Question

for_final.pdf Example 9.8-1: Find the complete response v(t) for t>0, assuming the circuit is at steady state at t=0 t=0 4 92 NNN 1H Vs = 6 e-3'u(t) v www (.* v(t)=44/3e2t+1/3e-5t_9e-3t (V) M. Cheng

Answer 1

41 a we lou Is + In steady state, vco-) = 100*6 = 6V ( By voltage division) 110) = 18 - RATA IA 6+4

At t=0, Vlot)= 6V ; (lot) = 1A Vecot) = v-i (6) = 6-1(6) 20 clot) - 6-6 mi =) L dilot) - 0 dicot), DA z o Assec at E -1A, 3 cove 2-1 dve lot)=-4 V/sec de

KUL in outer loop, Vs - 4 liit cdvc) -ve0 -0 Vs Ebeut) dt Ve - Vetrii vcs edict big w.. from © ¢ © dt vs - 4111 + Ledek * 6c de) - in die toit) - o

VAY Vo = point dit + 1 die (+ 10 +10) = Vs +6e3 By solution of higher order differential equation. +7 +10=0 LE CF + P.I Complementary function (C.F) • Inace stc, ezt Particular ins Regras (P.I) = 1,= 66 st 10+7(3)+3 6 -3t -36-37 -50 = ce tezensé i, 10) = la CitCz -3=1 G+C2 = 4 - 0 il'lo) - Opisec ichl= -50, est-26 e 2t the 3t iz (0) +54, +2C, = 9 - Solving ☺ and ☺ CIE Cz=13 i,t).= lest tu ezt 20-3t ve (t) = edi, + bi, ht + 3€-35 vace z je+44 € 27-9813t