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Problem 6-2. For the circuit shown in figure P6.5, find vc(t), ic(t), ix(t), and vy(t) for t≥ 0+. The switch has been in its starting position for a long time before moving at the time indicated. 5mA ↓ 2kQ 6ΚΩ_ix(t) ww ic(t)↓ 10μF 40V t=0 X + vc(t) 80V 8ΚΩ www + Vy(t)

Problem 6-2. For the circuit shown in figure P6.5, find vc(t), ic(t), ix(t), and vy(t) for t≥ 0+. The switch has been in its starting position for a long time before moving at the time indicated. 5mA ↓ 2kQ 6ΚΩ_ix(t) ww ic(t)↓ 10μF 40V t=0 X + vc(t) 80V 8ΚΩ www + Vy(t)

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 6-2: Analysis of a Circuit with Capacitor and Switch Dynamics** **Objective:** Determine the functions \( v_c(t) \), \( i_c(t) \), \( i_x(t) \), and \( v_y(t) \) for \( t \geq 0^+ \). **Circuit Description:** - A current source provides 5 mA. - A 2 kΩ resistor is connected in series with the current source. - The circuit features two voltage sources: one providing 40 V and another one providing 80 V. - A capacitor of 10 µF is connected parallel to the 40 V source, with the voltage across it labeled as \( v_c(t) \). - The circuit includes a 6 kΩ resistor where the current \( i_x(t) \) is flowing through. - An open switch is present in series with an 8 kΩ resistor. This switch is initially closed and labeled as \( t=0 \). Upon opening at \( t = 0 \), it affects the path of the current. - The current through the capacitor is denoted by \( i_c(t) \). - The voltage across the 8 kΩ resistor is labeled \( v_y(t) \). **Analysis Scenario:** The switch in the circuit has been in the closed position for a significant time period, ensuring that the circuit reaches a steady state before the switch is opened at \( t = 0 \). **Instructions:** - Find \( v_c(t) \), the voltage across the capacitor. - Find \( i_c(t) \), the current through the capacitor. - Determine \( i_x(t) \), the current through the 6 kΩ resistor. - Calculate \( v_y(t) \), the voltage across the 8 kΩ resistor for \( t \geq 0^+ \). Understanding the transition of the circuit from steady state to dynamic behavior when the switch is opened requires solving the above parameters using basic principles of circuit analysis such as Ohm’s Law, Kirchhoff's Laws, and properties of capacitors.
Transcribed Image Text:**Problem 6-2: Analysis of a Circuit with Capacitor and Switch Dynamics** **Objective:** Determine the functions \( v_c(t) \), \( i_c(t) \), \( i_x(t) \), and \( v_y(t) \) for \( t \geq 0^+ \). **Circuit Description:** - A current source provides 5 mA. - A 2 kΩ resistor is connected in series with the current source. - The circuit features two voltage sources: one providing 40 V and another one providing 80 V. - A capacitor of 10 µF is connected parallel to the 40 V source, with the voltage across it labeled as \( v_c(t) \). - The circuit includes a 6 kΩ resistor where the current \( i_x(t) \) is flowing through. - An open switch is present in series with an 8 kΩ resistor. This switch is initially closed and labeled as \( t=0 \). Upon opening at \( t = 0 \), it affects the path of the current. - The current through the capacitor is denoted by \( i_c(t) \). - The voltage across the 8 kΩ resistor is labeled \( v_y(t) \). **Analysis Scenario:** The switch in the circuit has been in the closed position for a significant time period, ensuring that the circuit reaches a steady state before the switch is opened at \( t = 0 \). **Instructions:** - Find \( v_c(t) \), the voltage across the capacitor. - Find \( i_c(t) \), the current through the capacitor. - Determine \( i_x(t) \), the current through the 6 kΩ resistor. - Calculate \( v_y(t) \), the voltage across the 8 kΩ resistor for \( t \geq 0^+ \). Understanding the transition of the circuit from steady state to dynamic behavior when the switch is opened requires solving the above parameters using basic principles of circuit analysis such as Ohm’s Law, Kirchhoff's Laws, and properties of capacitors.
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