Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Find the input resistance between points A and B of the following resistive network:
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### Problem Statement: Determine the value of the resistance, \( R \), in Ohms for the given circuit. ### Circuit Diagram: The circuit consists of a voltage source, \( v_s(t) \), a resistor \( R \), and an inductor with an inductance of 15 H. There are two voltage parameters: \( v_s(t) \) and \( v_0(t) \). ### Voltage Definitions: - \( v_s(t) = -3 + 6u(t) \) V - \( v_0(t) = +6e^{-0.8t} u(t) \) V Here, \( u(t) \) represents the unit step function. ### Graph Description: - The graph plots \( v_s(t) \) and \( v_0(t) \) over time (\( t \) in seconds). - \( v_s(t) \) is shown in red, while \( v_0(t) \) is shown in blue. - The time axis ranges from -1 to 5 seconds, and the voltage axis ranges from -10 to 10 volts. - At \( t = 0 \), \( v_s(t) \) jumps from -3 V to 3 V, remaining constant afterwards. - \( v_0(t) \) starts at 6 V for \( t = 0 \) and asymptotically approaches 0 V, demonstrating an exponential decay. ### Analysis Objective: Use the given information and graphs to determine the resistance \( R \) in the circuit.
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Transcribed Image Text:### Problem Statement: Determine the value of the resistance, \( R \), in Ohms for the given circuit. ### Circuit Diagram: The circuit consists of a voltage source, \( v_s(t) \), a resistor \( R \), and an inductor with an inductance of 15 H. There are two voltage parameters: \( v_s(t) \) and \( v_0(t) \). ### Voltage Definitions: - \( v_s(t) = -3 + 6u(t) \) V - \( v_0(t) = +6e^{-0.8t} u(t) \) V Here, \( u(t) \) represents the unit step function. ### Graph Description: - The graph plots \( v_s(t) \) and \( v_0(t) \) over time (\( t \) in seconds). - \( v_s(t) \) is shown in red, while \( v_0(t) \) is shown in blue. - The time axis ranges from -1 to 5 seconds, and the voltage axis ranges from -10 to 10 volts. - At \( t = 0 \), \( v_s(t) \) jumps from -3 V to 3 V, remaining constant afterwards. - \( v_0(t) \) starts at 6 V for \( t = 0 \) and asymptotically approaches 0 V, demonstrating an exponential decay. ### Analysis Objective: Use the given information and graphs to determine the resistance \( R \) in the circuit.
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