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The switch in the circuit has been open for a long time before closing at t = 0. Find İL(t) for t≥ 0. 120 mA 3009231.25mH3 150Ω 0.5 μF 3 V

The switch in the circuit has been open for a long time before closing at t = 0. Find İL(t) for t≥ 0. 120 mA 3009231.25mH3 150Ω 0.5 μF 3 V

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
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**Circuit Analysis Problem:** The switch in the circuit has been open for a long time before closing at \( t = 0 \). Find \( i_L(t) \) for \( t \geq 0 \). **Circuit Description:** 1. **Current Source:** - 120 mA downward. 2. **Resistor:** - 300 Ω connected in series with the current source. 3. **Inductor:** - 31.25 mH connected in parallel with the 300 Ω resistor. 4. **Switch:** - Initially open, closes at \( t = 0 \), positioned in series with the inductor. When closed, it allows the circuit to reconfigure affecting the rest of the elements. 5. **Resistor:** - 150 Ω connected in series with a parallel capacitor and voltage source. 6. **Capacitor:** - 0.5 μF connected in parallel with a 3 V voltage source. 7. **Voltage Source:** - 3 V with polarity marked in the circuit. **Objective:** - Solve for the inductor current \( i_L(t) \) for \( t \geq 0 \) after the switch is closed. This involves analyzing the transient and possibly steady-state behaviors of the circuit using techniques like Laplace Transforms or differential equations, considering the initial conditions set by the long open state of the switch. **Analytical Steps:** - Prior to \( t = 0 \), examine the circuit with the switch open to determine initial conditions. - At \( t = 0 \), the switch closes, causing a change in circuit configuration. - Utilize methods to solve for transient currents and voltages, focusing on \( i_L(t) \), based on inductor and capacitor behaviors.
Transcribed Image Text:**Circuit Analysis Problem:** The switch in the circuit has been open for a long time before closing at \( t = 0 \). Find \( i_L(t) \) for \( t \geq 0 \). **Circuit Description:** 1. **Current Source:** - 120 mA downward. 2. **Resistor:** - 300 Ω connected in series with the current source. 3. **Inductor:** - 31.25 mH connected in parallel with the 300 Ω resistor. 4. **Switch:** - Initially open, closes at \( t = 0 \), positioned in series with the inductor. When closed, it allows the circuit to reconfigure affecting the rest of the elements. 5. **Resistor:** - 150 Ω connected in series with a parallel capacitor and voltage source. 6. **Capacitor:** - 0.5 μF connected in parallel with a 3 V voltage source. 7. **Voltage Source:** - 3 V with polarity marked in the circuit. **Objective:** - Solve for the inductor current \( i_L(t) \) for \( t \geq 0 \) after the switch is closed. This involves analyzing the transient and possibly steady-state behaviors of the circuit using techniques like Laplace Transforms or differential equations, considering the initial conditions set by the long open state of the switch. **Analytical Steps:** - Prior to \( t = 0 \), examine the circuit with the switch open to determine initial conditions. - At \( t = 0 \), the switch closes, causing a change in circuit configuration. - Utilize methods to solve for transient currents and voltages, focusing on \( i_L(t) \), based on inductor and capacitor behaviors.
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