EECE 210 Homework, Spring 2008

Homework 8 Solution 15 P83 [a] in(0) = 300 = 75mA ip(0) = —45mA ic(0) = ~i,(0) - in(0) = 45 — 75 = —30mA b) a= 555 . = 12,500 (b] °= 2RG = 2000210)” we : : = 108 = IC (50 x 10-)(0.2 x 10-*) $1.2 = —12,500 + V1.5625 x 108 — 108 = —12,500 + 7500 51 = —5000 rad/s; 8p = 420,000 rad/s vy = Aye 500 4. Ao @7 20,0008 v(0) = A; + Ag = 15 du —30 x 1073 4 aO = —5000A; — 20,000A, = Dax = —15 x 10°V/s Ne Solving, A,;=10; A, =5 V = 10¢e7 500 4. Fe 20,0008 Wy t>0 . du [c] tc Ca = 0.2 x 107®[—-50,000¢®0% — 100,000e~20.0004} = —10e75000F _ 99¢—20,0008 mA ig = 50e °° 4 25 e770 mA i, = -ic — tp = 4000 — Fe mA, t>0 1 P810 [a] a= 55 = 0.5 rads > 1 we = 7g = 25.25 wa = 125.25 — (0.5)? = 5 rad/s v = Bye? cos 5t + Bye~*/? sin 5t v(0) = B, = 0; v = Boe~/? sin 5t ig(0t)=0A; — ig(0t) = 4A; S(O") = pag = 50Vi5 dt 50 = —aB, + wgBo = —0.5(0) + 5Bo Bz = 10 v = 10e~*/? sin 5t V, t>0 [b] “ = —5e'/? sin 5t + 10e7“/?(5 cos 5t) #0 when 10cosSt=sin5¢ or tanSt=10 Bt; = 147, t, = 294.23ms 5ta=147+7, t2 = 922.54ms 5tg=147+2m, ts = 1550.86 ms 2 fe] ty —t, =1256.6ms; Ty = 2 = 2 = 1256.6 ms Wa 5 T, 1256.6 [d] t2 — t; = 628.3 ms; z = > = 628.3ms [e] v(t:) = 10e~©14") sin 5(0.29423) = 8.59 V u(t) = 10e~ 4?) sin 5(0.92254) = —6.27V v(ts) = 10e~ 774) sin 5(1.55086) = 4.58 V 10> v™) P 8.29 1 1 ®= ORC = 2(400)(1.25 x 10-8) ~ 10 2 1 _ 1 _ 4 “o= TG = 25x 10-105) * 10 81,2 = —1000 + 1000? — 64 x 104 = —1000 + 600 rad/s 8, = —400 rad/s; 82 = —1600 rad/s UVo(0o) = 0 = Vz "Up = Ale 40% + Abe 1600 vo(0) = 12 = A, + Ay Note: ic(0t) =0 dv, (0) = 0 = —400A/ — 16004} dt Solving, Ai = 16V, AL=-4V Vo(t) = 16e~ 4 — 4e7 160% y, t>0 P8.42 [a] t <0: io = - =100mA; v9 = 500i, = (500)(0.01) = 50V t>0: R 50 _.. “= 97 = 3a5xioy 0 TS 1 1 2 = = 108 “= TG = Exitos Goxioy ox"? a=we .. critically damped ". ig(t) = Dytet + Dye 10" i,(0) = D2 = 100mA di a) =-aD,+D,=0 D, = 10°(100 x 107°) = 10,000 io(t) = 10,000te 2 + O0.1e7A, *¢>0 [b] vo(t) = Dste“!"* + Dae" Vo(0) = Ds = 50 dv, C=, (0) =-0.1 du, -0.1 FH = x07 = 775 * 10° V/s = —aDy + D3 Ds = 10°(50) — 25 x 10° = 25 x 10° Uo(t) = 25 x 10°te 1 + 50e VV, t>0