Long Shot #2 - BLAP Examples

[Thomas Klemm]

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 ]