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Kirchoff 's Current Law with Matrices
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Solving a Simple KCL Equation
Using Matrix Methods solve for loop currents
in the network in thefigure. (Dr. M. Fogiel, Director, Staff of Research
and Education Association, *The Electric Circuits Problem Solver*,
Problem 3.23).
(Figure drawn using Quickroute 4.0)
Since there are four loops in the network, we can write four loop equations.
Starting from the left side and going counterclockwise, the equations are
as shown below.
In[1]:= l1={1.5==5.11i_{1}
- 0.71i_{2} - 3.25i_{4}}
Out[1]= {1.5==-0.71i_{2
}- 3.25i_{4 }+ 5.11i_{1}}
In[2]:=l2 = {-1.3 == -0.71i_{1} + 1.86i_{2} - 0.92i_{3} - 0.23i_{4}} Out[2]={-1.3 == 1.86i_{2} - 0.92i_{3 }- 0.23i_{4 }- 0.71i_{1} }
To write the above notations in matrix form, you can either enter them
as lists of lists or use the *Mathematica* Basic Input palettes. For
arbitrary size matrix you can use the Input pull-down menu.
In[3]:=
The above output gives the result of the matrix as a lists of lists.
In solving for these matrices, the elimination needed to reduce the matrix
can be done automatically.
In[4]:=Solve[eqnL, {i1,
i2, i3, i4}]
Out[4]= {{i1->-2.04437,
i2->-4.25588, i3->-4.92696, i4->-2.74617
Solving for this type of matrix would be very tedious to do by hand
and might lead to a lot of errors. But as shown, the result was obtained
very simply using the *Mathematica* function **Solve**
in one single line of code, plus results are given to a specified number
of significant figures. This was another simple example that
undergraduates may encounter in an introductory course in circuit analysis.
It teaches the students the basic concepts in analyzing circuits.
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