SOLUTION: The network of currents i₁, i₂, i₃ are related in the following equations: z₁i₁ + z₃i₃ = V z₂i₂ - z₃i₃ = 0 i₁ - i₂ - i₃= 0 Determine an expression

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Question 1202978: The network of currents i₁, i₂, i₃ are related in the following equations:
z₁i₁ + z₃i₃ = V
z₂i₂ - z₃i₃ = 0
i₁ - i₂ - i₃= 0
Determine an expression for i₁, i₂, i₃ in terms of z₁, z₂, z₃ and V using method of the Cramer's rule.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!


Line up the i's with like subscripts vertically:



Make the denominator determinant D, whose elements are all
the coefficients of the i's on the left of the equal signs:





Now we make the numerator determinants.
The numerator determinant for the 1st variable Di1 is formed by
replacing the 1st column of the denominator determinant D by the numbers on the
right of the equal signs:





The numerator determinant for the 2nd variable Di2 is formed by
replacing the 2nd column of the denominator determinant D by the numbers on the
right of the equal signs:





The numerator determinant for the 3rd variable Di3 is formed by
replacing the 3rdd column of the denominator determinant D by the numbers on the
right of the equal signs:





Finally, we put the numerators over the same denominator D:







Edwin
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