1) Assume you have solved as circuit using the mesh current technique and found
ID: 1797433 • Letter: 1
Question
1) Assume you have solved as circuit using the mesh current technique and found the following equations:-25 + 6(ia - ib) + 8(ia - ic) = 0
2ib + 8(ib - ic) + 6(ib - ia) = 0
5i?+ 8(ic - ia) + 8(ic - ib) = 0
And i?= ia
Show your work! (you can check yourself with a calculators, but evaluate each determinant by hand)
a) Write these equations in square format
b) Show the resulting square matrix of the coefficients
c) Write the square format equations in the matrix form AB=C where A is the square matrix, B is the column matrix of unknown variables, and C is the column matrix of the right hand side of each equation.
d) Find the determinant of the square matrix A
e) Use Cramer’s method (with the answer to part d above being equal to ?) to find each of the unknown currents.
Explanation / Answer
-25 + 6(ia - ib) + 8(ia - ic) = 0
=>14ia-6ib-8ic=25
2ib + 8(ib - ic) + 6(ib - ia) = 0
=>-6ia+16ib-8ic=0
5ia+ 8(ic - ia) + 8(ic - ib) = 0
=>-3ia-8ib+16ic=0
writing this in matrix form is AB=C
[14 -6 -8] [ia] [25]
[-6 16 -8] [ib] = [0]
[-3 -8 16] [ic] [0]
determinent |A|=14(16x16 - (-8)x(-8)) - (-6)((-6)x16 - (-8)x(-3)) + (-8)((-6)x(-8) - 16x(-3)) = 1200
according to cramer's rule
ia=
{ |25 -6 -8|
|0 16 -8|
|0 -8 16| } / 1200 = 4A
ib=
{ |14 25 -8|
|-6 0 -8|
|-3 0 16| } / 1200 = 2.5A
ic=
{ |14 -6 25|
|-6 16 0|
|-3 -8 0| } / 1200 = 2A
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