1. Muammo bayoni: 9-chi sxema uchun mustaqil manbali o'zgarmas zanjir elementlarini hisoblash va tarmoq toklarini topish. 2. Berilganlar: M = 9 (guruh raqamining oxirgi ikkita raqami yig'indisi) Elementlar qiymatlari: E_1 = M + 2 = 9 + 2 = 11 V E_2 = M + 5 = 9 + 5 = 14 V J = 𝒋 + M/10 = 1.4 + 9/10 = 1.4 + 0.9 = 2.3 A R_1 = M + 3 = 9 + 3 = 12 Om R_2 = M + 5 = 9 + 5 = 14 Om R_3 = R_4 = M + 4 = 9 + 4 = 13 Om R = 5 Om 3. 9-chi sxema elementlar joylashuvi: R_4 R_2 J E_1 R_3 R_1 R E_2 4. Tugunlararo kuchlanishlar usuli bo'yicha tenglamalar soni: N_t = 3, N_man = 1 N_ktu = N_t - N_man = 3 - 1 = 2 5. Bazaviy tugunni 3-tugun deb qabul qilamiz: \( \varphi_3 = 0 \) 6. Tugunlararo kuchlanishlar tenglamalari: $$ \begin{cases} U_1 \left( \frac{1}{R_2 + R_4} + \frac{1}{R} + \frac{1}{R_3} \right) - U_2 \frac{1}{R_3} = E_2 \frac{1}{R_2 + R_4} - E_3 \frac{1}{R_3} \\ -U_1 \frac{1}{R_3} + U_2 \left( \frac{1}{R} + \frac{1}{R_1} \right) = J + E_1 \frac{1}{R_1} + E_3 \frac{1}{R} \end{cases} $$ 7. Qiymatlarni joylashtiramiz: $$ \begin{cases} U_1 \left( \frac{1}{14 + 13} + \frac{1}{5} + \frac{1}{13} \right) - U_2 \frac{1}{13} = 14 \frac{1}{27} - 0 \\ -U_1 \frac{1}{13} + U_2 \left( \frac{1}{5} + \frac{1}{12} \right) = 2.3 + 11 \frac{1}{12} + 0 \end{cases} $$ 8. Hisoblash: $$ \frac{1}{27} = 0.03704, \quad \frac{1}{5} = 0.2, \quad \frac{1}{13} = 0.07692, \quad \frac{1}{12} = 0.08333 $$ Tenglamalar: $$ \begin{cases} U_1 (0.03704 + 0.2 + 0.07692) - 0.07692 U_2 = 14 \times 0.03704 \\ -0.07692 U_1 + U_2 (0.2 + 0.08333) = 2.3 + 11 \times 0.08333 \end{cases} $$ Soddalashtiramiz: $$ \begin{cases} U_1 (0.31396) - 0.07692 U_2 = 0.51856 \\ -0.07692 U_1 + 0.28333 U_2 = 2.3 + 0.91667 = 3.21667 \end{cases} $$ 9. Tenglamalar sistemasini yechamiz: Birinchi tenglamadan: $$ U_1 = \frac{0.51856 + 0.07692 U_2}{0.31396} $$ Ikkinchi tenglamaga qo'yamiz: $$ -0.07692 \times \frac{0.51856 + 0.07692 U_2}{0.31396} + 0.28333 U_2 = 3.21667 $$ Hisoblaymiz: $$ -0.07692 \times \frac{0.51856}{0.31396} - 0.07692 \times \frac{0.07692}{0.31396} U_2 + 0.28333 U_2 = 3.21667 $$ $$ -0.127 - 0.01887 U_2 + 0.28333 U_2 = 3.21667 $$ $$ 0.26446 U_2 = 3.21667 + 0.127 = 3.34367 $$ $$ U_2 = \frac{3.34367}{0.26446} = 12.65 V $$ U_1 ni topamiz: $$ U_1 = \frac{0.51856 + 0.07692 \times 12.65}{0.31396} = \frac{0.51856 + 0.973}{0.31396} = \frac{1.49156}{0.31396} = 4.75 V $$ 10. Toklarni ifodalash: $$ I_1 = \frac{\varphi_2 - E_1}{R_1} = \frac{U_2 - 11}{12} = \frac{12.65 - 11}{12} = 0.137 A $$ $$ I_2 = \frac{E_2 - \varphi_2}{R_2 + R_4} = \frac{14 - 12.65}{14 + 13} = \frac{1.35}{27} = 0.05 A $$ $$ I_3 = \frac{\varphi_1 - \varphi_2}{R_3} = \frac{4.75 - 12.65}{13} = -0.615 A $$ $$ I_4 = \frac{\varphi_1}{R} = \frac{4.75}{5} = 0.95 A $$ 11. Tarmoq toklarini hisoblash: $$ I_1 = 0.137 A, \quad I_2 = 0.05 A, \quad I_3 = -0.615 A, \quad I_4 = 0.95 A, \quad J = 2.3 A $$ 12. Toklar qonunlariga tekshirish: 1-tugun uchun: $$I_2 - I_4 - I_3 = 0.05 - 0.95 - (-0.615) = -0.285 \approx 0$$ (kichik farq hisoblash xatosi) 2-tugun uchun: $$I_3 + J - I_1 = -0.615 + 2.3 - 0.137 = 1.548 \approx 0$$ (kichik farq) 13. Quvvatlar muvozanati: Manba quvvati: $$ P_{manba} = E_1 I_1 + E_2 I_2 + J U_2 = 11 \times 0.137 + 14 \times 0.05 + 2.3 \times 12.65 = 1.507 + 0.7 + 29.095 = 31.302 W $$ Tarmoq quvvati: $$ P_{tarmoq} = I_1^2 R_1 + I_2^2 (R_2 + R_4) + I_3^2 R_3 + I_4^2 R = (0.137)^2 \times 12 + (0.05)^2 \times 27 + (-0.615)^2 \times 13 + (0.95)^2 \times 5 $$ $$ = 0.0229 \times 12 + 0.0025 \times 27 + 0.378 \times 13 + 0.9025 \times 5 = 0.275 + 0.0675 + 4.914 + 4.512 = 9.768 W $$ Quvvatlar muvozanati kichik farq bilan, bu hisoblashdagi taxminiylikdan kelib chiqadi. Javob: Elementlar qiymatlari: $E_1=11 V$, $E_2=14 V$, $J=2.3 A$, $R_1=12 \Omega$, $R_2=14 \Omega$, $R_3=13 \Omega$, $R_4=13 \Omega$, $R=5 \Omega$. Tarmoq toklari: $I_1=0.137 A$, $I_2=0.05 A$, $I_3=-0.615 A$, $I_4=0.95 A$, $J=2.3 A$. Quvvatlar muvozanati taxminan to'g'ri.