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eeng:topics:kirchhoff_s_circuit_laws:start [2022/10/23 15:13] – [Table] rolfeeng:topics:kirchhoff_s_circuit_laws:start [2024/11/27 09:19] (current) – [WITH PROPER UNITS!] rolf
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 ====== Kirchhoff's Circuit Laws ====== ====== Kirchhoff's Circuit Laws ======
  
-2022-09-29, RB+2023-12-06, RB
  
 [[https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws|Wikipedia (en)]] [[https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws|Wikipedia (en)]]
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   - Junction Rule (Current)   - Junction Rule (Current)
   - Loop Rule (Voltage)   - 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]]**
  
  
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 $\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 $ $\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} $ $\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} $
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 # kirchhoff_exercise_01.m # kirchhoff_exercise_01.m
-# 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, 2015-04-12  # R. Becker, 2015-04-12 
  
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-===== Example 2: Wikipedia =====+==== Solution in Python ====
  
-  * [[https://en.wikipedia.org/w/index.php?title=Kirchhoff%27s_circuit_laws#Example|Kirchhoff's Circuit Laws - Example]]+This code block shows the solution of the LES in Python (numpy). Klick on the block title to download.
  
-===== Example 3: YouTube Channel Jesse Mason =====+<file python kirchhoff_exercise_01.py> 
 + 
 +# kirchhoff_exercise_01.py 
 +# This script solves a simple LES resulting from Kirchhoff's laws. 
 +# Example from NunezPhysics video tutorial: https://www.youtube.com/watch?v=zdE7xsbuNTg 
 +# R. Becker, 2021-10-23  
 + 
 +import numpy as np 
 + 
 +# 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] 
 +    ]) 
 + 
 +V = np.array([0.0, -24.0, -12.0]) 
 + 
 +# Inverse matrix 
 +Rinv = np.linalg.inv(R) 
 + 
 +# Matrix vector multiplication, aka dot product 
 +I = Rinv.dot(V) 
 + 
 +# Print currents 
 +print(I) 
 + 
 +</file> 
 + 
 + 
 +===== Example 2: YouTube Channel Jesse Mason ===== 
 + 
 +| {{youtube>SKdK_L4jbV0?400}} | 
 +| Excellent explanation of Kirchhoff's Laws by Jesse Mason. |
  
   * [[https://www.youtube.com/watch?v=Z2QDXjG2ynU|How to Solve a Kirchhoff's Rules Problem - Simple Example]], by 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]] | 
eeng/topics/kirchhoff_s_circuit_laws/start.1666538009.txt.gz · Last modified: 2022/10/23 15:13 by rolf