Question

Given the circuit in Figure 8.6, find vc(t) for all t>0. t=0 102 20 V * vc(t) 1/10 F 10H Figure 8.6

Answer 1

Given ciecut is 100 ntão Het 200 A Velt) -% OF we need to find Velt) ie above ciecuit switch switch is closed before tro means circuit already attains Then the crecuit becomes as teo (or) to to is opening at tio That means a for a duration that long deel steady state before tzo. follows- or 7i, 10) = 2 Amp + 2017 Velos voltage, that means zero. ucco-) is short circuited tore voltage is doopped across 10-2 resister Vc60) =07 [ {(co-) = 20 = 2 Amp : is off - at tzot switch opened that means, switch The Network becomes source free. → initial condition representations of cleouit is VI 10-) = Vic0+) = 0 , ILO)-i_(0+) = 2 amp

where co Vo=Vclot)=ov 20 = &Cot) = 2 Amp 31 & SLR to in the above ciecuit. substitute the above all values c ov 205) ov 25 10x2= 200. (0X220V ve Lt) + 102 2 Y los 2 apply KVL in above crecuit 20 = 2(5)10 +2 (5)105 20 = 265) [1041054] 265) = 20$ 10(1+52] 20) = 25 1+52 opply înverse loplace transfer to above equation E' [266)] = 1'[***] alt) = 2 cost t>o we have find voltage ewuation across capaciter we know wevent through copac'te ie 205) = 25 and impedance of copacitor - 19-2 Itse Then V(15) = 28 Ne(s) = 1752

apply inverse Laplace tranform Then L' [vers)] = {(i Volt) = gosint to voltage across copacitur far to is Volt) = 90 sínt tyo
the voltage across capacitor for t>0 is 20sint