Determine currents I1, I2, and I3 in the circuit of Fig. 13.89. Find the energy stored in the coupled coils at t = 2 ms. Take ω = 1,000 rad/s.
Calculate the currents
Answer to Problem 20P
The currents
Explanation of Solution
Given data:
Refer to Figure 13.89 in the textbook for the circuit with coupled coils.
The value of
Calculation:
Calculate the mutual inductance in frequency domain.
Modify the Figure 13.89 by transforming the current source
From Figure 1, consider that the loops 1 and 2 contain the currents
Apply Kirchhoff's voltage law to the loop 1 in Figure 1.
Apply Kirchhoff's voltage law to the loop 2 in Figure 1.
Write equations (1) and (2) in matrix form as follows.
Write the MATLAB code to solve the equation (3).
A = [(4+j*5) j*10;j*10 (8+j*5)];
B = [j*12; -20];
C = inv(A)*B
The output in command window:
C =
0.75354 + 2.34381i
-0.11429 - 0.87049i
From the MATLAB output, the currents
And
From Figure 1, consider the expression for the current
Substitute
Write the current
Substitute 2 ms for t in Equation (4).
Substitute 2 ms for t in Equation (5).
From Figure 13.81, find the inductor values.
Calculate the inductor
Substitute 1000 for
Calculate the inductor
Substitute 1000 for
And
Calculate the mutual inductance.
Substitute 0.01 H for
Write the expression for the total energy stored in the coupled coils.
Substitute 0.01 H for
Conclusion:
Thus, the currents
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Chapter 13 Solutions
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