**Educational Page: Analysis of a Series Resonant Circuit****Problem 21.3: For the series circuit depicted in Fig. 21.52:**a) **Find the value of \(X_L\) for resonance.**b) **Determine the magnitude of the current \(I\) at resonance.**c) **Find the voltages \(V_R\), \(V_L\), and \(V_C\) at resonance, and compare their magnitudes.**d) **Determine the quality factor of the circuit. Is it a high- or low-Q circuit?**e) **If the resonant frequency is 5 kHz, determine the value of \(L\) and \(C\).**f) **Find the bandwidth of the response if the resonant frequency is 5 kHz.**g) **What are the low and high cutoff frequencies?**---**Figure Explanation:**The schematic in Fig. 21.52 illustrates a series resonant circuit with the following components:- A voltage source \(E = 12 \, \text{V}\)- A resistor \(R = 100 \, \Omega\)- An inductor with inductive reactance labeled as \(X_L\)- A capacitor with capacitive reactance \(X_C = 2 \, \text{k}\Omega\)Voltages across the resistor, inductor, and capacitor are noted as \(V_R\), \(V_L\), and \(V_C\) respectively, with current \(I\) flowing through the circuit.

The given circuit is series RLC circuit. a) Find the value of XL for resonance. At Resonance: XL=XC…

21.3 For the series circuit in Fig. 21.52: a) Find the value of X. for resonance. R= 100 A b) Determine the magnitude of the current I at resonance. 12 V Xc 2 k c) Find the voltages Ya, Yı, and yc at resonance, and compare their magnitudes. d) Determine the quality factor of the circuit. Is it a high- or low-Q circuit? e) If the resonant frequency is 5 kHz, determine the value of L and C. f) Find the bandwidth of the response if the resonant frequency is 5 kHz. 9) What are the low and high cutoff frequencies?

21.3 For the series circuit in Fig. 21.52: a) Find the value of X. for resonance. R= 100 A b) Determine the magnitude of the current I at resonance. 12 V Xc 2 k c) Find the voltages Ya, Yı, and yc at resonance, and compare their magnitudes. d) Determine the quality factor of the circuit. Is it a high- or low-Q circuit? e) If the resonant frequency is 5 kHz, determine the value of L and C. f) Find the bandwidth of the response if the resonant frequency is 5 kHz. 9) What are the low and high cutoff frequencies?

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Question

**Educational Page: Analysis of a Series Resonant Circuit**

**Problem 21.3: For the series circuit depicted in Fig. 21.52:**

a) **Find the value of \(X_L\) for resonance.**

b) **Determine the magnitude of the current \(I\) at resonance.**

c) **Find the voltages \(V_R\), \(V_L\), and \(V_C\) at resonance, and compare their magnitudes.**

d) **Determine the quality factor of the circuit. Is it a high- or low-Q circuit?**

e) **If the resonant frequency is 5 kHz, determine the value of \(L\) and \(C\).**

f) **Find the bandwidth of the response if the resonant frequency is 5 kHz.**

g) **What are the low and high cutoff frequencies?**

---

**Figure Explanation:**

The schematic in Fig. 21.52 illustrates a series resonant circuit with the following components:

- A voltage source \(E = 12 \, \text{V}\)
- A resistor \(R = 100 \, \Omega\)
- An inductor with inductive reactance labeled as \(X_L\)
- A capacitor with capacitive reactance \(X_C = 2 \, \text{k}\Omega\)

Voltages across the resistor, inductor, and capacitor are noted as \(V_R\), \(V_L\), and \(V_C\) respectively, with current \(I\) flowing through the circuit.

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