagram: The circuit provided includes the following components and configuration: - A 24V DC voltage source connected in series. - A switch that closes at \( t = 0 \). - Two resistors, each of 60Ω resistance, connected in parallel. - Another resistor of 120Ω resistance connected in series with a 20 mF (millifarad) capacitor. - The voltage across the capacitor is denoted as \( v(t) \). Here is a more detailed breakdown: 1. **Voltage Source:** 24V. 2. **Switch:** Initially open and then closes at \( t = 0 \). 3. **Resistors:** - First Resistor: 60Ω. - Second Resistor: 60Ω (in parallel with the first resistor). - Third Resistor: 120Ω (in series with the capacitor). 4. **Capacitor:** 20 mF. 5. **Output Voltage:** \( v(t) \), the voltage across the capacitor. ### Step-by-Step Analysis: 1. **Determine Initial Conditions (t < 0):** - Before the switch closes, the circuit is at a steady-state condition. No current flows through the branches involving the switch. - At steady state, the capacitor acts as an open circuit. 2. **Determine Initial Values at t = 0:** - When the switch is closed at \( t = 0 \), the circuit begins to change, and the capacitor starts charging. 3. **Solving the Differential Equation:** - Use Kirchhoff’s Voltage Law (KVL) to formulate the differential equation for the circuit. - Solve the equation for \( v(t) \). 4. **Determine Final Values (t → ∞):** - Find the final voltage across the capacitor when the circuit reaches another steady-state. ### Solution Validity: - The solution for \( v(t) \) is valid for \( t \geq 0 \), from the moment the
Transcribed Image Text:### Problem Description: The circuit given is at steady-state when the switch closes at time \( t = 0 \). Determine \( v(t) \) for \( t \geq 0 \). **Instructions:** - Use the 4-step approach, listing each step and then showing the work clearly. - Box the final answer and make sure to write the units. - State for what time the solution is valid. ### Circuit Diagram: The circuit provided includes the following components and configuration: - A 24V DC voltage source connected in series. - A switch that closes at \( t = 0 \). - Two resistors, each of 60Ω resistance, connected in parallel. - Another resistor of 120Ω resistance connected in series with a 20 mF (millifarad) capacitor. - The voltage across the capacitor is denoted as \( v(t) \). Here is a more detailed breakdown: 1. **Voltage Source:** 24V. 2. **Switch:** Initially open and then closes at \( t = 0 \). 3. **Resistors:** - First Resistor: 60Ω. - Second Resistor: 60Ω (in parallel with the first resistor). - Third Resistor: 120Ω (in series with the capacitor). 4. **Capacitor:** 20 mF. 5. **Output Voltage:** \( v(t) \), the voltage across the capacitor. ### Step-by-Step Analysis: 1. **Determine Initial Conditions (t < 0):** - Before the switch closes, the circuit is at a steady-state condition. No current flows through the branches involving the switch. - At steady state, the capacitor acts as an open circuit. 2. **Determine Initial Values at t = 0:** - When the switch is closed at \( t = 0 \), the circuit begins to change, and the capacitor starts charging. 3. **Solving the Differential Equation:** - Use Kirchhoff’s Voltage Law (KVL) to formulate the differential equation for the circuit. - Solve the equation for \( v(t) \). 4. **Determine Final Values (t → ∞):** - Find the final voltage across the capacitor when the circuit reaches another steady-state. ### Solution Validity: - The solution for \( v(t) \) is valid for \( t \geq 0 \), from the moment the
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