Question

Solve all the problems shown below Problem 1 In a source free RLC series circuit If R=1092 ,L=5H ,and C= 2 mF 1) Find a.,0, and the characteristics roots $,$2. 2) Find the response i(t) knowing that v(0)=5V and i(0)=1A Problem 2 In a source free RLC parallel circuit If R=52 ,L= 1H ,and C= 10 m 1) Find a ,0, and the characteristics roots S1,S2. 2) Find the response V(t) knowing that v(O)=10V and i(0)=5A Problem 3 In a step response series RLC circuit, R=522 ,L=1H ,and C=0.5 F and Vs=24 V. i(0)=4 A ,v(0)=4 V Find v(t) and i(t) fort > 0. Problem 4 In a step response parallel RLC circuit, R-10 92 ,L= 20 H and C= 8 mF F and I=4 A. i(0)=4 A ,v(0)=15 V Find i(t) for t>0.

Answer 1

Pooblem 1 R-L02, LESH, C=2mf, Souace face RLC Series ckt 1) a = b = 15 0231] worze 5x2x603 wo - lovad/sec) S2,S2=- a - VaRo? = -1 + √1-102 = -1+3571j (52= -1 + jg.gn, S2=-1-jg04

2mF 5H ണ Vo RES 10.12 Isto + LAS + RSULO ot Differentiale it ILU + R&S(t) = 0 at dt2 of Eqno Take laplace toonsfoam 2 LSI(S) - iso + Rils)=0 T® [ + Ls+p] = V2 + L$() IS) 500 + 55+10) = a + s(1) 15) 115) 5+55 setias +500 St1 IS) S+1 [S+j2+(199)? 53+28+100 Take inuease laplace toans foom s(t) = et costa out) Pooblema R252, L=1H, C-lom , Souare free RLC baccelle ciscuit 1 02 303 ZRC 2(5)(10 - 10 (x=010) wo - 1 Two = load/sec

S1 S2 = -x & Va? coo? (S1, S2 = -10 1,50 SA C ome VO-10V 52 R 143L vo + t svezet + coreto Take laplace toons fcam VE + VS - $ + CSVES)-CVCO) 20 Vs +5)= CVCO) + $C) NB + $ + ) = (OC+3) VS) = (0-1S+5) 100 S2+205+(00 VS (IOS+500) (5+102 V LO (S+50) (St102 VO = 10 stio *6402 Take inuease laplace toonsfoam vitalo (elokuoteoty [V - 10 e lot (2+40t)

Problems Step besponse sepies RLC CH R-5, L-IH, CEOSF, Vs = 24V, $(0)=4A, V(o)=uv mommm 14 512 - 05F Not st VS UH) = R$4+2 ose + + Siktad Take Laplace ton cam V = R149) + LS 169 – <$(0) + 19 - VC Cene + + 5) = 16) (5+5+ }} 28+hs I(S) = 255+2 2.367 6367 - T($) +4.56 St0438 Take fauease la place 2367e-456+ s(t) = 6357 e 0438 + lut = 24+ 6.67e ausst 2.3676 4:56t Problema Slep espone borblol RLC CE - 20H, C&F, TS-4A , Ś()UA, VO) = 15V a RC = 2X10X8x163 2= 625 waz 2 22.5, S.,S2 = -x + √22coo? awo (oxeadompel] -0.521, -11.97 562 Is + ge-05214 + C2 e 11976 -11 SH)= 24+ 0 e 0.5214 te 11.97€

s(): U= 24tcitc2 at C = -20 stoje 19844 24 dos V v=Locate VH = 2014 (Dutcie osett ce119)) Vo = 201 -oselge oselt. 12.97924 1197) VOOS 15 = 201-6:5216,- 1197027 9.5216 +11.97625-075 -- solve aan we find c.&la =-2084, 2=0.8446 The defoe, stva 24-20-848 sente o suu 60-119H