Concept explainers
Find the expressions for voltages
Answer to Problem 63E
The expressions for nodal voltages
Explanation of Solution
Given data:
Formula used:
Consider the general expression for inductive impedance.
Here,
Consider the general expression for capacitive impedance.
Here,
Calculation:
Refer to Figure in the respective question.
From Figure , at
Substitute
Substitute
Case 1:
Consider
Substitute
Substitute
Redraw Figure, as shown in Figure 1.
Apply KCL at node
Simplify the equation as follows.
Apply KCL at node
Write the equations (1) and (2) in matrix form.
Write the Matlab code to solve equation (3)
A = [(i*3.1792) (-i*3.2); (-i*3.2) (0.5+i*3.2)];
B = [(0.004+i*0);(0)];
C = inv(A)*B
Matlab Output:
C =
0.0080908 - 0.0009194i
0.0080382 + 0.0003366i
Polar equations of node voltages are as follows.
Case 2:
Consider
Substitute
Substitute
Redraw Figure, as shown in Figure 2.
Apply KCL at node
Simplify the equation as follows.
Apply KCL at node
Write the equations (4) and (5) in matrix form.
Write the Matlab code to solve equation (3)
A = [(i*2.373) (-i*2.4); (0.5+i*2.4) (-i*2.4)];
B = [(i*0.004);(-i*0.004)];
C = inv(A)*B
Matlab Output:
C =
-0.000861 - 0.015953i
-0.002518 - 0.015774i
Polar equations of node voltages are as follows.
Find nodal voltage
Substitute
Convert
Find nodal voltage
Substitute
Conclusion:
Thus, the expressions for nodal voltages
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