Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Given the following circuit below, at \( t = 0 \) the switch opens: ![Circuit Diagram] ### Circuit Components and Layout: - **Voltage Source (\( V_S \))**: 12V - **Inductor (\( L \))**: 2 mH - **Resistors**: - \( R_1 = 10 \, \text{k}\Omega \) - \( R_2 = 5 \, \text{k}\Omega \) ### Circuit Description: - The circuit includes a DC voltage source, \( V_S = 12 \, \text{V} \), connected in series with a switch. - At \( t = 0 \), the switch opens. - The inductor \( L \) and resistor \( R_1 \) are in parallel. - Output voltage across \( R_1 \), denoted as \( v_0(t) \). - Resistor \( R_2 \) is connected in the parallel branch with the inductor-resistor pair. ### Task: (a) Use the differential equation method to determine the output voltage \( v_0(t) \).
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Transcribed Image Text:Given the following circuit below, at \( t = 0 \) the switch opens: ![Circuit Diagram] ### Circuit Components and Layout: - **Voltage Source (\( V_S \))**: 12V - **Inductor (\( L \))**: 2 mH - **Resistors**: - \( R_1 = 10 \, \text{k}\Omega \) - \( R_2 = 5 \, \text{k}\Omega \) ### Circuit Description: - The circuit includes a DC voltage source, \( V_S = 12 \, \text{V} \), connected in series with a switch. - At \( t = 0 \), the switch opens. - The inductor \( L \) and resistor \( R_1 \) are in parallel. - Output voltage across \( R_1 \), denoted as \( v_0(t) \). - Resistor \( R_2 \) is connected in the parallel branch with the inductor-resistor pair. ### Task: (a) Use the differential equation method to determine the output voltage \( v_0(t) \).
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