Concept explainers
Obtain the Thevenin equivalent circuit for the circuit in Fig. 13.83 at terminals a-b.
Calculate the Thevenin equivalent to the circuit at terminals a-b.
Answer to Problem 14P
TheThevenin equivalent circuit parameters are
Explanation of Solution
Given data:
Refer to Figure 13.83 in the textbook for the circuit with coupled coils.
Consider that the value of the source voltage.
Calculation:
Calculate the Thevenin voltage.
Modify the Figure 13.83 by converting the current source
Consider that the two coils are connected series aiding.
Substitute
Apply Kirchhoff's voltage law to the loop 1 contains current
Substitute
Re-arrange the equation.
From Figure 1, consider the following expression using Kirchhoff's voltage law.
Re-arrange the Equation.
Substitute Equation (1) in (2).
Simplify the equation as follows.
To obtain Thevenin impedance
In Figure 2, consider that the loops 1 and 2 contain the currents
Write the Kirchhoff's voltage law expression to Figure 2 using super mesh analysis.
From Figure 2, write the current expression.
Substitute
Apply Kirchhoff's voltage law to the loop 1 contains current
Re-arrange the equation.
Substitute Equation (4) in (5).
Write the expression for Thevenin’s equivalent impedance.
Substitute
Conclusion:
Thus, the Thevenin equivalent circuit parameters are
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