GATE EE 2025 Set 1 — Question 52
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Electric Circuits → Magnetic Circuits & Inductance → Coupled Coils
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Question
Consider two coupled circuits, having self-inductances and , that carry non-zero currents and , respectively. The mutual inductance between the circuits is with unity coupling coefficient. The stored magnetic energy of the coupled circuits is minimum at which of the following value(s) of ?
Correct answer
(A) -(M)/(L₁); (D) -(L₂)/(M)
Solution
The energy stored in two magnetically coupled circuits isWrite and keep fixed:This is a parabola in opening upwards (), so the minimum is atThis is option (A).With unity coupling coefficient, , soThe two expressions are numerically identical, so option (D) describes the same minimising ratio and is equally correct. (At this ratio , consistent with unity coupling.)Options (B) and (C) both equal , which differs from unless , so they are rejected.Answer: (A) and (D)
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