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--- eeng:topics:kirchhoff_s_circuit_laws:start [2022/10/23 15:17] – [Solution in Matlab / Octave] rolf
+++ eeng:topics:kirchhoff_s_circuit_laws:start [2024/11/27 09:19] (current) – [WITH PROPER UNITS!] rolf
@@ Line 2: / Line 2: @@
 ====== Kirchhoff's Circuit Laws ======
--09-29, RB
+-12-06, RB
 [[https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws|Wikipedia (en)]]
@@ Line 10: / Line 10: @@
   - Junction Rule (Current)
   - Loop Rule (Voltage)
+===== Literature =====
+  * **University Physics II - Thermodynamics Electricity and Magnetism (OpenStax) \\ [[https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/10%3A_Direct-Current_Circuits/10.04%3A_Kirchhoff's_Rules|10.04 Kirchhoff's Rules]]**
@@ Line 86: / Line 90: @@
 $\begin{pmatrix} -1 & -1 & 1 \\ -6 & 3 & 0 \\ 0 & -3& -6 \end{pmatrix}\Omega\begin{pmatrix} I_1 \\ I_2 \\ I_3 \end{pmatrix}A = \begin{pmatrix} 0 \\ -24 \\ -12 \end{pmatrix}V $
-Devide by $\Omega A$ (=$V$)$:
+Divide by $\Omega A$ (=$V$):
 $\begin{pmatrix} -1 & -1 & 1 \\ -6 & 3 & 0 \\ 0 & -3& -6 \end{pmatrix}\begin{pmatrix} I_1 \\ I_2 \\ I_3 \end{pmatrix} = \begin{pmatrix} 0 \\ -24 \\ -12 \end{pmatrix} $
@@ Line 107: / Line 111: @@
 # kirchhoff_exercise_01.m
-# This script solves a simple LES resulting from Kirchhoff's laws
+# This script solves a simple LES resulting from Kirchhoff's laws.
-# Example from NunezPhysics Video tutorial: https://www.youtube.com/watch?v=zdE7xsbuNTg
+# Example from NunezPhysics video tutorial: https://www.youtube.com/watch?v=zdE7xsbuNTg
 # R. Becker, 2015-04-12
@@ Line 135: / Line 139: @@
 # kirchhoff_exercise_01.py
-# This is a script solve a simple LES resulting Kirchhoff's laws
+# This script solves a simple LES resulting from Kirchhoff's laws.
-# Extended video tutorial: https://www.youtube.com/watch?v=zdE7xsbuNTg
+# Example from NunezPhysics video tutorial: https://www.youtube.com/watch?v=zdE7xsbuNTg
-# R. Becker, 2012-10-23
+# R. Becker, 2021-10-23
-# A*x = b <=> x = A^-1 * b (another notation x = A\b)
+import numpy as np
-A = [-1 -1 1 ; -6 3 0 ; 0 -3 -6]
+# A matrix is an array of rows, which are arrays. Thus a matrix is a two dimensional array.
+# The numpy.array() function is used to create 2D array (aka matrix) from a list of row lists.
+R = np.array(
+    [
+        [-1.0, -1.0,  1.0],
+        [-6.0,  3.0,  0.0],
+        [ 0.0, -3.0, -6.0]
+    ])
-b = [0 -24 -12]' # ' means "transpose". Here result is column vector
+V = np.array([0.0, -24.0, -12.0])
-x = A\b
+# Inverse matrix
+Rinv = np.linalg.inv(R)
-# alternative:
+# Matrix vector multiplication, aka dot product
-# x = A^-1 * b
+I = Rinv.dot(V)
-# or
-# x = inv(A) * b
+# Print currents
+print(I)
 </file>
-===== Example 2: Wikipedia =====
+===== Example 2: YouTube Channel Jesse Mason =====
-  * [[https://en.wikipedia.org/w/index.php?title=Kirchhoff%27s_circuit_laws#Example|Kirchhoff's Circuit Laws - Example]]
+| {{youtube>SKdK_L4jbV0?400}} |
+| Excellent explanation of Kirchhoff's Laws by Jesse Mason. |
-===== Example 3: YouTube Channel Jesse Mason =====
   * [[https://www.youtube.com/watch?v=Z2QDXjG2ynU|How to Solve a Kirchhoff's Rules Problem - Simple Example]], by Jesse Mason
+===== Example 3: Wikipedia =====
+/*
+  * [[https://en.wikipedia.org/w/index.php?title=Kirchhoff%27s_circuit_laws#Example|Kirchhoff's Circuit Laws - Example]]
+*/
+| {{https://upload.wikimedia.org/wikipedia/commons/thumb/7/77/Kirshhoff-example.svg/540px-Kirshhoff-example.svg.png?400&direct}} |
+| Source: [[https://en.wikipedia.org/w/index.php?title=Kirchhoff%27s_circuit_laws#Example|Wikipedia (en): Kirchhoff's Circuit Laws - Example]] |