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The switch opens after having been closed a long time. Find the inductor current, inductor voltage, capacitor current and capacitor voltage at the following three times: t = 0-, t = 0+, t->infinity i: 2 mH + V: ic 20 kN =0 10 mA 30kN Ve 6 µF

The switch opens after having been closed a long time. Find the inductor current, inductor voltage, capacitor current and capacitor voltage at the following three times: t = 0-, t = 0+, t->infinity i: 2 mH + V: ic 20 kN =0 10 mA 30kN Ve 6 µF

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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**Problem 48** The switch opens after having been closed a long time. Find the inductor current, inductor voltage, capacitor current, and capacitor voltage at the following three times: \( t = 0^- \), \( t = 0^+ \), \( t \rightarrow \infty \). **Circuit Diagram:** - A circuit powered by a current source of 10 mA. - A switch is included in the circuit, labeled with \( t = 0 \). - The circuit has an inductor with an inductance of 2 mH. - There is a 30 kΩ resistor in series with the inductor. - A capacitor with a capacitance of 6 μF is connected in parallel with a 20 kΩ resistor. - \( i_l \) denotes the inductor current. - \( i_c \) represents the capacitor current. - \( v_l \) is the voltage across the inductor. - \( v_c \) is the voltage across the capacitor. **Description:** - **Before \( t = 0 \):** The switch is closed, allowing the inductor to reach a steady state where it behaves like a short circuit. - **At \( t = 0^- \):** All circuit elements are in the steady state prior to the switch opening. - **At \( t = 0^+ \):** The switch opens, leading to transient behavior as the system transitions from its initial conditions. - **As \( t \rightarrow \infty \):** The system reaches a new steady state after the transient effects have dissipated.
Transcribed Image Text:**Problem 48** The switch opens after having been closed a long time. Find the inductor current, inductor voltage, capacitor current, and capacitor voltage at the following three times: \( t = 0^- \), \( t = 0^+ \), \( t \rightarrow \infty \). **Circuit Diagram:** - A circuit powered by a current source of 10 mA. - A switch is included in the circuit, labeled with \( t = 0 \). - The circuit has an inductor with an inductance of 2 mH. - There is a 30 kΩ resistor in series with the inductor. - A capacitor with a capacitance of 6 μF is connected in parallel with a 20 kΩ resistor. - \( i_l \) denotes the inductor current. - \( i_c \) represents the capacitor current. - \( v_l \) is the voltage across the inductor. - \( v_c \) is the voltage across the capacitor. **Description:** - **Before \( t = 0 \):** The switch is closed, allowing the inductor to reach a steady state where it behaves like a short circuit. - **At \( t = 0^- \):** All circuit elements are in the steady state prior to the switch opening. - **At \( t = 0^+ \):** The switch opens, leading to transient behavior as the system transitions from its initial conditions. - **As \( t \rightarrow \infty \):** The system reaches a new steady state after the transient effects have dissipated.
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