Question

Problem 3: At a time we will define to be t = 0 all the capacitors in the circuit are uncharged and I will close switch S1. At time ti = 50 us I simultaneously open Sand close switch S2. What is the current through the left most resistor at t2 = 75 us? (10 points) 100 nF 1002 w 100 S2 1002 100 nF W 100 12 200 nF Si 10 V

Answer 1

andardles This given circuit is reducable. Marlies r Toolf oor Hy oon loon Torf Resistor in Parallet 100 A Capacitor is Yarallel ♥ 20 Lt c'- loopf +20out C'= 3oouf) R 100 Xod 100 +100 100XIOU 200 R²-son for t o switch so will get close. c left t oouf oor R im Trov series Now cand 100 of are in c' x100 uf C'' = - c' +100 uf c". 70, 400 ["=754) series – 100de, loose, R' are in R"- vout 1000+R" P" = 2500

Equivalent circuit for the left R" et wah lov as Intial voltage across Capacitor given is zero so Vecot) = or In Steady State Capacitor will get fully charged and Vecool=lov Time Constant - R" (" = 250x 75MF I - 1875048 so bennel Velt) = - Capacitor voltage Ve() + (Ve (0) -- Ve()-€ +/+ 10+(0-10] è torson 048) for to Vih= loin etkinson fa tyo Velt)= 10

GO Voltage at t, -5our Calculating voltage at to sour VE, 6) = 10C- min) v Valt) – 0.0266 v circuit for y our at t= sousV e = 0.02665 as no and for t- o [ Stead State] & Ve=ov active source available. 80 (t-so- Gennae V' (t) = Capacitor voltage for tysaus V(0) + ( VC Fouf) – V() - 78750 (t-sous) Vilt - ot(0.0266-0 ē - 18750 us (t-soud) é 1875ous v Vé(t)= 0.0266 –

Calculating Capacitor Current .. I c = c dvelt dt Ic= 75uFX 0.0266 -(t-sous) e 1875ous A -- 75x10-6 yo.0266 -(t-sous 1875o.us 1875oxios Ic - 6.0266 (t-5048) 1875ous 250 90 from circuit – I - – Ic I- 0.0266 250 It-5048) 1875 048 A for tu 75 un 0.0266 250 (75-50) un 18750 48 -7548) = = 1.06258 X10-4 A 106.3XGA I = 106.3 MA Any