Question

Problem 3 The switch has been closed for al0. At t0, the switch is opened. Calculate the capacitor voltage v(t) for t > 0. 15Ω 6 2 12 Q t=0 24 V+ 25 Ω 3 H 60Ω 1/27 F Figure 3

Answer 1

Find v_c(t) = ? for t > 0 at t < 0 at t = 0^- inductor rightarrow short circuit capacitor rightarrow open circuit i_l(0^-) = 0 (open circuit) v_c(0^-) = volt apply kcl at node v_c - 24/12 + v_c/60 + v_c/40 v_c[1/12 + 1/60 + 1/40] = 2 v_c(1/8) = 2 v_c(6) = 16 volt \r\n at t = 0^+ in laplace domain 15 ohm and 25 ohm are in series equivalent is 40 ohm 40 ohm is in parallel with 60 ohm so r_eq = 60 times 40/60 + 40 = 24 ohm 24 ohm is in series with 6 ohm so r'_eq = 30 ohm simplified circuit kvl in loop i(s) = 16/s/30 + 3s + 27/s rightarrow 16/s times s/3s^2 + 30s + 27 i(s) = 16/3s^2