+ VL Problem 1: Appearing to the right is our familiar RLC series circuit. The voltage source, va, is a con- stant voltage, and because of the capacitor in the loop the particular (steady-state) solution for i1 is zero. Ap- pearing below is the solution for the current through the circuit. Note: This is an easy look-up-the-formula- and-plug-in-the-numbers problem. Don't worry, it gets better. + Va + R i1-part (t) = 0 S Kjeªit + K2eª2t, |Kjeªit + K2teª1t, if a1 = a2. i1(t) = i1-comp(t) +ij-part (t) if a1 # a2; i1 !-comp(t) where R R + 2L'V(2L 1 R R 1 aj = - and a2 = LC 2L 2L LC (a) In design X the supply is va = 5 V, and the component values are R= 100 kN, L = 20 mH, and C= 30 μF. What is the resonant frequency, wo, of design X? Is design X () underdamped, O critically damped, or O overdamped? Show your work. (b) Starting with design X, choose values of R that will result in each damping case. One of those values will be the R= 100 kN from design X. For an underdamped circuit change R to: For a critically damped circuit change R to: For an overdamped circuit change R to:
+ VL Problem 1: Appearing to the right is our familiar RLC series circuit. The voltage source, va, is a con- stant voltage, and because of the capacitor in the loop the particular (steady-state) solution for i1 is zero. Ap- pearing below is the solution for the current through the circuit. Note: This is an easy look-up-the-formula- and-plug-in-the-numbers problem. Don't worry, it gets better. + Va + R i1-part (t) = 0 S Kjeªit + K2eª2t, |Kjeªit + K2teª1t, if a1 = a2. i1(t) = i1-comp(t) +ij-part (t) if a1 # a2; i1 !-comp(t) where R R + 2L'V(2L 1 R R 1 aj = - and a2 = LC 2L 2L LC (a) In design X the supply is va = 5 V, and the component values are R= 100 kN, L = 20 mH, and C= 30 μF. What is the resonant frequency, wo, of design X? Is design X () underdamped, O critically damped, or O overdamped? Show your work. (b) Starting with design X, choose values of R that will result in each damping case. One of those values will be the R= 100 kN from design X. For an underdamped circuit change R to: For a critically damped circuit change R to: For an overdamped circuit change R to:
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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