Question

Problem 1. (50 points) In the circuit, the initial currents in inductors L1 and L2 have been established by sources not shown. The switch is opened at t = 0. a) Find 11, 12, and is for t 2 0. b) Calculate the initial energy stored in the parallel inductors. c) Determine how much energy is stored in the inductors as t o 412 M 1 = 0) 8a13;" 4a13; 34, (5 H) 3L, (20 H) (1) 4022 3151 31012 Problem 2. (50 points) The initial voltages on capacitors C and C2 in the circuit have been established by sources not shown. The switch is closed at t = 0. a) Find vi(t), vz(t), and v(t) for t 2 0 and iſt) fort 20 b) Calculate the initial energy stored in the capacitors C and C2. c) Determine how much energy is stored in the capacitors as t o 1 = 0 40+ (5 uF) 4(1) (1) 250 k12 24VC2 (20 mF) oz(1)

Answer 1

5H& 20h are pocartel 5x20 - heq ty heq = 44 Req - 4012 (4+ (151)] = 4011[4+ is ] - 8iz. Reg = 4011 (4 +6) = 40x10 20+10 Ert) to initial value of Cwerent sq Vi Ra3802 110) 4+8 = 12A P = Leg = A 2 = 1 / 2 Req :: Source free rah circuit (lt) = 12 ē at À toht20 ::144) = (x8 = 12x8 ēdt 968 2t v dom +20 . te te the I or ser taip The "la+fudt I 15X10 15H0 , , % *at - 8 - 1=-* 7** * { = 96-45cale TE, = 1:6-9.62t top + 20 lg = 2.4-2.4826_A t -16-94 ppt let 20

& = vit) - Vit) 476 10. By cwevent diviston Reele Iz - Ult) x 15 -96x72t x15 To 15+10 10x25 ig -5.76 ēqt to +20 b) w=44&0) + £ 62 660) = 4 *5*8%+4x20x4° W60) = 320J c) At ty0 €, com = F-6A-0, 660) = -46 +0 i WC) = +44 () + 4 de gener (20) = *5* 1«6*+{ x20 x(16)2. 960) = 327

At initial voltage V 20) = 24-4:201 q- gicgare Series : 20x5X106 xrot -= Gellf: (20+5)x106 T= R.ceq = 4 x 106 x 250x103 = 18. ilt) . Source free R-c circuit E lt) 250kn LiNLU) = Y() et le Cq20r Vlt) = 20ět vi 7 {xt) = vlt) min = 20 - Boet MA bor+ 20 = {) 250kr 250x10 - 10 :: V=Histidt :: ) = o p * Poxobet d-d -1866) Flitt 1624. nov toh + 20 ) Yig le) = brots seortöbet dt + 24 stutt let het inte - My Lt) = tett zov b6 2.20 6) £c vlo) - xs xs x4 - 40u W = 4 qy410) = 4 x 20 xjöbx 24% = 5760J. :- 40+5760 = 5800u. c) At tido Vico) = 160_205-20. 19 600) = 480 +20 = 20

wbo) = 49 Vilo) + 4G ve 2 600) = +(5+20) x106x 202 (206) = 500.7