Question

(15 pts) Problem 8: For the circuit below with V = 10 V: a) Derive the expressions for vet) and vo(t) for t<0 and t20 b) Determine vc(t) and vo(t) for t equal to 8 ms. ΙΚΩ X=0 2k8} 11 The v vc on Zon 2ks} . "

Answer 1

to tzo Capacitor reacher steady state and acts as Open cawuit: here VQ = lov i writé ka ppualias veco) avevo at Node vi vi-10 v tuzo 6000 1000 2000+4000 VoC)lox_2000 2000+5060 v Ciboot 6600 + como Je homo >V C1-333 x163 J = 0.01 VOCO )= 2.857 volta - V = 7.5 volts Tucco-)= V1 = 705 voll @t-o switch opened and canacitor voltage doesn't change immediately i VC Cor) = V(CO )= 7.5 volte This is the cucuit for t-ot 4ker Ikr 5kr wordt Voof 9. here u=705V VCO)/7.87 of VoCot)=vx 2000 1000+5000+2000 = 75% 2000 Vo Cot )=1875 volto as t o Capacitor fully discharges, & hence Vc C)=0 volo 4 Vo Cao = o VOLG

Time Constant T = Reqxc . tutettu 2000+4000 6000 1000 +5000+2000 24 e este trabao Scoo Rep=457832x104 - Rep = 2181821) = Repxc= 2181.82* IX100 ~ T-2182x10-5 sec for too Vect )= V Coo) - CveCoo-vecom) Jetta = 0-60-7.57e-t/2.1827103 Tuelt?=7056-458.333t volle Vo Ct) = Vocos ) - ( Vocas) – Vocot) Je? -tia = 0.-(0-1.8757e-/2-182x17 3 Vo Ct) = 108756-45863337 volle -458.333 X 8 X10 **8x103 bi velty @ Brise. A vc Cemsec ) = 7. 50 Vc Comer) =0.192 volto Vo Comse () = 1.875 e-458-333x8x153 VoC8msec)= 0.048 volló