Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
98. Which of these formulas would be used to determine t a. b. C. fR L= C = ..... 1 2TVLC 1 4π2fp?C R 1 4π²f²L

98. Which of these formulas would be used to determine t a. b. C. fR L= C = ..... 1 2TVLC 1 4π2fp?C R 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
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
See similar textbooks
icon
Related questions
Question
**Title: Determining the Resonant Value of Inductance in AC Circuits** **Introduction:** In alternating current (AC) circuits, resonance occurs when the reactive components (inductive and capacitive) balance each other out. This principle is particularly important when working with LC (inductor-capacitor) circuits. The resonance frequency \( f_R \) is a key parameter and can be used to derive relationships for other quantities like inductance \( L \). **Question:** Which of these formulas would be used to determine the resonant value of inductance? **Options:** a. \( f_R = \frac{1}{2\pi \sqrt{LC}} \) b. \( L = \frac{1}{4\pi^2 f_R^2 C} \) c. \( C = \frac{1}{4\pi^2 f_R^2 L} \) **Explanation:** - **Option a** provides the formula for calculating the resonant frequency \( f_R \) in terms of inductance \( L \) and capacitance \( C \). - **Option b** rearranges the resonance frequency formula to solve for inductance \( L \) in terms of \( f_R \) and \( C \). - **Option c** rearranges the same principle to solve for capacitance \( C \) given \( L \) and \( f_R \). **Conclusion:** For determining the resonant value of inductance, **Option b** is the appropriate formula. This equation shows how to derive \( L \) using the known values of resonant frequency and capacitance in the circuit. Understanding these relationships is crucial for designing circuits that operate efficiently at specific frequencies.
Transcribed Image Text:**Title: Determining the Resonant Value of Inductance in AC Circuits** **Introduction:** In alternating current (AC) circuits, resonance occurs when the reactive components (inductive and capacitive) balance each other out. This principle is particularly important when working with LC (inductor-capacitor) circuits. The resonance frequency \( f_R \) is a key parameter and can be used to derive relationships for other quantities like inductance \( L \). **Question:** Which of these formulas would be used to determine the resonant value of inductance? **Options:** a. \( f_R = \frac{1}{2\pi \sqrt{LC}} \) b. \( L = \frac{1}{4\pi^2 f_R^2 C} \) c. \( C = \frac{1}{4\pi^2 f_R^2 L} \) **Explanation:** - **Option a** provides the formula for calculating the resonant frequency \( f_R \) in terms of inductance \( L \) and capacitance \( C \). - **Option b** rearranges the resonance frequency formula to solve for inductance \( L \) in terms of \( f_R \) and \( C \). - **Option c** rearranges the same principle to solve for capacitance \( C \) given \( L \) and \( f_R \). **Conclusion:** For determining the resonant value of inductance, **Option b** is the appropriate formula. This equation shows how to derive \( L \) using the known values of resonant frequency and capacitance in the circuit. Understanding these relationships is crucial for designing circuits that operate efficiently at specific frequencies.
Expert Solution
Step 1

Explanation is given in processing steps 

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Inductor
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS