Question

5.) In the series RLC circuit shown in Figure 2, switches S1 and 52 both open at ta 0. Solve the differential equation for loop current 1(t) when the resistor R has a value of 2 Ohms. Be sure to show all work and specify values for alpha, wo , W d, 51, 52, (0), V(o), etc. if they are required for the solution (e.g. s1 and s2 are only needed for an overdamped solution. (300 pts) a - Wo=- wo- Is the circuit overdamped, underdamped or critically damped ? {circle one} S 2 = 11(0+) = _ Vc(0+) = - dll (0+)/dt = dve (O+)/dt = Il(t) = Vo(t) =

Answer 1

For to o tom Vilco) ;((o)= 90 You en ru - 8+2+8+2 2(0)+4.5) V(o)= il(o) x Vecos = 1877 (2+2) =4.5x4 for too ; du 2+2 2x2 231 0.5 F + Wormee Marcos = 1 65W=> given system is cortically damped Response is ic t) - (A, + Azt)e-at i(t) = (A + Azt) et t-o => ilo) - A, a) [A, 24.5) No (t) = į Siltidt = hs 19.5+Azt) et dt Vect= 2[4.5tet - Azet ] Gil J VeLo) = 28o. Ae] =) -2A2=18

0 => if t) = (4.5+69+) et A de = (4.5-94) etc) + ét (-2) dillot) + = -45 - - -|3.5 Velt) = 26-4.5tet +9e-t] duc Cats La sté? 6) -4. 5e +90 dt dvc Lot) at =260-4.5-9] = -27 dv.com) -27 İLt) = (4.5-9+) et A No (t) = (-4.5++9)ré tv