Concept explainers
Find current ix in the ideal transformer circuit shown in Fig. 13.114.
Calculate the current
Answer to Problem 49P
The value of current
Explanation of Solution
Given data:
Refer to Figure 13.114 in the textbook for the ideal transformer circuit.
From Figure 13.114, the value of
Calculation:
Consider the expression for the capacitive reactance.
Substitute
Modify the Figure 13.114 by transforming the time-domain circuit with coupled-coils to frequency domain of the circuit with coupled-coil. The frequency domain equivalent circuit is shown in Figure 1.
Apply Kirchhoff's current law at node 1 in Figure 1.
Multiply by 2 on both sides of the Equation.
Apply Kirchhoff's current law at node 2 in Figure 1.
Multiply by 6 on both sides of the Equation.
Consider the expression for the turns ratio or transformation ratio.
Substitute
Consider the expression for the turns ratio or transformation ratio.
Substitute
Write equations (1), (2), (3), and (4) in matrix form as follows.
Write the MATLAB code to solve the equation (5).
A = [2 0 (1+j*0.2) (j*(-0.2)); 0 6 (j*0.6) (-1-j*0.6); 0 0 3 1; 1 3 0 0];
B = [12;0;0;0];
C = inv(A)*B
The output in command window:
C =
4.5000 + 0.0000i
-1.5000 + 0.0000i
1.8293 - 1.4634i
-5.4878 + 4.3902i
From the MATLAB output, the values of
Write the expression for the current
Substitute
Substitute
Convert the polar form to time-domain form.
Conclusion:
Thus, the value of current
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