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Create a Matrix From Linear Equations and Determine Current Using MATLAB

Question

a) An analysis of an electrical resistor circuit with two dc voltage sources E1 and E2 produces following equations from which the loop currents i1,i2 and i3 are determined:

(R1 + R2 + R3)i1 - R2i2 - R3i3 = -E1

-R2i1 + (R2 + R4 + R5)i2 - R5i3 = 0

-R3i1 - R5i2 + (R3 + R5 + R6)i3 = E2

Let R1 = R3 = R5 = 1 ohm, R2 = R4 = R6 = 2 ohm, E1= 2V and E2=3V, Display the matrices formed using the above equations and determine the loop currents i1,i2 and i3

b) For each of the following set of linear equations, find x and y. Also comment on the existence and uniqueness of the solution (i.e no / unique / infinite solutions) by finding out required ranks and comparing it with number of unknowns. If it has a unique solution, find the determinant and inverse of A.

(A is the coefficient matrix in AX=B).

i) x + y = 6 ; −3x + y = 2

ii) -6x + 2y = 2 ; −3x + y = 2

c) Rewrite the equations given in (b) as equations of straight lines. Find the point of intersection (x and y co-ordinates of the point where the lines intersect) and plot the lines. Compare your findings from (c) with your results from (b) with respect to existence and uniqueness.

Summary

This question belongs to MATLAB software and discusses about application of MATLAB in physics to solve linear equations and to determine current and voltage in a given circuit.  

Answer is in MATLAB format

 

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