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Assume that the circuit below has reached steady state by the time t = 0. The switch is opened at t = 0. 1. Determine i(0*) and v(0¹). dv 2. Find (0¹) and (0¹). 3. Find i (0) and v(∞o). 4. Write down i(t) for t> 0. 12 V + 4 Ω 4 Ω t = 0 S1 10 mF 2 Ω + 【v(t) i(t) 4Ω 250 mH

Assume that the circuit below has reached steady state by the time t = 0. The switch is opened at t = 0. 1. Determine i(0*) and v(0¹). dv 2. Find (0¹) and (0¹). 3. Find i (0) and v(∞o). 4. Write down i(t) for t> 0. 12 V + 4 Ω 4 Ω t = 0 S1 10 mF 2 Ω + 【v(t) i(t) 4Ω 250 mH

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 Statement: Assume that the circuit below has reached steady state by the time \( t = 0^- \). The switch is opened at \( t = 0 \). 1. Determine \( i(0^+) \) and \( v(0^+) \). 2. Find \( \frac{di}{dt}(0^+) \) and \( \frac{dv}{dt}(0^+) \). 3. Find \( i(\infty) \) and \( v(\infty) \). 4. Write down \( i(t) \) for \( t > 0 \). ### Circuit Description: The circuit includes: - A 12 V voltage source. - Four resistors \( (4 \, \Omega, 4 \, \Omega, 4 \, \Omega, \text{and } 2 \, \Omega) \). - A capacitor of \( 10 \, \text{mF} \). - An inductor of \( 250 \, \text{mH} \). - A switch \( S1 \) which opens at \( t = 0 \). The circuit is configured as follows: - The voltage source connects to a \( 4 \, \Omega \) resistor in series. - A branch with a \( 4 \, \Omega \) resistor is present. - A series combination of a capacitor \( 10 \, \text{mF} \) and a \( 2 \, \Omega \) resistor is paralleled with this resistor. - The switch \( S1 \) is in series with these components and opens at \( t = 0 \). - Another path contains a \( 4 \, \Omega \) resistor and an inductor \( 250 \, \text{mH} \). - Current \( i(t) \) flows through the inductor and voltage \( v(t) \) is across the capacitor. ### Tasks: - Analyze the initial conditions and transients in the circuit for \( t > 0 \) after the switch \( S1 \) is opened. - Determine how the current and voltage evolve over time, particularly at \( t = 0^+ \) and at steady state \( t = \infty \). This exercise involves solving differential equations to represent circuit responses and using techniques such as Kirchhoff’s laws and characteristic equations of capacitors and inductors.
Transcribed Image Text:### Problem Statement: Assume that the circuit below has reached steady state by the time \( t = 0^- \). The switch is opened at \( t = 0 \). 1. Determine \( i(0^+) \) and \( v(0^+) \). 2. Find \( \frac{di}{dt}(0^+) \) and \( \frac{dv}{dt}(0^+) \). 3. Find \( i(\infty) \) and \( v(\infty) \). 4. Write down \( i(t) \) for \( t > 0 \). ### Circuit Description: The circuit includes: - A 12 V voltage source. - Four resistors \( (4 \, \Omega, 4 \, \Omega, 4 \, \Omega, \text{and } 2 \, \Omega) \). - A capacitor of \( 10 \, \text{mF} \). - An inductor of \( 250 \, \text{mH} \). - A switch \( S1 \) which opens at \( t = 0 \). The circuit is configured as follows: - The voltage source connects to a \( 4 \, \Omega \) resistor in series. - A branch with a \( 4 \, \Omega \) resistor is present. - A series combination of a capacitor \( 10 \, \text{mF} \) and a \( 2 \, \Omega \) resistor is paralleled with this resistor. - The switch \( S1 \) is in series with these components and opens at \( t = 0 \). - Another path contains a \( 4 \, \Omega \) resistor and an inductor \( 250 \, \text{mH} \). - Current \( i(t) \) flows through the inductor and voltage \( v(t) \) is across the capacitor. ### Tasks: - Analyze the initial conditions and transients in the circuit for \( t > 0 \) after the switch \( S1 \) is opened. - Determine how the current and voltage evolve over time, particularly at \( t = 0^+ \) and at steady state \( t = \infty \). This exercise involves solving differential equations to represent circuit responses and using techniques such as Kirchhoff’s laws and characteristic equations of capacitors and inductors.
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