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Node Voltages Calculation in Resistive Circuit using Matlab

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Determine the voltage at each node of the circuit:

FROM ABOVE CIRCUIT, we can write the following set of equations:

$\begin{matrix}   \begin{align}  & {{I}_{{{R}_{4}}}}={{I}_{{{R}_{1}}}}+{{I}_{{{R}_{3}}}} \\ & {{I}_{{{R}_{2}}}}={{I}_{{{R}_{3}}}} \\ & {{V}_{1}}={{V}_{A}} \\\end{align} & \cdots  & (1)  \\\end{matrix}$

Or

\[\begin{matrix}   \begin{align}  & \frac{{{V}_{C}}}{{{R}_{4}}}=\frac{{{V}_{1}}-{{V}_{C}}}{{{R}_{1}}}+\frac{{{V}_{B}}-{{V}_{C}}}{{{R}_{3}}} \\ & \frac{{{V}_{1}}-{{V}_{B}}}{{{R}_{2}}}=\frac{{{V}_{B}}-{{V}_{C}}}{{{R}_{3}}} \\\end{align} & \cdots  & (2)  \\\end{matrix}\]

We can rewrite it as:

\[\begin{matrix}   \begin{align}  & \frac{{{V}_{1}}}{{{R}_{1}}}=\left( \frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{3}}}+\frac{1}{{{R}_{4}}} \right){{V}_{C}}-\frac{{{V}_{B}}}{{{R}_{3}}} \\ & \frac{{{V}_{1}}}{{{R}_{2}}}=-\frac{{{V}_{C}}}{{{R}_{3}}}+\left( \frac{1}{{{R}_{3}}}+\frac{1}{{{R}_{2}}} \right){{V}_{B}} \\\end{align} & \cdots  & (3)  \\\end{matrix}\]

The above equations can be written in terms of matrix:

$[A]=[B]*[C]$

Whereas:

$[A]=\left[ \begin{matrix}   \frac{{{V}_{1}}}{{{R}_{1}}}  \\   \frac{{{V}_{1}}}{{{R}_{2}}}  \\\end{matrix} \right]$

$[B]=\left[ \begin{matrix}   \frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{3}}}+\frac{1}{{{R}_{4}}} & -\frac{1}{{{R}_{3}}}  \\   -\frac{1}{{{R}_{3}}} & \frac{1}{{{R}_{3}}}+\frac{1}{{{R}_{2}}}  \\\end{matrix} \right]$

$[C]=\left[ \begin{matrix}   {{V}_{C}}  \\   {{V}_{B}}  \\\end{matrix} \right]$

By using following equation, we can obtain unknown variables:

$[C]={{[B]}^{-1}}[A]$

Let’s calculate unknown elements using Matlab:

Matlab Code for Node Voltages Calculation

%Simple Resistive Network
clear all;close all;clc
%%Circuit Elements 
V1= 2; % Source Voltage
R1= 330;
R2= 70; % Resistances in Ohm from Circuit 
R3= 160;
R4= 270;
B=[1/R1+1/R3+1/R4 -1/R3 ; ...
-1/R3 1/R3+1/R2]; % Elements of V1, VB, and VC in equation (3)
A=[V1/R1; V1/R2]; % Inputs Vector
C=inv(B)*A; % Output Matrix
% Node Voltages
V_C=C(1,1)
V_B=C(2,1)
%============================================================

Results:

V_C =

    1.3316

V_B =

    1.7966

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About Ahmad Faizan

Mr. Ahmed Faizan Sheikh, M.Sc. (USA), Research Fellow (USA), a member of IEEE & CIGRE, is a Fulbright Alumnus and earned his Master’s Degree in Electrical and Power Engineering from Kansas State University, USA.

2 comments

  1. I like this tutorial.So simple and inspiring!

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