Question

For the circuit of Fig. 5, find v (t) for t > 0. 612 V1=0 + 카 412 v 6 uF 9V Fig. 5

Answer 1

® Find Vt) for to 64 + yn Xto gav Surt for to: (switch is opened) Capacitor Open Cicuted 16)=OV + VO) for t70o (switch is closed) Capacito) → te circuited Open V60) =90 9v .ba 14 vo Time Constant G): - Reg Ceg Req = 6a Ceg = 6uF Gr M Rea 9 I = 6X6X106 15 36 efec. > Ve) - Ww+66) - Vo]ēt VH = 9-9ē 436x106 VU = 96-27777.77) Volle

® find Vit for to VO)= Oy; Pclo) = 5A 20 It ich stereo t +0.57 vt) 30.5H Rasa dll) 0 t har t R * v=ver / Lewat atbly kce at VH, > vel Z f ),de + ickt) = 0 differentiate with respect to th; 1 dust / / / vtt)dt + dt dt 7 helical + ][ élet). dt]+ din * differentiate worth srespect to it', 1 dict) Bilt ata dict) t ata 0.5X0.5) dt 0.5X0:5) diet) dio ty +49(t) =0 det SO dt ㅋ t 1 ict) + RC dt LC 1 pc =0 → + ata

2= Moot D?+ 4.0+4=0 Detap+20+4=0 DlD+2)+2CD+2) = 0 (D+2) (0+0=0 D= Ploty are spal and repeated ica) = 6 + Cat)eat Pc 0) = 5 G → i'(t) = -26 @attaczlézt + tif2jēxt) PO-05-29 +62 Cas26 = 2x5=10 + c(t) = 5 +10+)?# Ambe - VE) Ź ſice).dt V(t) = 2 2 [15e²dt. + flotestat 1 6+10+)et, at 0.5 a {5€)+10 (- En 50] Vee-set 10 text_sead Vt = -10ěät-lotéit Vt)= -10 ē at [ 1+t] vett