Question

o by completing For the circuit, determine Vx C+) for t the following steps. ictly & I ign a) Determine the initial values Velt=0') and inco) 4123ca 02 4+3u(+) ! Buco 6) Draw the s-domain equivalent circuit and then, determine Vacs) lo Determine the values vx ct=c+) and wx Ct = 0) by analyzing the circuit in the time domain. Use initial and final value theorems to verify both. vx Ct = 0+) and rx Ct = go) Laplace transform of Vx(s) to find d) Take the inverse Vx Ct) for +70,

Answer 1

06 T 1.25mA 4 +3u8 242 3UCH at tro, Capacitor Short circuit, inductor open circuit Veron) Voo) = 0 Volt (10-) = 4.1 Amp Enni 3) s-domain equivalent circuit E NX'S) {un 2011 $oo 23 x too 214800 16005 2s+8.00

212 V 16oos 25.to 342 Varos! par (443/s) 25² + 800) + V. Icoos 3 +800+ 4005 +4005 1600s gs? +65 + 3 200 + 24 16oos Va [ 28 + 8005 +800] = 88?+65 +, 4400 + 2400 Va = 85$+65?+ 44005 + Qu.. s(25?+80051800) Vy (3) - Va - 3/5 853+6524 4400S +2000 - 3(25's mostra s( 25+ 8005 +800) Nx (5) - 853 + 2000s. . 85 +2000 43²+1000 25?+80057800 S2Voost to S (25² +80051800 at t ot Chord 1077 capacitar o.c. inductor se Ncco-) Velo):0V Applying kul equation J. In a 1 Amp Eur 34 (1, -1) + 433 3: 213-41, : ol 1

Also, 7 = 4I3 За : а from ean 3-7x4-41, 41,- 49-3 - 4971992. J = 37 = 2.312 . Iz = Irl= 1.312 Xx Ct=ot) = 4 (J, ~23) = 4(2.312 - . 2.25 Volts 2 at t=% Cd.c, Lese Appte kurat terminal Ya Tv Her. Vx: 7-3 = 4Volts : Vxlt: w) = 4 Velts BV Nytt Vay+CYOV)] et Stead

d) Inwege laplace transform Nars) - us²+1000 s²yoostuoo s²+25oo stuoostuoo Vy(s) : 1 - (400s +150) S2+40ost 400 yoost 150 (s+20)² + 3605 initial value NxlS1 = us2+ lao S? + UOD SHUOO 45 2 1000 SL s4oos sto 52 initial vah final value = Sto 45²4 low - S'd yoo styoo .. I ovo UMS.. 2.