GATE EE 2025 Set 1 — Question 52
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+2 / -0HardMutual Inductance & Dot ConventionNetwork Elements & SourcesElectric CircuitsCoupled CoilsMagnetic Circuits & InductanceElectromagnetic Fields
Electric Circuits → Magnetic Circuits & Inductance → Coupled Coils
Last updated
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 stored magnetic energy in a coupled circuit is given by . For minimum energy, the mutual term must be subtractive: .
Let . Then .
To find the minimum, differentiate with respect to : .
If we consider the relative signs of currents, the ratio is for subtractive polarity.
Given unity coupling coefficient, .
Thus, and .
Therefore, . Both options (A) and (D) represent the same value.
Let . Then .
To find the minimum, differentiate with respect to : .
If we consider the relative signs of currents, the ratio is for subtractive polarity.
Given unity coupling coefficient, .
Thus, and .
Therefore, . Both options (A) and (D) represent the same value.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Magnetic Circuits & Inductance
2026 Set 1 Q15A uniform ring charge of radius carries a total charge . Which one of the following options…2026 Set 1 Q16A positive point charge with velocity enters a region having electric field…2026 Set 1 Q23A circuit with ideal elements is shown. [figure] Which one of the following options correctly…2026 Set 1 Q24For the circuit shown, which one of the following options correctly identifies the Thevenin’s…2026 Set 1 Q25Refer to the four circuits shown. Which one of the following options for and …