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Mesh Analysis using Matlab | Loop Analysis using Matlab

In this tutorial, we will find current which is flowing through resistor RB and the power supplied by the voltage source of 10V.

Mesh Analysis using Matlab

First, let’s assign currents for each loop as I1, I2 and I3 and the power supplied by the source is 10*I1 as we can see from the circuit.

Now, let’s write the loop equations for each loop:

Loop 1:

$\begin{align}  & 10({{I}_{1}}-{{I}_{2}})+30({{I}_{1}}-{{I}_{3}})-10=0 \\ & \begin{matrix}   40{{I}_{1}}-10{{I}_{2}}-30{{I}_{3}}=10 & \cdots  & (1)  \\\end{matrix} \\\end{align}$

Loop 2:

$\begin{align}  & 10({{I}_{2}}-{{I}_{1}})+15{{I}_{2}}+5({{I}_{2}}-{{I}_{3}})=0 \\ & \begin{matrix}   -10{{I}_{1}}+30{{I}_{2}}-5{{I}_{3}}=0 & \cdots  & (2)  \\\end{matrix} \\\end{align}$

Loop 3:

$\begin{align}  & 30({{I}_{3}}-{{I}_{1}})+5({{I}_{3}}-{{I}_{2}})+30{{I}_{3}}=0 \\ & \begin{matrix}   -30{{I}_{1}}-5{{I}_{2}}+65{{I}_{3}}=0 & \cdots  & (3)  \\\end{matrix} \\\end{align}$

Now, let’s write (1), (2), and (3) in matrix form as:

$\left[ \begin{matrix}   40 & -10 & -30  \\   -10 & 30 & -5  \\   -30 & -5 & 65  \\\end{matrix} \right]\left[ \begin{matrix}   {{I}_{1}}  \\   {{I}_{2}}  \\   {{I}_{3}}  \\\end{matrix} \right]=\left[ \begin{matrix}   10  \\   0  \\   0  \\\end{matrix} \right]$

Now, we will write a small piece of Matlab code to compute all loop currents, a current through RB and power supplied by the voltage source.

clear all;close all;clc
% Loop Analysis using Matlab
R_Mat = [40 -10 -30;
-10 30 -5; % Impedance (or Resistance) Matrix obtain from Loop equations
-30 -5 65];
V_vec = [10 0 0]'; % Voltage Vector (again from Loop equations)
%% % Loop Currents Calculations 
I_Loop = inv(R_Mat)*V_vec;
% Calculate current flowing through Resistor R_B
I_RB = I_Loop(3) - I_Loop(2); % (I=I3-I2)
fprintf('The current flowing through Resistor R_B is %8.3f A \n',I_RB)
% Calculate the total power supplied by 10V source
P_Source = I_Loop(1)*10; % (P=10*I_1)
fprintf('The power supplied by voltage source of 10V is %8.4f watts \n',P_Source)

Results:

The current flowing through Resistor R_B is    0.037 A

The power supplied by voltage source of 10V is   4.7531 watts

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.

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