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Problem 6-6. For the circuit shown in figure P6-6, find vċ(t) and iċ(t) for t ≥ 0+. The switches have been in their starting positions for a long time before moving at the times indicated. 5kQ + t = 10ms 15V ic(t)↓ 3μF Vc(t) 10ΚΩΣ 2mA (F t = 0 X. 30V 10ΚΩ ww

Problem 6-6. For the circuit shown in figure P6-6, find vċ(t) and iċ(t) for t ≥ 0+. The switches have been in their starting positions for a long time before moving at the times indicated. 5kQ + t = 10ms 15V ic(t)↓ 3μF Vc(t) 10ΚΩΣ 2mA (F t = 0 X. 30V 10ΚΩ ww

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 6-6: Circuit Analysis for Time-Dependent Behavior** **Objective:** For the circuit illustrated in Figure P6-6, determine the expressions for \( v_c(t) \) and \( i_c(t) \) for \( t \geq 0^+ \). The circuit switches have remained in their initial positions for a long duration before switching at the times specified. **Circuit Description:** - **Resistor (5kΩ):** Located in series with a 15V DC voltage source and a switch, which changes position at \( t = 10 \, \text{ms} \). - **Capacitor (3μF):** Connected in parallel in the path of \( v_c(t) \) and \( i_c(t) \). The capacitor voltage and current change with time. - **Resistors (10kΩ each):** There are two 10kΩ resistors in the circuit. One is in series with the capacitor and the other is in series with a 30V DC voltage source and another switch, which changes position at \( t = 0 \). - **Current Source (2mA):** In parallel with the second 10kΩ resistor and the 30V source. **Switch Details:** - At \( t = 0 \), the right switch changes position, impacting the circuit configuration. - At \( t = 10 \, \text{ms} \), the left switch moves, further altering the circuit dynamics. **Analysis Approach:** 1. **Initial Conditions:** Analyze the circuit behavior before the switches operate to determine initial conditions for voltages and currents. 2. **Transient Response:** Calculate the transient response of the capacitor voltage \( v_c(t) \) and the capacitor current \( i_c(t) \) after switch changes. 3. **Time Domain Evaluation:** Use techniques such as the Laplace transform, Thevenin equivalent circuits, or direct integration to solve for \( v_c(t) \) and \( i_c(t) \) in the time domain post-switch actuation. This analysis helps in understanding how the circuit evolves over time and the impact of switching actions on transient and steady-state circuit performance.
Transcribed Image Text:**Problem 6-6: Circuit Analysis for Time-Dependent Behavior** **Objective:** For the circuit illustrated in Figure P6-6, determine the expressions for \( v_c(t) \) and \( i_c(t) \) for \( t \geq 0^+ \). The circuit switches have remained in their initial positions for a long duration before switching at the times specified. **Circuit Description:** - **Resistor (5kΩ):** Located in series with a 15V DC voltage source and a switch, which changes position at \( t = 10 \, \text{ms} \). - **Capacitor (3μF):** Connected in parallel in the path of \( v_c(t) \) and \( i_c(t) \). The capacitor voltage and current change with time. - **Resistors (10kΩ each):** There are two 10kΩ resistors in the circuit. One is in series with the capacitor and the other is in series with a 30V DC voltage source and another switch, which changes position at \( t = 0 \). - **Current Source (2mA):** In parallel with the second 10kΩ resistor and the 30V source. **Switch Details:** - At \( t = 0 \), the right switch changes position, impacting the circuit configuration. - At \( t = 10 \, \text{ms} \), the left switch moves, further altering the circuit dynamics. **Analysis Approach:** 1. **Initial Conditions:** Analyze the circuit behavior before the switches operate to determine initial conditions for voltages and currents. 2. **Transient Response:** Calculate the transient response of the capacitor voltage \( v_c(t) \) and the capacitor current \( i_c(t) \) after switch changes. 3. **Time Domain Evaluation:** Use techniques such as the Laplace transform, Thevenin equivalent circuits, or direct integration to solve for \( v_c(t) \) and \( i_c(t) \) in the time domain post-switch actuation. This analysis helps in understanding how the circuit evolves over time and the impact of switching actions on transient and steady-state circuit performance.
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