Question

Part A Use the mesh-current method to find the power delivered by the dependent voltage source in the circuit seen in figure, if vg 726 V 5Ω 15Ω 10 Ω 25 Ω | 20 ie Tap image to zoom Express your answer with the appropriate units. pdel= 1 Value Units

Find Pdel

Answer 1

Let the loop currents be i_a, i_b & i_c as shown in circuit. From diagram, We can P_del = 726 times i_a Applying Mesh analysis, Write loop equations 1) 726 - 5 i_a - 15 (i_a - i_c) - 10 (i_a - i_b) = 0 726 - 5 i_a - 15 i_a + 15 i_c - 10 i_a + 10 i_b = 0 30 i_a - 10 i_b - 15 i_c = 726 ---(i) 2) - 25 i_c - 50 (i_c - i_b) - 15 (i_c - i_a) = 0 - 25 i_c - 50 i_c + 50 i_b - 15 i_c + 15 i_a = 0 15 i_a + 50 i_b - 90 i_c = 0 ---(ii) 3) we can write from circuit using KCL, i_1 = i_b - i_c 20 i_1 - 10 (i_b - i_a) - 50 (i_b - i_c) = 0 substitute i_1 = i_b - i_c in equation 20 i_b - 20 i_c - 10 i_b + 10 i_a - 50 i_b + 50 i_c = 0 10 i_a - 40 i_b + 30 i_c = 0 ---(iii) Solving Simultaneous equations (i), (ii) & (iii) i_a = 231/5 -= 46.2 A, i_b = 297/10 = 29.7 A & i_c = 121/5 = 24.2 A Hence P_del = 726