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Given the circuit in Figure 16-3, what is the magnitude of the circuit impedance (Z)? XL=6kN X; = 3 k2 rele 10 V R=8kN rms Figure 16-3

Given the circuit in Figure 16-3, what is the magnitude of the circuit impedance (Z)? XL=6kN X; = 3 k2 rele 10 V R=8kN rms Figure 16-3

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
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**Question 7:** Given the circuit in Figure 16-3, what is the _magnitude_ of the circuit impedance (Z)? **Description of Figure 16-3:** The diagram illustrates an electrical circuit that has the following components: - A source providing 10 V (rms). - An inductor (`XL`) with an inductive reactance value of 3 kΩ. - A resistor (`R`) with a resistance value of 8 kΩ. Additionally, there is another inductive reactance (`XL`) component shown outside of the main loop with a value of 6 kΩ, but it is unclear how it is connected based on the given image. **Explanation:** To find the magnitude of the circuit's total impedance (Z), you can use the impedance values of the resistor and inductor. The impedance \( Z \) of a series circuit containing resistors and inductive reactance can be calculated using: \[ Z = \sqrt{R^2 + X_L^2} \] Where: - \( R \) is the resistance. - \( X_L \) is the total inductive reactance. Given inside the circuit: - \( X_L = 3 \, \text{k}\Omega \) - \( R = 8 \, \text{k}\Omega \) Calculate \( Z \) as follows: \[ Z = \sqrt{(8\, \text{k}\Omega)^2 + (3\, \text{k}\Omega)^2} \] \[ Z = \sqrt{64 + 9} \, \text{k}\Omega \] \[ Z = \sqrt{73} \, \text{k}\Omega \] Therefore, the magnitude of the circuit impedance \( Z \) is \(\sqrt{73}\, \text{k}\Omega\).
Transcribed Image Text:**Question 7:** Given the circuit in Figure 16-3, what is the _magnitude_ of the circuit impedance (Z)? **Description of Figure 16-3:** The diagram illustrates an electrical circuit that has the following components: - A source providing 10 V (rms). - An inductor (`XL`) with an inductive reactance value of 3 kΩ. - A resistor (`R`) with a resistance value of 8 kΩ. Additionally, there is another inductive reactance (`XL`) component shown outside of the main loop with a value of 6 kΩ, but it is unclear how it is connected based on the given image. **Explanation:** To find the magnitude of the circuit's total impedance (Z), you can use the impedance values of the resistor and inductor. The impedance \( Z \) of a series circuit containing resistors and inductive reactance can be calculated using: \[ Z = \sqrt{R^2 + X_L^2} \] Where: - \( R \) is the resistance. - \( X_L \) is the total inductive reactance. Given inside the circuit: - \( X_L = 3 \, \text{k}\Omega \) - \( R = 8 \, \text{k}\Omega \) Calculate \( Z \) as follows: \[ Z = \sqrt{(8\, \text{k}\Omega)^2 + (3\, \text{k}\Omega)^2} \] \[ Z = \sqrt{64 + 9} \, \text{k}\Omega \] \[ Z = \sqrt{73} \, \text{k}\Omega \] Therefore, the magnitude of the circuit impedance \( Z \) is \(\sqrt{73}\, \text{k}\Omega\).
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