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21 & 121L Midterm Theory 69. Which of these formulas would be used to determine the resonant value of ca a. b. C. fR = C = 1 2TVLC 1 47²f²C 1 4π²f²L

21 & 121L Midterm Theory 69. Which of these formulas would be used to determine the resonant value of ca a. b. C. fR = C = 1 2TVLC 1 47²f²C 1 4π²f²L

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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**Title:** Midterm Theory: Understanding Resonant Capacitance in Circuits **Question 69:** Which of these formulas would be used to determine the resonant value of capacitance? **Options:** a. \( f_R = \frac{1}{2\pi \sqrt{LC}} \) (circled) b. \( L = \frac{1}{4\pi^2 f_R^2 C} \) c. \( C = \frac{1}{4\pi^2 f_R^2 L} \) **Explanation:** This question is focused on identifying the correct formula to calculate the resonant value of capacitance in an electrical circuit. Resonance occurs in circuits containing inductors and capacitors, where the impedance is minimized and the circuit can oscillate at a particular frequency with maximum amplitude. The options provide different formulas involving frequency (\( f_R \)), inductance (\( L \)), and capacitance (\( C \)). The correct formula for calculating the resonant capacitance is option (c): \[ C = \frac{1}{4\pi^2 f_R^2 L} \] This formula relates the resonant frequency to the capacitance and inductance of the circuit.
Transcribed Image Text:**Title:** Midterm Theory: Understanding Resonant Capacitance in Circuits **Question 69:** Which of these formulas would be used to determine the resonant value of capacitance? **Options:** a. \( f_R = \frac{1}{2\pi \sqrt{LC}} \) (circled) b. \( L = \frac{1}{4\pi^2 f_R^2 C} \) c. \( C = \frac{1}{4\pi^2 f_R^2 L} \) **Explanation:** This question is focused on identifying the correct formula to calculate the resonant value of capacitance in an electrical circuit. Resonance occurs in circuits containing inductors and capacitors, where the impedance is minimized and the circuit can oscillate at a particular frequency with maximum amplitude. The options provide different formulas involving frequency (\( f_R \)), inductance (\( L \)), and capacitance (\( C \)). The correct formula for calculating the resonant capacitance is option (c): \[ C = \frac{1}{4\pi^2 f_R^2 L} \] This formula relates the resonant frequency to the capacitance and inductance of the circuit.
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