Linear Algebra and the C Language/a04p

__NOTOC__ Analysis of an electrical circuit thumb| Studying the circuit in a clockwise direction, we can write: At node A: Input = Output I2 + I3 = I1 At node B : Input = Output I4 = I3 + I5 At node C : Input = Output I6 + I5 = I4 At node D : Input = Output I1 = I6 + I2 Then: a) -I1 +I2 +I3 = 0 -I3 +I4 -I5 = 0 -I4 +I5 +I6 = 0 +I1 -I2 -I6 = 0 Left part of the circuit: -90 +I1 R1 + I2 R2 = 0 b) +I1 R1 + I2 R2 = +90 Central part of the circuit: -I2 R2 + I3 R3 + I4 R4 + I6 R6 = 0 c) -I2 R2 + I3 R3 + I4 R4 + I6 R6 = 0 Right part of the circuit: 90 - I5 R5 - I4 R4 = 0 d) -I4 R4 -I5 R5 = -90 External part of the circuit: -90 + I1 R1 + I3 R3 + 90 - I5 R5 + I6 R6 = 0 e) +I1 R1 + I3 R3 - I5 R5 + I6 R6 = 0 Then: a) -I1 +I2 +I3 = +0 -I3 +I4 -I5 = +0 -I4 +I5 +I6 = +0 +I1 -I2 -I6 = +0 b) +I1 R1 +I2 R2 = +90 c) -I2 R2 +I3 R3 +I4 R4 +I6 R6 = +0 d) -I4 R4 -I5 R5 = -90 e) +I1 R1 +I3 R3 -I5 R5 +I6 R6 = +0 With R1 = 15, R2 = 60, R3 = 15, R4 = 15, R5 = 60, R6 = 15 a) -I1 +I2 +I3 = +0 -I3 +I4 -I5 = +0 -I4 +I5 +I6 = +0 +I1 -I2 -I6 = +0 b) +I1 15 +I2 60 = +90 c) -I2 60 +I3 15 +I4 15 +I6 15 = +0 d) -I4 15 -I5 60 = -90 e) +I1 15 +I3 15 -I5 60 +I6 15 = +0 Let's rectify the system: I1 I2 I3 I4 I5 I6 a) -1 +1 +1 +0 +0 +0 +0 +0 +0 -1 +1 -1 +0 +0 +0 +0 +0 -1 +1 +1 +0 +1 -1 +0 +0 +0 -1 +0 b) +15 +60 +0 +0 +0 +0 +90 c) +0 -60 +15 +15 +0 +15 +0 d) +0 +0 +0 -15 -60 +0 -90 e) +15 +0 +15 +0 -60 +15 +0 The code in C language: double ab[RA*(CA+Cb)]={ // I1 I2 I3 I4 I5 I6 -1, +1, +1, +0, +0, +0, +0, +0, +0, +0, +0, -1, +1, -1, +0, +0, +0, +0, +0, +0, +0, -1, +1, +1, +0, +0, +0, +1, -1, +0, +0, +0, -1, +0, +0, +0, +15, +60, +0, +0, +0, +0, +0, +0, +90, +0, -60, +15, +15, +0, +15, +0, +0, +0, +0, +0, +0, -15, -60, +0, +0, +0, -90, +15, +0, +15, +0, -60, +15, +0, +0, +0 }; thumb| The solution is given by solving the system: I1 I2 I3 I4 I5 I6 +1.00 -0.00 -0.00 +0.00 -0.00 +0.00 -0.00 -0.00 +2.00 +0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +2.00 +0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 +0.00 I1 = 2, I2 = 1, I3 = 1, I4 = 2, I5 = 1, I6 = 1,