Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Question
**Find the value of the impedance \( Z_L \) for maximum power transfer in the circuit shown in Figure 14-29.** ### Circuit Description The circuit consists of the following components: 1. **Voltage Source**: - 12 V with a phase angle of 0° (denoted as \( 12 \angle 0^\circ \text{V} \)). 2. **Impedances**: - A resistor with 15 Ω. - A capacitor with impedance \(-j4 \Omega\). - An inductor with impedance \(j8 \Omega\). - A resistor with 20 Ω. 3. **Current Source**: - 4 A with a phase angle of 0° (denoted as \( 4 \angle 0^\circ \text{A} \)). 4. **Load Impedance \( Z_L \)**: - The load impedance is denoted by \( Z_L \), for which the maximum power transfer condition is being evaluated. ### Circuit Diagram Explanation - The circuit is a parallel combination of elements connected to both the voltage source and the current source. - On one branch of the circuit, directly following the voltage source, is a capacitor with \(-j4 \Omega\). - Parallel to the capacitor is a series combination of a 15 Ω resistor, an inductor with \(j8 \Omega\), and a 20 Ω resistor, all leading to the load impedance \(Z_L\). - The current source is in series with the 20 Ω resistor before reaching \( Z_L \). ### Objective The objective is to find the value of \( Z_L \) that allows for maximum power transfer.
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Transcribed Image Text:**Find the value of the impedance \( Z_L \) for maximum power transfer in the circuit shown in Figure 14-29.** ### Circuit Description The circuit consists of the following components: 1. **Voltage Source**: - 12 V with a phase angle of 0° (denoted as \( 12 \angle 0^\circ \text{V} \)). 2. **Impedances**: - A resistor with 15 Ω. - A capacitor with impedance \(-j4 \Omega\). - An inductor with impedance \(j8 \Omega\). - A resistor with 20 Ω. 3. **Current Source**: - 4 A with a phase angle of 0° (denoted as \( 4 \angle 0^\circ \text{A} \)). 4. **Load Impedance \( Z_L \)**: - The load impedance is denoted by \( Z_L \), for which the maximum power transfer condition is being evaluated. ### Circuit Diagram Explanation - The circuit is a parallel combination of elements connected to both the voltage source and the current source. - On one branch of the circuit, directly following the voltage source, is a capacitor with \(-j4 \Omega\). - Parallel to the capacitor is a series combination of a 15 Ω resistor, an inductor with \(j8 \Omega\), and a 20 Ω resistor, all leading to the load impedance \(Z_L\). - The current source is in series with the 20 Ω resistor before reaching \( Z_L \). ### Objective The objective is to find the value of \( Z_L \) that allows for maximum power transfer.
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