a) Find the roots of the characteristic equation that governs the transient behavior of the voltage shown in Fig. 8.5 if R = 200 Q, L = 50 mH, and C = 0.2 µF. + Vo b) Will the response be overdamped, underdamped, How did he get the value b) The voltage response wi < a?. inside the red circle c) For R = 312.5 Q, %3D Solution 106 ) For the given values of R, L, and C, a (625)(0.2) 106 a = 64 x 106 = ( 1 a = %3D %3D = 1.25 x 104 rad/s, 2RC (400)(0.2) As wó remains at 10 1 (10°)(10) S1 = = -8000 1 = 10° rad?/s². LC (50)(0.2) S2 = -8000 %3D From Eqs. 8.14 and 8.15, d) For critical damping 05 x 10 108 2RC or 1 = -12,500 + 7500 = -5000 rad/s, 2R and S2 = -1.25 x 10 - V1.5625 x 10 – 10 10 R = (2 × 10

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-5A, + 19.365A,
A2
1.033
dt
19.365
i(f) = e (4cos19.365t +1.033 sin19.365t)
a) Find the roots of the characteristic equation that
governs the transient behavior of the voltage
shown in Fig. 8.5 if R = 200 0, L = 50 mH, and
C = 0.2 µF.
ic
b) Will the response be overdamped, underdamped,
How did he get the value
b) The voltage response
w3 < a?.
inside the red circle
c) For R = 312.5 0,
Solution
106
a) For the given values of R, L, and C,
a =
(625)(0.2)
106
64 x 106
1
= (
%3D
α
= 1.25 x 104 rad/s,
2 RC
(400)(0.2)
As w remains at 10 1
(10°)(10º)
S1 = -8000
1
= 10° rad?/s?.
%3D
LC
(50)(0.2)
S, = -8000
From Eqs. 8.14 and 8.15,
d) For critical damping
1
E05 x 10%
108
-
2RC
or
= -12,500 + 7500 = -5000 rad/s,
2R
and
S2 = -1.25 x 104 - V1.5625 × 108 – 10*
10
|
R =
(2 × 10
Given the circuit in Fig 8 95 fnd ilt) and vft) for t
Transcribed Image Text:-5A, + 19.365A, A2 1.033 dt 19.365 i(f) = e (4cos19.365t +1.033 sin19.365t) a) Find the roots of the characteristic equation that governs the transient behavior of the voltage shown in Fig. 8.5 if R = 200 0, L = 50 mH, and C = 0.2 µF. ic b) Will the response be overdamped, underdamped, How did he get the value b) The voltage response w3 < a?. inside the red circle c) For R = 312.5 0, Solution 106 a) For the given values of R, L, and C, a = (625)(0.2) 106 64 x 106 1 = ( %3D α = 1.25 x 104 rad/s, 2 RC (400)(0.2) As w remains at 10 1 (10°)(10º) S1 = -8000 1 = 10° rad?/s?. %3D LC (50)(0.2) S, = -8000 From Eqs. 8.14 and 8.15, d) For critical damping 1 E05 x 10% 108 - 2RC or = -12,500 + 7500 = -5000 rad/s, 2R and S2 = -1.25 x 104 - V1.5625 × 108 – 10* 10 | R = (2 × 10 Given the circuit in Fig 8 95 fnd ilt) and vft) for t
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