Question

10) For the network in Fig.: a. Find the total impedance ZT and the admittance YT. b. Find the currents I, 12, and 13. c. Verify Kirchhoff's current law by showing that Is-I+ 12+ 13. d. Find the power factor of the network, and indicate whether it is leading or lagging ZT 15Ω 13

Answer 1

C rightarrow 1/j w_c = k_c/j = -j x_c L rightarrow j w l = j x_L v = 60 v total Impedance (z_T) = (2 + j) Vertical-bar Vertical-bar (3) Vertical-bar Vertical-bar (16 + 8 j) = [(2 + j) 3/5 + 9] Vertical-bar Vertical-bar [16 + 8 j] = 1.1793 + 0.3387 j admittance M (t) = 1/Z_T = 1/1.1793 + 0.338 j = 47/60 - 9/40 j = 0.7833 - 0.225 j rightarrow I_1 = v/2 + j = 60/2 + j = 24 - 12 j I_2 = v/3 = 60/3 = 20 I_3 = v/16 + 8 j = 2 - 1.5 j I_s = v/z_T = 47 - 13.5 j rightarrow K c l apply at node A - I_s + I_1 + I_2 + I_3 = 0 rightarrow I_s = I_1 + I_2 I_3 = (24 + 12 j) + 20 + (3 - 1.5 j) = 47 - 12.5 j From (1) & (2) I_s = I_1 + I_2 + I_3 power factor cos phi = v_r/v I_s = 47 - 13.5 j v_R

Answer 2

which book does this problem belong to