Long Shot #2 - BLAP Examples

[jebem]

(08-14-2014 06:37 PM)Thomas Klemm Wrote:  We can introduce 5 currents \(I_1, ..., I_5\) in each of the "loops" of the ladder:


Using Kirchhoff's voltage law we can write 5 equations:
\[
\begin{align}
2I_1+5(I_1-I_2) &= 7\\
2I_2+4(I_2-I_3)+5(I_2-I_1) &= 0 \\
2I_3+7(I_3-I_4)+1I_3+4(I_3-I_2) &= 0\\
2I_4+3(I_4-I_5)+7(I_4-I_3) &= 0\\
2I_5+1I_5+3(I_5-I_4) &= 0
\end{align}
\]

This results in this system of linear equations:
\[
\begin{bmatrix}
7 & -5 & 0 & 0 & 0 \\
-5 & 11 & -4 & 0 & 0 \\
0 & -4 & 14 & -7 & 0 \\
0 & 0 & -7 & 12 & -3 \\
0 & 0 & 0 & -3 & 6
\end{bmatrix} \cdot \begin{bmatrix}
I_1\\
I_2\\
I_3\\
I_4\\
I_5
\end{bmatrix}=\begin{bmatrix}
7\\
0\\
0\\
0\\
0
\end{bmatrix}
\]

You could use the HP-48 to solve that:

[7 0 0 0 0]
ENTER
[[7 -5 0 0 0]
-5 11 -4 0 0
0 -4 14 -7 0
0 0 -7 12 -3
0 0 0 -3 6]
/

This will give you:

[ 1.625 .875 .375 .25 .125 ]

Thank You for sharing your knowledge, Thomas!
Excellent practical example of mathematics application in the field.

This exercise reminds me of one of my EE teachers from the 70's.
He tried hard to educate us on the Kirchhoff laws.
He used to smoke a pipe all the time, even during the class (!).
Those were the times when an educated adult was allowed to smoke everywhere and anytime.

I have added the current legend to the diagram: