Suppose that the phasor voltage across Z_B, with polarity as indicated in Fig. 9-13, is sought. Choosing meshes as in Fig. 9-12 would entail solving for both I₁ and I₂, then obtaining the voltage as V_B = (I₂ − I₁)Z_B. In Fig. 9-13 three loops (two of which are meshes) are chosen so as to make I₁ the only current in Z_B. Furthermore, the direction of I₁ is chosen such that V_B = I₁Z_B . The matrix equation is set up:

Transcribed Image Text:

Z₁ + ZB -ZA 0 -ZA Z₁ + Zc+ZD A ZD 0 ZD ZD +Z₁ E 1₁₂ 1₂ 2 1₂ 3 a V₁₂ a V₁ b