The GATE Grind

GATE 2025 IN – Question 24

Electrical Circuits and Machines · Transients and two-port networks · 1 mark · Multiple choice

Figure (a) is represented by the equivalent T-model in Figure (b). The inductances $L_1,L_2,L_3$ in the T-model are

Diagram for GATE 2025 IN question 24
  1. $L_1=7\ \mathrm H,\ L_2=6\ \mathrm H,\ L_3=-4\ \mathrm H$
  2. $L_1=-1\ \mathrm H,\ L_2=-2\ \mathrm H,\ L_3=4\ \mathrm H$
  3. $L_1=3\ \mathrm H,\ L_2=2\ \mathrm H,\ L_3=9\ \mathrm H$
  4. $L_1=1\ \mathrm H,\ L_2=-2\ \mathrm H,\ L_3=-4\ \mathrm H$

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Correct answer: (A) $L_1=7\ \mathrm H,\ L_2=6\ \mathrm H,\ L_3=-4\ \mathrm H$

Explanation

The opposite dot orientation gives mutual term $-sM$, so the T shunt inductance is $L_3=-M=-4$ H.

Match the self terms: $L_1+L_3=3$ H and $L_2+L_3=2$ H.

Thus $L_1=7$ H and $L_2=6$ H: **A**.

These are the formal equivalent-circuit values for the stated data.

The supplied $M=4$ H violates $M^2\le L_aL_b=6\ \mathrm{H^2}$ for ordinary passive coupled inductors.