Question

A series RLC circuit is connected to an independent voltage source Vs = 160 V with a switch closing at t = 0. If R = 4.8 kohm, L = 4 mH, C = 0.25 mF, find the s-domain and time domain (when t > 0) representations of the current, a) if there is no stored energy in the circuit. b) if the 100 mJ stored energy is equally shared between the inductor and the capacito

Answer 1

(6) Xto M 10. (0) 16.01. M(t). I licu ht Ag the inductor, Leaplace trausform M(%) St 1 ($8()-1()) AL I(1) - LUCO For the capacitor, Ve(t) = { q (t) e silt) 100 + sicu) et I Laplace trausforu Valk) = Velo) + Ielb s domain is shown below: T(A) The ckt R=4.8ko 160 Vol L = 4mt C-0.25mf -VCOM Figa T(%) - (8) +9L1166) *** -VCC%) (R+5+4) S.Vs (5) + shi (0) - Velo) (BR+ sh + in the circuit. no stored energy (as If there is il (6)=0; VCO)-0 s Ve(s) (3R +8+2+£) [4800.5+$** 4x103 46625x163) S+(1-2x106) +10 5. (1980

1.3334x109 1(8) May 160 (3?+0.2 x 10's)+10) 160 (5+0.8333)(8+1.1999x106) ku K21 + i kll (S40.8333) (+1.1999x105) Lim ($40.8333)T(6) -(1.3338109) (841.1999x18) 7(3) =(-1.3 334x107 6+60.8333) Кур. lim (11999810 ilu time domain, -0.83335 e for t>o

(b) of woomI slosed energy is equally shared between the inductor and the capacitor : dando & -SOMI / (( (6) ² EL >> ļx (ml)*(160)) = (50m3) = 2(0) =5A. &- $(66) = \x6.25mF)x(VCO)= (50 m3) VCO)= 207 to plugging in the values in equ. (1), we get 1(8) 8(0.009x5) 52(0.004)+ 3(4800) +0.25x163) -) (8) = (160+0.028-20 (52 +0.2X105)3+106) (0.028 +140) (1-2x106y5+106) 0.028+7000) | Its) 84+1-2x188+109) current in s domain (3) beden 0.02(6+7000 (3+0.8333) (37181.1999x106) K2 K22 + (3+0.8333) lim (3+0.8333) IC) -0.167X164) 0.8333) 0.01988 lim (5+1.1999x106) (5) (3+1:1999x105) K2 K22= (37-1.1999x109) In time domain, -0.83337 A :i(t) = (1.167x104) ē +6.01988) el 1999x1096) (for too)