Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
(a) Determine the first and second derivatives of llt) and hence show that /(t) is a solution of equation (1). (b) Show that the stationary points of ur at time t: tan ot a (c) Determine the partial derivatives OL' ƏC (d) The change in the resonant frequency for a small change in the inductance, AL, and capacitance, AC, is given by Δω, - AL+· -AC ƏL Use your result from (c) to derive an expression for Awo.

(a) Determine the first and second derivatives of llt) and hence show that /(t) is a solution of equation (1). (b) Show that the stationary points of ur at time t: tan ot a (c) Determine the partial derivatives OL' ƏC (d) The change in the resonant frequency for a small change in the inductance, AL, and capacitance, AC, is given by Δω, - AL+· -AC ƏL Use your result from (c) to derive an expression for Awo.

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
icon
Concept explainers
Question

Can you please help me with all parts of the question?

Thank you

The current, I, in an RLC circuit is given by the equation: R d²I dI + 2a -+ oI = 0 (1) dt? dt V where the damping factor, a, and resonant frequency, o, - Vo +a² , are dependent on the values of the resistor, R, capacitor, C, and inductor L: 1 R and @, = 2L a = VLC A solution of equation (1) is given by -at I(t) = e sin ot (2) (a) Determine the first and second derivatives of Ilt) and hence show that /(t) is a solution of equation (1). (b) Show that the stationary points of ur at time t: tan ot = a (c) Determine the partial derivatives రిo్ do (d) The change in the resonant frequency for a small change in the inductance, AL, and capacitance, AC, is given by AL + ÔL Δωρ -AC Use your result from (c) to derive an expression for Awo.
Transcribed Image Text:The current, I, in an RLC circuit is given by the equation: R d²I dI + 2a -+ oI = 0 (1) dt? dt V where the damping factor, a, and resonant frequency, o, - Vo +a² , are dependent on the values of the resistor, R, capacitor, C, and inductor L: 1 R and @, = 2L a = VLC A solution of equation (1) is given by -at I(t) = e sin ot (2) (a) Determine the first and second derivatives of Ilt) and hence show that /(t) is a solution of equation (1). (b) Show that the stationary points of ur at time t: tan ot = a (c) Determine the partial derivatives రిo్ do (d) The change in the resonant frequency for a small change in the inductance, AL, and capacitance, AC, is given by AL + ÔL Δωρ -AC Use your result from (c) to derive an expression for Awo.
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Thermistors
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.
Similar questions
  • SEE MORE QUESTIONS
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