Question

5) In the following circuit find an equation for v(t) the voltage across the capacitor for t>O. You may assume the circuit is in the steady-state just before the switch opens at t-0. 6 N 50 -Mu IH 3 10 ml Add equation 6) For the following circuit find an equation for v(t) fort > 0. You can assume that the circuit had reached the steady-state condition before the switch opened at t -0. to 20 2H 1F TVE) in

Please solve the two problems shown and show work. thank you!

Answer 1

5 for t20 steady state ou. vt In (6) e (0) in (6-) = 12 = 2A But IL (6) = ln (0) = {(ot)=2A NC (6)=or (short Indentor) But Nc6-) - VC(O) =Vclot) = OV for to het us draw circuit s-domain in

X Bus & has vis Ves) veet) Lz14, calomp Kch at x Node- No Sith llot NB) V(COT) 25 + 2/cs 20 Put All reaturen Vest 1.2 los V )- o Toxr's s 2 + V )+2 SV18 zo ~(8) + ] = - 100 hs V (S) +205 tlool loos W(S) = -200 -200 3320stloo (st102 take Inverse haplone VA) = – 2007 ēlotul

for 220 steady sterte Din(6-) W (o) (۱ in (0) = 6 = 2A But in 6) = ln (o)= licot) = 2A (0) = in 6)*2 u= 20 But co=Vco) = vc of) =2v for to s-domain circuit AELCOP) OTO 25 ves Mo ^ 6 ( vs)-vclo SO Kch at x Node. (8) - 6 - 2 LLCOP) 2+28 put all valuer- (8) - 2 – 242 2+28 SV(S) - 6-43 2811787 + 10)-2 V )-2 =0

„ 8) ts = 2 + vos 201787 +87= 2 + stats 2[1487 6+45 28[145] r(s) [23² + 25 +1] = 4s + 452+6+45 W(S) = 2 82+2 5+1 1.482 +os+ 6 2 83 45+3 (5+1) + - - - 2 + 2572 = 2+2 [sth] (3+2) 2 V8 (sth) 2 + 2 (+) terke anvesse ha plane VA? = 284+kent Cos(o.54) teostsin (o.sty Juz? VG = 2 st+zent I los(o.5t)+7 -0.57p sin 6.5t 1492 wolt

Moto I-domain Circuit els) ²c Ž ăs c leclut) if wcp) = 0 =D tes Ve كلما BLS or encom zis can if incof) zo b us ③ R= Remain as it is.

A Note ASA) & ht: Aug & T. e Atua) 2 STA CORAZ) Uw This sin (A) ut <htig STAZ - ßt e cos (At) LA) 2 StB (STB)²+ A² e Bt vin (A+)44) Th hoto * A (S+B) + A² if XC4) to X(s) esto x G-to) 2 htiy x(3). X (At) { bata in X (74) At xA) a Ty X (s+A)