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clc
disp("Problem 4.4")
printf("\n")
//From figure 4.7
//Let us consider a tree with 5,6,7,8 as tree branches
//Correspondingly links be 1,2,3,4
//By adding links one after other Loops can be formed
//The fundamental loops are..
disp("L1={1,5,6} L2={2,5,6,7,8} L3={3,6,7,8} L4={4,6,7}")
disp("1 is written if the direction of flow is along the direction of loop")
disp("-1 is written if the direction of flow is opposite to the direction of loop")
disp("0 is written if the branch is not a part of loop")
disp("The loop incidence matrix is")
B=[1 0 0 0 -1 1 0 0
0 1 0 0 1 -1 1 1
0 0 1 0 0 -1 1 1
0 0 0 1 0 -1 1 0]
disp(B,"B=")
//The above matrix has branches as columns and the number of loops as rows
//As we need to find branch currents(8 in number)in terms of loop currents(4 in number)
//Let i=[ i1 also iL=[ iL1
// i2 iL2
// i3 iL3
// i4 iL4 ]
// i5
// i6
// i7
// i8]
//We know i=BT*iL
//i=[ i1 [1 0 0 0 iL=[ iL1
// i2 0 1 0 0 iL2
// i3 0 0 1 0 * iL3
// i4 = 0 0 0 1 iL4 ]
// i5 -1 1 0 0
// i6 -1 -1 -1 -1
// i7 0 1 1 1
// i8] 0 1 1 0 ]
disp("The branch currents are")
disp("i1=iL1")
disp("i2=iL2")
disp("i3=iL3")
disp("i4=iL4")
disp("i5=-iL1+iL2")
disp("i6=iL1-iL2-iL3-iL4")
disp("i7=iL2+iL3+iL4")
disp("i8=iL2+iL3")
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