Question

Given the following information about a 2nd order transient circuit, solve for the coefficient az in the capacitor voltage 132-1 - wnt v 12–1 + a2e + vc ()for t>0. Vc (t) = = e-śwnt (az existin C = 8 mF Vcl0+) = 8V Vclinfinity) = 3V ic(0+) = 4 A Wn = 43 rad/sec zeta = 1.19

Answer 1

unter weather Giren, Velti = e Gwent (x, wat veri +Veloo) 2 wortet = 43-1-1941 & pereg. Given q=1.10 wn= uz rad kec Lawn = -1,19 (43) = -51.17 Ve ego when t=do Velut) = x,tt2 &=xitam VCOT)=8V Given) Now, as For Capacitor alt=1 d Vlt) dt ile = dvet2 dt at t-ot ilot) - dvlot) Given icloty C=8MF dvlot) u dom dt iltl dt =4A 500 mots 8mF Volts

consider eqo part 0 doelt) dt - gunt writer-it tewn) Xpe toge at toot egunt & univerfit from-ter- dve lt2 leo = agoni, ta, unter i dt Now considet p Now differentiate, Part 2 of eq 0 We will get similar result Ź & unterit sunt tewn) -ewnt.writest at t-ot o fantasi) -G wn az & Writer y dvelt? at tae ds dt 2 combining Eqg, and and substituting values of ewn and when dvclut) = -51.172, t&, -27-7375-5141742 X2 27-7378 -23.43254-78.90752 23.43254, +78.9075 Ka- dt = ic Coty c - 500 = solving Eq m 46 x = 20-3922, -12 3922