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3. A coil has an inductive reactance of 75 Q and a wire resistance of 18 Q. What is the Q of this coil?

3. A coil has an inductive reactance of 75 Q and a wire resistance of 18 Q. What is the Q of this coil?

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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**Question 3:** A coil has an inductive reactance of 75 Ω and a wire resistance of 18 Ω. What is the Q of this coil? **Explanation of Concepts:** The quality factor (Q) of a coil is a dimensionless parameter that describes the ratio of its inductive reactance to its resistance. It is an indicator of the coil's efficiency and performance in resonant circuits. A higher Q factor signifies a lower rate of energy loss relative to the stored energy of the coil. **Formula:** \[ Q = \frac{X_L}{R} \] where: - \( Q \) is the quality factor. - \( X_L \) is the inductive reactance. - \( R \) is the resistance. **Calculation:** Using the given values: - \( X_L = 75 \, \Omega \) - \( R = 18 \, \Omega \) \[ Q = \frac{75 \, \Omega}{18 \, \Omega} \approx 4.17 \] Therefore, the Q of the coil is approximately 4.17.
Transcribed Image Text:**Question 3:** A coil has an inductive reactance of 75 Ω and a wire resistance of 18 Ω. What is the Q of this coil? **Explanation of Concepts:** The quality factor (Q) of a coil is a dimensionless parameter that describes the ratio of its inductive reactance to its resistance. It is an indicator of the coil's efficiency and performance in resonant circuits. A higher Q factor signifies a lower rate of energy loss relative to the stored energy of the coil. **Formula:** \[ Q = \frac{X_L}{R} \] where: - \( Q \) is the quality factor. - \( X_L \) is the inductive reactance. - \( R \) is the resistance. **Calculation:** Using the given values: - \( X_L = 75 \, \Omega \) - \( R = 18 \, \Omega \) \[ Q = \frac{75 \, \Omega}{18 \, \Omega} \approx 4.17 \] Therefore, the Q of the coil is approximately 4.17.
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