Concept explainers
Calculate the impedance
Answer to Problem 25P
The impedance
Explanation of Solution
Given data:
Refer to Figure 13.94 in the textbook for the circuit with coupled coils.
The coupling co-efficient is 0.5.
Calculation:
Consider the expression for the mutual inductance.
Substitute 0.5 for k, 1 H for
From Figure 13.94, the value of
Consider the expression for the inductive reactance.
Substitute 1 H for L and
Substitute 2 H for L and
Consider the expression for the capacitive reactance.
Substitute 0.5 F for C and
Modify the Figure 13.94 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.
Write the expression for the impedance
Consider the expression for the reflected impedance
Substitute 2 for
Substitute
Simplify the Equation as follows.
Write the expression for the current
Substitute
The value of current
Convert the current from polar form to time domain form.
MATLAB code:
The MATLAB code using equations (3), (4) and (5) is,
M=0.5;
R2=3;
w=2;
L2=1;
ZL=4*j;
ZR=(w^2 * M^2)/(R2 + j*w*L2 + ZL);
Zab= (2-1*j)*(1+2*j+ZR)/(2-j+1+2*j+ZR)
Io=12/(Zab+4)
Then the MATLAB output is,
Zab = 1.4354 + 0.4639i
Io = 2.1918 - 0.1871i
Form the MATLAB output, impedance
Form the MATLAB output, current
The output is satisfied with analytical solution.
Conclusion:
Thus, the impedance
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Chapter 13 Solutions
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