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i(t) = 3-4.5e6f A for t>0 2.5 H + v(t) i(t)

i(t) = 3-4.5e6f A for t>0 2.5 H + v(t) i(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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The input to the circuit is shown below. Determine the inductor voltage, v(t) for t > 0

### Transcription and Explanation for Educational Use **Equation:** \[ i(t) = 3 - 4.5e^{-6t} \, \text{A for } t > 0 \] This equation describes the time-dependent behavior of current \( i(t) \) in amperes as a function of time \( t \). The expression includes: - A constant current term of 3 A. - An exponential decay term \( -4.5e^{-6t} \), which indicates how the current changes over time, decreasing as \( t \) increases. **Circuit Diagram:** The diagram represents an electrical circuit with: - A **2.5 Henry (H) inductor** depicted as a coil at the top of the diagram. - The inductor is labeled with the inductance value "2.5 H". - A voltage across the inductor marked \( v(t) \) with terminals labeled "+" and "-". - A current through the inductor marked \( i(t) \) with an arrow indicating the direction of current flow. This setup represents a typical RL (Resistor-Inductor) circuit used to study transient responses in electrical engineering. The inductor's presence suggests that the circuit is part of a study on how inductance influences current and voltage over time, particularly after the initial time (\( t = 0 \)).
Transcribed Image Text:### Transcription and Explanation for Educational Use **Equation:** \[ i(t) = 3 - 4.5e^{-6t} \, \text{A for } t > 0 \] This equation describes the time-dependent behavior of current \( i(t) \) in amperes as a function of time \( t \). The expression includes: - A constant current term of 3 A. - An exponential decay term \( -4.5e^{-6t} \), which indicates how the current changes over time, decreasing as \( t \) increases. **Circuit Diagram:** The diagram represents an electrical circuit with: - A **2.5 Henry (H) inductor** depicted as a coil at the top of the diagram. - The inductor is labeled with the inductance value "2.5 H". - A voltage across the inductor marked \( v(t) \) with terminals labeled "+" and "-". - A current through the inductor marked \( i(t) \) with an arrow indicating the direction of current flow. This setup represents a typical RL (Resistor-Inductor) circuit used to study transient responses in electrical engineering. The inductor's presence suggests that the circuit is part of a study on how inductance influences current and voltage over time, particularly after the initial time (\( t = 0 \)).
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