Question

Figure 1 shows a circuit after some switch-flipping and is now at time t = 0. It contains a capacitor that was charged to v.(0") = 75 V and an inductor that was charged to i (0°) = 3 A. 10) Is this circuit overdamped, underdamped, or critically damped [2 points A) Is this circuit displaying a natural or step response? (2 points) Solve for y(t) fort > 0 [8 points) +35w 13.230.išao Ous. "

Answer 1

254 HX 1.5A Joy = 1000 40x25u = 160000 @ Be - box BBM = 1000 c = ( Room )(254) $3+ + c =0 5 + 1000s +160000 =0 wn2 = 160000 [wn = 1160000 = 400 2$con - 1000 => { = 1000 = 1000 2 on { - 1.25 { > 1 They overdamped Circuit. ② Circuit iz step responce. © Apply Laplace To Ya! Va ve LICO) 75 Yeho o.15 f4om 15 2x400 Transform 0.75 250ms

Assume Node Ve. Apply Nodal Analasys Vx-73 Vet 0.75 + x = 1.5 40k (250m) to 15 S + - 40k - (250m)s 0.75 (250m)s GOK tu (250m)s (40k) (40) vel scamos no centro akcionala) - , was sco) a ves] - Clasram)s - 1.87 (Yook )s Va [los Floks +6M] - [ 750 S - 6ook] Va= 750s - book lost loks +1o6M 155-60k [5+ 1ks + 160000] Va = 755-60k (S+200)65+800) = + I (8) 3 250mg + 3 Vat 0.75 = x • 250ms 755-60k + 3 (250m)s(3+200) 68+800) S Iq(3) -

Ix(s) - 5 + 25 200) 4800)"} In(B) = x + 28+200) S780) Apply anverse laplace Transform -800 t txt) = § + Be se y I getto