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R₁ 0.75 X R3 W 0.52 i(t) R₂ · 0,5 Ω www 2H Hii v(t) 1 C 0.5 F

R₁ 0.75 X R3 W 0.52 i(t) R₂ · 0,5 Ω www 2H Hii v(t) 1 C 0.5 F

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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**Circuit Analysis Problem** **Problem Statement:** The switch in the circuit shown in the figure below has been closed for a long time before it is opened at \( t = 0 \). Determine the current \( i(t) \) for \( t \ge 0 \). **Circuit Diagram:** - The circuit consists of a voltage source \( V_s = 4 \text{ V} \), a series resistor \( R_1 = 0.75 \Omega \), two parallel resistors \( R_2 = 0.5 \Omega \) and \( R_3 = 0.5 \Omega \), an inductor \( L = 2 \text{ H} \), and a capacitor \( C = 0.5 \text{ F} \). - Before \( t = 0 \), the switch is closed, allowing the circuit to reach a steady state. - At \( t = 0 \), the switch is opened, and the current \( i(t) \) through the inductor and the voltage \( v(t) \) across the capacitor are analyzed for \( t \ge 0 \). **Figure:** ``` ___ ___ +4V ___|R1|_____|R3|___ v(t) 0.75Ω 0.5Ω |____ ____ | | | _|_ R2 C L 0.5Ω 0.5F 2H | | _|_ ______ ___ ___ ``` **Analysis:** To find the current through the inductor \( i(t) \), the characteristic equation of the differential equation describing the circuit dynamics can be expressed as: \[ s^2 + a_1s + a_0 = 0 \] **Question:** What is the value of \( a_1 \) in the characteristic equation? **Explanation of Graphs/Diagrams:** The circuit diagram shown above is a representation of the electrical setup under analysis. This circuit includes a voltage source \( V_s = 4 \text{ V} \) that powers the circuit. The resistor \( R_1 = 0.75 \Omega \) is in series with the parallel combination of resistors \( R_2 = 0.5 \Omega \) and \( R_3 =
Transcribed Image Text:**Circuit Analysis Problem** **Problem Statement:** The switch in the circuit shown in the figure below has been closed for a long time before it is opened at \( t = 0 \). Determine the current \( i(t) \) for \( t \ge 0 \). **Circuit Diagram:** - The circuit consists of a voltage source \( V_s = 4 \text{ V} \), a series resistor \( R_1 = 0.75 \Omega \), two parallel resistors \( R_2 = 0.5 \Omega \) and \( R_3 = 0.5 \Omega \), an inductor \( L = 2 \text{ H} \), and a capacitor \( C = 0.5 \text{ F} \). - Before \( t = 0 \), the switch is closed, allowing the circuit to reach a steady state. - At \( t = 0 \), the switch is opened, and the current \( i(t) \) through the inductor and the voltage \( v(t) \) across the capacitor are analyzed for \( t \ge 0 \). **Figure:** ``` ___ ___ +4V ___|R1|_____|R3|___ v(t) 0.75Ω 0.5Ω |____ ____ | | | _|_ R2 C L 0.5Ω 0.5F 2H | | _|_ ______ ___ ___ ``` **Analysis:** To find the current through the inductor \( i(t) \), the characteristic equation of the differential equation describing the circuit dynamics can be expressed as: \[ s^2 + a_1s + a_0 = 0 \] **Question:** What is the value of \( a_1 \) in the characteristic equation? **Explanation of Graphs/Diagrams:** The circuit diagram shown above is a representation of the electrical setup under analysis. This circuit includes a voltage source \( V_s = 4 \text{ V} \) that powers the circuit. The resistor \( R_1 = 0.75 \Omega \) is in series with the parallel combination of resistors \( R_2 = 0.5 \Omega \) and \( R_3 =
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