MATLAB Question (Please provide code) where R = 1 ohm. Simplifying these equatio

Question

MATLAB Question (Please provide code)

where R = 1 ohm. Simplifying these equations yields the following system of equations: 11*i1 3*i2 = 30, 3*i1 + (R + 5)*i2 i3 = 5, i2 + 3*i3 = 25

Solving a Known Case Given the system of equations, we wish to know the values of all the currents when R is fixed. You may use any of the methods you have learned in previous labs for solving systems of equations. Find the values of I1, I2, and I3 when R = 1. Verification: R = 1 à I1 = 3.00, I2 = 1.00, I3 = -8.00

Part 2 – Variable Light Bulb Resistance You are given again the same system of equations, except the light bulb’s resistance value is specified by the range, 0 R 100 ohms. Find and save the values of I1, I2, and I3 in memory over the range of R specified. Then, plot the absolute values of the currents. Use small increments of R to get smooth lines (i.e. increments of 0.05 or 0.01). Label all axes, title your plot, and add an appropriate legend. Answer the following questions: 1. Explain what happens to the current I3 as R gets really big? What does this mean in terms of choosing a wire size for loop I3? HINT: Wire size is chosen based on the maximum current expected to go through it. 2. Why do we plot absolute values of the currents and not include the signs? HINT: Which resistor has more current going through it: one with 3 amps or -5 amps?

Part 3 — Maximum Power The power delivered to the bulb is RI2 where R is the resistance of the bulb and I is the current. Find the power to the bulb as a function or R and plot it. Determine the maximum power to the bulb and the value of R for which it occurs. MATLAB Linear Algebra Question

Explanation / Answer

Part-1

>> R=1;
>> a=[11 -3 0; -3 R+5 -1; 0 -1 3]

a =

    11    -3     0
    -3     6    -1
     0    -1     3

>> b=[30;5;-25]

b =

    30
     5
   -25

>> c=inv(a)*b

c =

    3.0000
    1.0000
   -8.0000

Part-2:

clear all
close all
clc
for R=0:0.05:100
     a=[11 -3 0; -3 R+5 -1; 0 -1 3];
     b=[30;5;-25];
     I = inv(a)*b;
     plot(R,I(1))
     hold on
     plot(R,I(2))
     hold on
     plot(R,I(3))
     title('plot for R Vs I')
     xlabel('R varies from 0 to 100 ohms')
     ylabel('Current (A)')
     legend('I1','I2','I3')
end

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