Question

(a) In the circuit shown in Figure-6, the switch was on position-a for a long time. Q6: At t 0, the switch is moved to position-b. Calculate Vc(0*) and i(0). 4] b) Draw the Laplace Transformed circuit at t20. (c) Solve Vc(t) 1 5 Ohms 1E1 2 H E2 10V Vc 1/4 F Figure-6

Answer 1

For t < 0 switch is in position a for long time, i.e circuit is in steady state t rightarrow infinity, s rightarrow 0 capacitor = 1/sc = 0. Inductor = SL = s.c The new circuit is after shorting inductor and opening capacitor V_c(0^-) = V_c(0^+) = 20 V i(0^-) = i(0^+) = 0 Amp \r\n for t greaterthanorequalto 0 switch is moved to position b The equivalent circuit is t greaterthanorequalto 0 10 rightarrow 10 u(t) In Laplace transform L rightarrow SL = S middot 2 = 2S C rightarrow 1/SC = 1/S middot 1/4 = 4/5 V_c rightarrow V_c() 10 u(t) rightarrow 10/s i rightarrow i(s) Applying mesh analysis 10/s - 5 (i(s) - 2s(i(s)) - V_c(s) = 0 voltage across capacitor = V_c(s) = i(s)/sc = i(s) middot 4/s \r\n 10/s = i(s)(5 + 2s + 4/s) 10/s = i(s)(5s + 2s^2 + 4/s) i(s) = 10/2s^2 + 5s + 4 = 10/2(s^2 + 2.5 + 2) i(s)