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There are 4 permutations: natural response and step response for both parallel and for series RLC circuits

There are 4 permutations: natural response and step response for both parallel and for series RLC circuits

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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1. There are 4 permutations: natural response and step response for both parallel and for series RLC circuits 2. Find a=1/2RC for parallel and a-R/2L for series 3. Find co²=1/LC and compare a² to co² 4. Choose form of solution for second-order diff eqn with constant coeff's If a wo, then x(1) Xr+ A₁ exp Sit+ A2 exp S₂ąt where S₁2=-a +√(a²-c0²) If a<, then x(t) = X + B₁ exp (-at) cos wat + B₂ exp (-at) sin coat where co =√(₂²-a²) If a, then x(t) = Xr+ D₁ t exp (-at) + D₂ exp (-at) 5. Determine from circuit if X<= 0 or not. 6. Find coeff's A, B, D by evaluating x(0) and dx(0)/dt. x(0) is given by circuit conditions and dx(0)/dt can be found by knowing that i-C dv/dt =-i-i-lo-V/R or by knowing that VL - L di/dt and v₁(0)= -1,R - Vo. In either case, I, and V, are determined by the circuit. Solve equations simultaneously for A, B, D. 7. Write full equation for x(t) and test for x(0) and x(co).
Transcribed Image Text:1. There are 4 permutations: natural response and step response for both parallel and for series RLC circuits 2. Find a=1/2RC for parallel and a-R/2L for series 3. Find co²=1/LC and compare a² to co² 4. Choose form of solution for second-order diff eqn with constant coeff's If a wo, then x(1) Xr+ A₁ exp Sit+ A2 exp S₂ąt where S₁2=-a +√(a²-c0²) If a<, then x(t) = X + B₁ exp (-at) cos wat + B₂ exp (-at) sin coat where co =√(₂²-a²) If a, then x(t) = Xr+ D₁ t exp (-at) + D₂ exp (-at) 5. Determine from circuit if X<= 0 or not. 6. Find coeff's A, B, D by evaluating x(0) and dx(0)/dt. x(0) is given by circuit conditions and dx(0)/dt can be found by knowing that i-C dv/dt =-i-i-lo-V/R or by knowing that VL - L di/dt and v₁(0)= -1,R - Vo. In either case, I, and V, are determined by the circuit. Solve equations simultaneously for A, B, D. 7. Write full equation for x(t) and test for x(0) and x(co).
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