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in position A for a The switch in the circuit shown has been long time. At t=0, the switch moves to B. Determine vi(t) and ; (+) for t>o. Also, i(t). Also, sketch Vilt) and 4k2 24V + 1 I 3kn M A * t-o $ 5kr. B na 0.5mF + 30V

in position A for a The switch in the circuit shown has been long time. At t=0, the switch moves to B. Determine vi(t) and ; (+) for t>o. Also, i(t). Also, sketch Vilt) and 4k2 24V + 1 I 3kn M A * t-o $ 5kr. B na 0.5mF + 30V

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 Statement:** The switch in the circuit shown has been in position A for a long time. At \( t = 0 \), the switch moves to B. Determine \( v_C(t) \) and \( i_C(t) \) for \( t > 0 \). Also, sketch \( v_C(t) \) and \( i_C(t) \). **Circuit Description:** - **Voltage Sources:** - A 24 V source is connected on the left side of the circuit. - A 30 V source is connected on the right side of the circuit. - **Resistors:** - A 3 kΩ resistor is connected in series with the left voltage source. - A 5 kΩ resistor is connected in parallel with the capacitor. - A 4 kΩ resistor is connected in series with the right voltage source. - **Capacitor:** - A 0.5 mF capacitor is placed in parallel with the 5 kΩ resistor. - **Switch:** - The switch can be in position A or B: - At \( t=0 \), it moves from A to B. - When connected to A, the capacitor charges through the 24 V source. - When moved to B, the circuit rearranges to include the 30 V source. **Objective:** - Analyze the circuit behavior after the switch moves to position B. - Determine \( v_C(t) \) and \( i_C(t) \) for \( t > 0 \), which is the voltage across and the current through the capacitor, respectively. - Sketch the time response of \( v_C(t) \) and \( i_C(t) \). **Analysis Approach:** 1. **Initial Conditions:** - Calculate the initial voltage across the capacitor before the switch is moved. 2. **Behavior for \( t > 0 \):** - Use differential equations or circuit theorems (Thevenin/Norton) for transient analysis. - Determine the time constant of the circuit for the \( t > 0 \) scenario. 3. **Sketching:** - Plot \( v_C(t) \) and \( i_C(t) \) showing exponential growth or decay based on the derived equations. This setup and analysis will guide students in understanding the dynamics of RC circuits during switching and transient states.
Transcribed Image Text:**Problem Statement:** The switch in the circuit shown has been in position A for a long time. At \( t = 0 \), the switch moves to B. Determine \( v_C(t) \) and \( i_C(t) \) for \( t > 0 \). Also, sketch \( v_C(t) \) and \( i_C(t) \). **Circuit Description:** - **Voltage Sources:** - A 24 V source is connected on the left side of the circuit. - A 30 V source is connected on the right side of the circuit. - **Resistors:** - A 3 kΩ resistor is connected in series with the left voltage source. - A 5 kΩ resistor is connected in parallel with the capacitor. - A 4 kΩ resistor is connected in series with the right voltage source. - **Capacitor:** - A 0.5 mF capacitor is placed in parallel with the 5 kΩ resistor. - **Switch:** - The switch can be in position A or B: - At \( t=0 \), it moves from A to B. - When connected to A, the capacitor charges through the 24 V source. - When moved to B, the circuit rearranges to include the 30 V source. **Objective:** - Analyze the circuit behavior after the switch moves to position B. - Determine \( v_C(t) \) and \( i_C(t) \) for \( t > 0 \), which is the voltage across and the current through the capacitor, respectively. - Sketch the time response of \( v_C(t) \) and \( i_C(t) \). **Analysis Approach:** 1. **Initial Conditions:** - Calculate the initial voltage across the capacitor before the switch is moved. 2. **Behavior for \( t > 0 \):** - Use differential equations or circuit theorems (Thevenin/Norton) for transient analysis. - Determine the time constant of the circuit for the \( t > 0 \) scenario. 3. **Sketching:** - Plot \( v_C(t) \) and \( i_C(t) \) showing exponential growth or decay based on the derived equations. This setup and analysis will guide students in understanding the dynamics of RC circuits during switching and transient states.
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