Question

tul 62 Me M Exercise 04 22 Determine the value of all loop currents. 103 loops) using the following arsov 3652 numenca metlieds: - Jacobi ise Gaussian Elimination - Gaus-Sadel

Answer 1

Applying kui in loop 1, 2 and 3 we get, After solution 62. = 40 - 45,- 312 = 20 L2= 9:18 A 61,- 201, +8550 = 35, -10f2+433=0 / 2= 5:57A 812 - 125,=-20 3 452-613=-20) 12 = 7:05 A Writing the above equations in matrix form Ax=b where A: 59-3 07 x= [1, 2, 1,] 18 4-6) 6 = [20 -20]" a) Jacobi Method: Suppose we ave a guess solution: Then the next improved solution for ith iteration will be x [ b; - 2;, x,(k) - air x,(k) - aia xk) 7° Orx(k), (W) r(k) where ! i = x; + for i=1,2,3 (x+1) ail (K) The iteration dii sequence terminates when I r(K)|| where e is very small, for its iterations, considering initial guers as SSS 11.11 3.5 4.78 Iteration 8.75 3:33 71625 31957 5.66 7.96 viss 5.97. 8.41 . 6.36 b) In this 8.585 5.07 6:52. method (Gauss. Seidal) x. (k+1) – Il bi- the next iteration is given as xi o Ganss- Elimination : I jR; - 9x;()] Ax=b is transformed such that solution is same. Ux-ß Atter transformation Uto his B 115, T2= - 4x9:04-15 = 5:57 Loa - 3.94 J 1, - 20+3* 5.57 9:18 A 4 + ) n 7:04 3 07. so, d=-2777 201 After transformation U