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i(0) = 4 = A di (0) v(0) di jegu dt dt di (-5A, cos19.365t - 5A, sin19.365t –19.365A, sin19.365t + 19.365A, cos19.365t) dt di(0) -5A, +19.365A, dt A 5A 1.033 19.365 i(t) = e (4cos19.365t +1.033 sinl9.365t) a) Find the roots of the characteristic equation that governs the transient behavior of the voltage shown in Fig. 8.5 if R = 200 2, L = 50 mH, and C = 0.2 µF. ic C Vo iR RE b) Will the response be overdamped, underdamped, or critically damped? c) Repeat (a) and (b) for R = 312.5 0. D What value of R causes the response to be criti- cally damped? b) The voltage response is overdamped because w3 < a?. c) For R = 312.5 0, Solution 10 a) For the given values of R, L, and C, a = = 8000 rad/s, (625)(0.2) a = 64 x 10 = 064 10 rad/s. 10 = 1.25 x 10 rad/s, %3D 2RC (400)(0.2) As wmains at 10 rad?/s, Si = -8000 + j6000 rad/s, 1 (10)(10) = 10 rad/s. LC (50)(0.2) S2 = -8000 - j6000 rad/s. From Eqs. 8.14 and 8.15, d) For cical dampine 125 x 10 V15625 108 108 10% How did he get the value 50 0. inside the red circle

i(0) = 4 = A di (0) v(0) di jegu dt dt di (-5A, cos19.365t - 5A, sin19.365t –19.365A, sin19.365t + 19.365A, cos19.365t) dt di(0) -5A, +19.365A, dt A 5A 1.033 19.365 i(t) = e (4cos19.365t +1.033 sinl9.365t) a) Find the roots of the characteristic equation that governs the transient behavior of the voltage shown in Fig. 8.5 if R = 200 2, L = 50 mH, and C = 0.2 µF. ic C Vo iR RE b) Will the response be overdamped, underdamped, or critically damped? c) Repeat (a) and (b) for R = 312.5 0. D What value of R causes the response to be criti- cally damped? b) The voltage response is overdamped because w3 < a?. c) For R = 312.5 0, Solution 10 a) For the given values of R, L, and C, a = = 8000 rad/s, (625)(0.2) a = 64 x 10 = 064 10 rad/s. 10 = 1.25 x 10 rad/s, %3D 2RC (400)(0.2) As wmains at 10 rad?/s, Si = -8000 + j6000 rad/s, 1 (10)(10) = 10 rad/s. LC (50)(0.2) S2 = -8000 - j6000 rad/s. From Eqs. 8.14 and 8.15, d) For cical dampine 125 x 10 V15625 108 108 10% How did he get the value 50 0. inside the red circle

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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i(0) = 4 = A di (0) v(0) jegu dt dt e" (-5A, cos19.365t – 5A, sin19.365t –-19.365A, sin19.365t +19.365A, cos19.365t) dt di(0) 5A, -5A +19.365A, A, 19.365 1.033 dt i(t) = e (4cos19.365t +1.033sin19.365t) a) Find the roots of the characteristic equation that governs the transient behavior of the voltage shown in Fig. 8.5 if R = 200 2, L = 50 mH, and C = 0.2 µF. + IR Vo R b) Will the response be overdamped, underdamped, or critically damped? c) Repeat (a) and (b) for R = 312.5 N. D What value of R causes the response to be criti- cally damped? b) The voltage response is overdamped because w < a?. c) For R = 312.5 N, Solution 106 a) For the given values of R, L, and C, a = (625)(0.2) = 8000 rad/s, 106 a = 64 x 10 = 064 v 10° rad/s?. %3D = 1.25 x 10 rad/s, 2RC (400)(0.2) As wmains at 10 rad/s?, S1 = -8000 + j6000 rad/s, 1 (10)(10) = 10 rad?/s?. LC (50)(0.2) S2 = -8000 - j6000 rad/s. From Eqs. 8.14 and 8.15, d) For cical dampine 125 x 101 V15625 y 108 108 = 10% How did he get the value 50 0. inside the red circle 6 V ww
Transcribed Image Text:i(0) = 4 = A di (0) v(0) jegu dt dt e" (-5A, cos19.365t – 5A, sin19.365t –-19.365A, sin19.365t +19.365A, cos19.365t) dt di(0) 5A, -5A +19.365A, A, 19.365 1.033 dt i(t) = e (4cos19.365t +1.033sin19.365t) a) Find the roots of the characteristic equation that governs the transient behavior of the voltage shown in Fig. 8.5 if R = 200 2, L = 50 mH, and C = 0.2 µF. + IR Vo R b) Will the response be overdamped, underdamped, or critically damped? c) Repeat (a) and (b) for R = 312.5 N. D What value of R causes the response to be criti- cally damped? b) The voltage response is overdamped because w < a?. c) For R = 312.5 N, Solution 106 a) For the given values of R, L, and C, a = (625)(0.2) = 8000 rad/s, 106 a = 64 x 10 = 064 v 10° rad/s?. %3D = 1.25 x 10 rad/s, 2RC (400)(0.2) As wmains at 10 rad/s?, S1 = -8000 + j6000 rad/s, 1 (10)(10) = 10 rad?/s?. LC (50)(0.2) S2 = -8000 - j6000 rad/s. From Eqs. 8.14 and 8.15, d) For cical dampine 125 x 101 V15625 y 108 108 = 10% How did he get the value 50 0. inside the red circle 6 V ww
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