Question

5. Find the current is(t) using mesh analysis in the s-domain. (20 pts) F 4H mm HH 4e-2t u(t) V i2(1) 2eu(t) V 102

Answer 1

А L[a é at uts] = له. sta - induchor =.sl. Capacitor се 3 دراما 45 301 - 4 2 + low +) M S+2 I(3) IL (3) S+1 Loop I 4 + T (5) S+2 510() +10[ 309–5(d) = film( +10] -10[7.] = 4 8+2

2 Loop 2? AS[IG) - st 20 + 10[1411 – 5 (5) -10 11(1) + 1:09 [ 43+10] 2 9 +1 2 I() [43 +0] 371 +10 I, (5) S+) 2 10 IL (5) I(s) + 3 (s +) (45+10) 45+1 substrate ② in 3 10 51» (J +e] - + -)0 (3) 13 T(s) (5+1)(43+10) 4 St I, (3) 2 colo 10 +10+ 43+1 (5+1) (49+10)

3 20 I, (5) 3(43+1) + 10 s (45+1) +105 (5+1)(49+10) S(43+1) 20 125+3 +10[45+3)+103 I, (s) (3+1) (49+10) s(4+1) Il(s) 123 +3 + 409 +10 3 + 103 = 3145+1) (3+1) (43+10) I (0) 40 9 + 323+3 § + 20 M 3(43+1) (5+1) (45+10) 20x3 (43+1) I, () (5+1) (43+18) (40 9 + 325+3)

20x3 (45+1) I, (3) (3+1)(43+0) 40 [s+ mesta 1.5 (48+1) 11() = (3+) (45+io) $ +0.83 + 0-0 -075) Bopay Rodos -0.870.8-4(2071) 2(1) Roodsa 0.10845, -0. -0.68154 IF($) = 1.5(45+1) (8+) (43+10) (5+0-10845) (3+0.69154) 4 By partial frachum 7 () А. B C р + + S+) 45+10 S+0.10845 S+0.69154 A: I;(). (5+) S 51C.(5+ is[46-1+0) [46-1) 40) (-14010845][-+0.69154) 3=-1

Aa 2.7272 1. () +1) B - (⑨) (43+lo) (estio) (+) ( -10 4 +0.10345) o.3754 ST 10 뿜 B = ②.081 C= (④). (8+ 010845) S= -0.10845 1.5| 4(-0.10845) +) c = l (-019843 +) +16)(- ㅇ) 0345 + 0- 69154) = 0.17078 DE IT(S) (3+6954) Se - 0.61154 1. [ 44-4154) +1) ( - 69154 +1) ( 4 (-69154)+1) ( - 6.1154 + 0/0 8447 D = 2,03630

6 By substiteling A, B, CD 2.036028 -2.7272 2.001 0:17078 + Ir (9) + S+0.69154 3+1 3+0.10845 (43+10) -2.7272 2.081 0.17078 I,(9) = 2.036818 + + + S+1 4(5+ Sto. 10845 5+0.69154 -2.7272 0-52025 0.10078 2.036818 T; (5) + + + S +1 S + 2.5 Sto./0845 S +0-69154 - By inverse Laplace framform 669154 1.7272 e -2.54 - 0.108456 +0.52025 e +0.170780 +2.6368 e Glt)