Question

29 Find the Thévenin equivalent network for each circuit shown in Fig. 3-70. o a 5їх 12 A ( 10 ЗА ( o a o b 12 32 3iy 4 S2 o b Fig. 3-70 See Prob. 29

Answer 1

KCL at A Rightarrow 12 + 3 = i_x Rightarrow i_x = 15 A KVL in XAYZ path Rightarrow -V_Th + 5 i_x + 10 i_x = 0 Rightarrow V_Th = 15 i_x = 15 (15) Rightarrow V_th = 225 V To find R_th, apply 1A source between aa' and kill all other independent sources. KVL Rightarrow -v_p + 5 i_x + 10 i_x = 0 Rightarrow v_p = 15 i_x = 15 (1) = 15 V therefore R_th = v_p/1 = 15/1 = 15 Ohm b) As there is no independent source in this circuit, we can conclude that V_th = 0 (It is a passive network) To find R_th, apply 1A source between bb' KCL at B Rightarrow i_M = 1 - i_y KCL at A Rightarrow i_N = i_M + 3 i_y = 1 - i_y + 3 i_y = 1 + 2 i_y