Mutual inductance satisfies M = k√(L1L2), where 0 ≤ k ≤ 1. The maximum occurs at perfect coupling k = 1: Mmax = √(1×2) mH = √2 mH ≈ 1.414 mH.
Formula / Key Relation
M = k√(L₁L₂)
0 ≤ k ≤ 1
Mmax = √(1×2) mH
= 1.414 mH
Detailed Explanation
Concept & ReasoningThe coefficient of coupling k represents the fraction of flux from one coil linking the other. Physical passive coupling cannot exceed k = 1. Therefore the largest possible mutual inductance is the geometric mean of the two self-inductances. Substituting 1 mH and 2 mH gives 1.414 mH. A mutual inductance larger than that would imply k > 1 and is physically impossible.How to Solve It in the ExamMaximum mutual inductance = geometric mean of self-inductances.Important Exam PointCheck units before taking the square root; both inductances must be in the same unit.Related Revision PathThis question sits in the revision…
Concept & Reasoning
The coefficient of coupling k represents the fraction of flux from one coil linking the other. Physical passive coupling cannot exceed k = 1. Therefore the largest possible mutual inductance is the geometric mean of the two self-inductances. Substituting 1 mH and 2 mH gives 1.414 mH. A mutual inductance larger than that would imply k > 1 and is physically impossible.
How to Solve It in the Exam
Maximum mutual inductance = geometric mean of self-inductances.
Important Exam Point
Check units before taking the square root; both inductances must be in the same unit.
Related Revision Path
This question sits in the revision path Electrical Machines → Magnetic Coupling → Mutual Inductance .
Quick Trick
Maximum mutual inductance = geometric mean of self-inductances.
Common Mistake
Do not add L1 and L2; mutual inductance depends on their geometric mean and coupling coefficient.
Exam Tip
Check units before taking the square root; both inductances must be in the same unit.
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