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(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...
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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.
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