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1.5e 'u(t) + 2u (1) V I FIGURE 15.47 2.7 Ω ww i(t) + 1.1 Hv(1) 4. For the circuit of Fig. 15.47, draw an s-domain equivalent and analyze it t obtain a value for v(t) if i(0) is equal to (a) 0; (b) 3 A.

1.5e 'u(t) + 2u (1) V I FIGURE 15.47 2.7 Ω ww i(t) + 1.1 Hv(1) 4. For the circuit of Fig. 15.47, draw an s-domain equivalent and analyze it t obtain a value for v(t) if i(0) is equal to (a) 0; (b) 3 A.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Transcription and Explanation for Educational Website **Figure 15.47** This image displays a simple electrical circuit consisting of a voltage source, a resistor, and an inductor. - **Voltage Source**: The source provides a voltage of \(1.5e^{-t}u(t) + 2u(t)\) volts, where \(u(t)\) is the unit step function. - **Resistor**: Connected in series with the circuit, the resistor has a value of \(2.7 \, \Omega\). - **Inductor**: The inductor in series with the circuit has a value of \(1.1 \, \text{H}\). The circuit shows the current \(i(t)\) flowing through the components, and the voltage \(v(t)\) is across the inductor. --- **Task Description:** 4. For the circuit in Fig. 15.47, you are required to draw an s-domain equivalent of the circuit and analyze it to determine the value of \(v(t)\) given that: - \(i(0)\) is equal to (a) 0; (b) 3 A. **Instructions:** To solve this task: - **S-Domain Transformation**: Transform the time-domain circuit components (resistor and inductor) into the s-domain using Laplace transforms. - **Resistor in S-Domain**: The resistance remains the same at \(2.7 \, \Omega\). - **Inductor in S-Domain**: The inductor is represented as \(1.1s \, \text{H}\) in the s-domain with an initial condition in series, if applicable. - **Analyze**: Use the s-domain equivalent to solve for the voltage across the inductor, \(V(s)\), and apply the inverse Laplace transform to find \(v(t)\). This exercise helps illustrate the process of converting time-domain circuits to the s-domain for analysis, which simplifies solving differential equations involved in circuit behavior, especially with initial conditions.
Transcribed Image Text:### Transcription and Explanation for Educational Website **Figure 15.47** This image displays a simple electrical circuit consisting of a voltage source, a resistor, and an inductor. - **Voltage Source**: The source provides a voltage of \(1.5e^{-t}u(t) + 2u(t)\) volts, where \(u(t)\) is the unit step function. - **Resistor**: Connected in series with the circuit, the resistor has a value of \(2.7 \, \Omega\). - **Inductor**: The inductor in series with the circuit has a value of \(1.1 \, \text{H}\). The circuit shows the current \(i(t)\) flowing through the components, and the voltage \(v(t)\) is across the inductor. --- **Task Description:** 4. For the circuit in Fig. 15.47, you are required to draw an s-domain equivalent of the circuit and analyze it to determine the value of \(v(t)\) given that: - \(i(0)\) is equal to (a) 0; (b) 3 A. **Instructions:** To solve this task: - **S-Domain Transformation**: Transform the time-domain circuit components (resistor and inductor) into the s-domain using Laplace transforms. - **Resistor in S-Domain**: The resistance remains the same at \(2.7 \, \Omega\). - **Inductor in S-Domain**: The inductor is represented as \(1.1s \, \text{H}\) in the s-domain with an initial condition in series, if applicable. - **Analyze**: Use the s-domain equivalent to solve for the voltage across the inductor, \(V(s)\), and apply the inverse Laplace transform to find \(v(t)\). This exercise helps illustrate the process of converting time-domain circuits to the s-domain for analysis, which simplifies solving differential equations involved in circuit behavior, especially with initial conditions.
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