Question

Problem 1. Determine vc(t) and iL(t) for the following circuit if is1 = 0.04 cos(1000t) and is2 = 0.02 cos(1000t − 90o )

Assessment Problem 1. Determine v.() and i.(t) for the following circuit if i 0.04 cos(10001) and i, -0.02 cos(1000t -909) 100mH 200Ω 2002 200Ω HI Assessment Problem 2. Determine the Thevenin equivalent cireuit for the tollowing as ming that w 100 rad/ec 4Ω 112. 10mE 20mH

Answer 1

Apply 1A test source for R_th = > R_th = V_2/1 Omega Apply kcl at node - (1) & (2) = > V_1/7 + V_1 - 2V_x/- j1 + V_1 - V_2/1 = 0 = > V_1/7 + V_1 - 2 (- 4 V_1/7)/-j1 + V_1 - V_2/1 Vertical-bar V_x = (V_1/7) (- 4) = -4v_1/7 = 0 = > V_1 [1/7 - 1/J + 8/- j7 + 1/1] - V_2/1 = 0 = > (1.142 + j2.142) V_1 - V_2 = 0 rightarrow (1) = > V_2 - V_1/1 + V_2/j_2 = 1 = > - V_1/1 + V_2 (1/1 + 1/j2) = 1 = > - V_1 + (1 - j 0.5) V_2 = 1 rightarrow (2) \r\n By solving equations (1) & (2) = > V_1 = (0.3079 - j 0.3987)V = > V_1 = V_2 = (1.2058 + j 0.2044)V = 1.222 angle 10 . 67 degree V Z_th = R_th = V_1/1 = (1.2058 + j 0.2041) Omega Thevenin's equivalent circuit \r\n i_5_1 = 0.04 cos (1000 t) A = 0.04 angle 0 degree A i_5_2 = 0.02 cos (1000 t - 90 degree) = 0.02 angle - 90 degree A w = 100 mH = > Z_L = jwL = j times 1000 times 100m fro c = 10 mu F = > Z_c = 1/jwc