Question

5. The circuit elements in the circuit in Figure 1 are R=1250, L=200mH, and C= 5uF. The initial inductor current is -0.3A and the initial capacitor voltage is 25V. a) Calculate the initial current in each branch of the circuit. b) Find v(t) and it(t) fort > 0. + IR V. 200mH 110 12503 5uF 0 2

Answer 1

-0.3 A Initial current , lot) = Initial voltage, Velo*)= 25V Pu parallel circuit voltage is same VR (O) = V(o)= V.CO): 250 25 0.24 ir Cof)= VR COP) 125 KEL (o)tic (ot) tirdzo iccot) = -ic cot) + lipca') izo - +0.3-0.2 FIA ir lot)=0-27, (04) --6-3A, , (d):0.1A b) resonant frequency face 1 RC 2 RC 2 x 128x5x100 280110?x Saino ac 800 - 1000rad/sec wah w under damped system

vre (A, Coswet + A, sinwat) S, and -2²_wa S, =-4t d² wyt S27-800 - √8002_1000 = -800+ $8002-20002 =- 800 - 600) Si 800+6009 VCO) =Vccot)= A, = 25V dv ( 6 ) iclo) =-2A,+ Wd Az 8 60+25+ booo Az stroG A = 66.667 2 tro cat VIH- (A, cos watta; sin wat) e coot VCH (25 cos 600++ 66.667 Sin 600 t) v - e expression for (H) is .at at lH = 2 + B, e cos wat + B₂ e sinwat nosource 2 20 -at Sin wat H = B, e coswat & B, e eltes watt tzo (0) - Bu -0.32 B

die Vecot) = dt 25 = 125 die Vc (0) 200 x103 dt t-o dil 6) = wd B, -KB, dt 125 = 6 OD B, - 800(-0.3) 125 = 600 B, + 240 Bas 3 o.1 9167 il (H) = (-0.3 € Root cosboot - 800 t 0.192e sin boot) -800+ -ee iCH (to. +0.3 cos Goot +0.192 sin godt) A