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For the given circuit, find vo(t) when (0) = 6 A and v(t) = 0 V. 252 i(t) 0.4 H m 3Ω The voltage vo(t): = vo (0) e-t/¹, where vo(0) = S. V and T =

For the given circuit, find vo(t) when (0) = 6 A and v(t) = 0 V. 252 i(t) 0.4 H m 3Ω The voltage vo(t): = vo (0) e-t/¹, where vo(0) = S. V and T =

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 Problem Explanation for Educational Website** **Objective:** Determine the voltage \( v_o(t) \) for the given circuit when the initial current \( i(0) = 6 \, \text{A} \) and the source voltage \( v(t) = 0 \, \text{V} \). **Circuit Description:** The circuit consists of: - A series combination of a 2-ohm resistor (\(2 \, \Omega\)) and a 0.4 H inductor (\(0.4 \, \text{H}\)). - An input current \( i(t) \) flows into the series combination. - Parallel to the inductor, there is a 3-ohm resistor (\(3 \, \Omega\)). - The output voltage \( v_o(t) \) is measured across the 3-ohm resistor. **Equation to Solve:** The output voltage \( v_o(t) \) is given by the equation: \[ v_o(t) = v_o(0) \, e^{-t/\tau} \] where: - \( v_o(0) \) is the initial voltage across the 3-ohm resistor. - \( \tau \) is the time constant of the circuit. **Tasks:** - Determine the initial voltage \( v_o(0) \). - Calculate the time constant \( \tau \). Please fill in the calculated values: - \( v_o(0) = \boxed{\,\,\,} \, \text{V} \) - \( \tau = \boxed{\,\,\,} \, \text{s} \) **Conclusion:** This exercise involves analyzing a simple RL circuit to determine its transient response using initial conditions and the time constant formula.
Transcribed Image Text:**Circuit Problem Explanation for Educational Website** **Objective:** Determine the voltage \( v_o(t) \) for the given circuit when the initial current \( i(0) = 6 \, \text{A} \) and the source voltage \( v(t) = 0 \, \text{V} \). **Circuit Description:** The circuit consists of: - A series combination of a 2-ohm resistor (\(2 \, \Omega\)) and a 0.4 H inductor (\(0.4 \, \text{H}\)). - An input current \( i(t) \) flows into the series combination. - Parallel to the inductor, there is a 3-ohm resistor (\(3 \, \Omega\)). - The output voltage \( v_o(t) \) is measured across the 3-ohm resistor. **Equation to Solve:** The output voltage \( v_o(t) \) is given by the equation: \[ v_o(t) = v_o(0) \, e^{-t/\tau} \] where: - \( v_o(0) \) is the initial voltage across the 3-ohm resistor. - \( \tau \) is the time constant of the circuit. **Tasks:** - Determine the initial voltage \( v_o(0) \). - Calculate the time constant \( \tau \). Please fill in the calculated values: - \( v_o(0) = \boxed{\,\,\,} \, \text{V} \) - \( \tau = \boxed{\,\,\,} \, \text{s} \) **Conclusion:** This exercise involves analyzing a simple RL circuit to determine its transient response using initial conditions and the time constant formula.
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