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

First, let’s assign currents for each loop as I_{1}, I_{2} and I_{3} and the power supplied by the source is 10*I_{1} 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 R_{B} 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