Question 6.9. Refer to Figure P6.9 and assume that G X = 1.1 X, = 0.7 X, = 1.0 r = 0.1 We are given Po2 = 1.0. Find 02, 212, 221, SGI, SG2, 161, 162, Eal, and Eaz. SGI 562 11/0 V = 0.9/02 24 - 10.4 Figure P6.9 Soi = 1/-30° Sp2 = 1/-30°

Sol:given values,calculations for \theta_{2}\begin{aligned}P & =\frac{v_{1} v_{2}}{x} \sin \theta_{2} \\0.133 & =\frac{(0.9)(1)}{0.4} \sin \theta_{2} \\\sin \theta_{2} & =\frac{0.0532}{0.9} \\\theta_{2} & =\sin ^{-1} 0.0591 \\\theta_{2} & =3.38^{\circ} \\& =\end{aligned}\begin{array}{l}\theta_{12}=\frac{v_{1}}{z_{2}}\left[v_{1}-0.9 \cos \theta_{2}\right] \\=\frac{1}{0.4}[1-0.9 \cos (3.38)] \\=2.5 \times 0.101 \\\theta_{12}=-0.252 \\\theta_{G_{12}}=-0.752 \\0.748 \\0.5 \\\end{array}(injecting)calculation for \theta_{21}\begin{aligned}\theta_{21} & =\frac{v_{2}}{z}\left[v_{2}-v_{1} \cos \theta_{2}\right] \\& =\frac{0.9}{0.4}\left[0.9-\cos \left(3.38^{\circ}\right)\right] \\\theta_{21} & =2.25 \times-0.0982 \\\theta_{21} & =-0.220 \\\theta_{42} & =-0.72 \quad 0.220 \quad 0.0 .72 \\& =\end{aligned}Calculations for S_{H_{1}} \therefore\begin{array}{l} S_{a_{1}}=P_{a_{1}}+j a_{a_{11}} \\S_{a_{1}}=0.733+j 0.752 \\S_{a_{1}}=1.05445 .73^{\circ} \\2\end{array}Calculations for \mathrm{SC}_{2}-\begin{array}{l}S_{G_{2}}=P_{C_{2}}-j Q_{G_{2}} \\S_{G_{2}}=1-j 0.72 \\s_{c_{2}}=1.23\left[-35.75^{\circ}\right. \\\end{array}calculations\begin{aligned}= & I_{a_{1}}- \\I_{a_{1}} & =\frac{S_{a_{1}}}{v_{1}} \\& =\frac{1.05445 .73^{\circ}}{140^{\circ}} \\I_{a_{1}} & =1.05445 .73^{\circ} \\& =\end{aligned}Calculations for I_{G_{2}}.\begin{aligned}I_{C_{2}} & =\frac{S_{G_{2}}}{V_{2}} \\& =\frac{1.23 L-35.75^{\circ}}{0.943 .38^{\circ}} \\I_{G_{2}} & =1.36 L^{-39.13^{\circ}} \\& =\end{aligned}Calculations for t_{a_{1}}:\begin{array}{c}\epsilon_{a_{1}}=v_{1} \mid \theta_{1}+I_{a_{1}}, \theta \times z \theta_{2} \\\left.\left.\epsilon_{a_{1}}=110^{\circ}+(1.05) 45.73^{\circ}\right) \times(0.4) 3.38^{\circ}\right) \\\epsilon_{a_{1}}=110^{\circ}+0.42\left(49.11^{\circ}\right. \\\epsilon_{a_{1}}=1.31413 .98^{\circ}\end{array}\begin{array}{l}\text { Calculations for } t_{a_{2}} \\ = \\ \epsilon_{a_{2}}=v_{2} \mathrm{LO}_{2}+I_{a_{2}} \mathrm{LO}_{2} \times z \mathrm{O}_{2} \\ \epsilon_{a_{2}}=0.9\left(3.38^{\circ}+\left(1.36+-39.13^{\circ}\right) \times(0.4) 3.38^{\circ}\right) \\ t_{a_{2}}=1.36 \quad-11.12^{\circ}\end{array}   Please give thumbs up ...