Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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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 \(\sqrt{73}\, \text{k}\Omega\).](https://content.bartleby.com/qna-images/question/dd3494d7-16cb-4f96-a1a3-f69334a1e65b/2f10b7d5-fb10-4ae6-ad1d-646cacdaa62d/ru1xl2j_processed.png)
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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