Concept explainers
Write a set of mesh equations for the circuit in Fig. 3.110. Use MATLAB to determine the mesh currents.
Figure 3.110
For Prob. 3.66.
Write the mesh current equations, and find the mesh currents in the circuit of Figure 3.110 using mesh analysis and MATLAB.
Answer to Problem 66P
The matrix form of mesh current equations is
Explanation of Solution
Given data:
Refer Figure 3.110 in the textbook for mesh analysis.
Calculation:
Apply Kirchhoff’s voltage law to loop 1 with current
Apply Kirchhoff’s voltage law to loop 2 with current
Apply Kirchhoff’s voltage law to loop 3 with current
Apply Kirchhoff’s voltage law to loop 4 with current
Apply Kirchhoff’s voltage law to loop 5 with current
Represent the equations (1), (2), (3), (4), and (5) in matrix form.
MATLAB code:
Write the MATLAB code to solve the equations (1), (2), (3), (4), and (5) as follows in MATLAB code editor, and save it as “node366”, and then run the code. The result will shows in main command window.
syms i1 i2 i3 i4 i5
eq1 = 30*i1 -4*i2 -6*i3 -2*i4 +0*i5 == -12;
eq2 = -4*i1 +30*i2 +0*i3 -2*i4 -6*i5 == -16;
eq3 = -6*i1 +0*i2 +18*i3 -4*i4 +0*i5 == 30;
eq4 = -2*i1 -2*i2 -4*i3 +12*i4 -4*i5 == 0;
eq5 = 0*i1 -6*i2 +0*i3 -4*i4 +18*i5 == -32;
sol = solve([eq1, eq2, eq3, eq4, eq5], [i1, i2, i3, i4, i5]);
val1 = sol.i1;
val2 = sol.i2;
val3 = sol.i3;
val4 = sol.i4;
val5 = sol.i5;
i1= sprintf('%.4f A',val1)
i2= sprintf('%.4f A',val2)
i3= sprintf('%.4f A',val3)
i4= sprintf('%.4f A',val4)
i5= sprintf('%.4f A',val5)
The output in command window:
i1 = '-0.2779 A'
i2 = '-1.0488 A'
i3 = '1.4682 A'
i4 = '-0.4761 A'
i5 = '-2.2332 A'
Conclusion:
Therefore, the matrix form of mesh current equations is,
And the value of currents
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