GATE EE 2024 Set 1 — Question 49
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Electric Circuits → Network Elements & Sources → Mutual Inductance & Dot Convention
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Question
For the circuit shown in the figure, the source frequency is . The mutual inductance between the magnetically coupled inductors is with their self inductances being and . The Thevenin’s impedance, , between the terminals and in is _________ (rounded off to 2 decimal places).
Correct answer
5.32 to 5.34
Solution
Given:
To find looking into terminals and , we first find the input impedance of the coupled inductor network. The reflected impedance from the secondary to the primary is:
The total impedance of the primary side of the coupled inductor is:
Now, looking into from the left, the circuit consists of a resistor in series with the parallel combination of a resistor and the branch containing the resistor and the coupled inductor network:
Rounding to two decimal places, .
To find looking into terminals and , we first find the input impedance of the coupled inductor network. The reflected impedance from the secondary to the primary is:
The total impedance of the primary side of the coupled inductor is:
Now, looking into from the left, the circuit consists of a resistor in series with the parallel combination of a resistor and the branch containing the resistor and the coupled inductor network:
Rounding to two decimal places, .
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