# Why does the effective reluctance between two windings change?

The effective reluctance between the two windings should remain same, no matter on which arms they are placed. The pair of arms with less cross sectional area will offer more reluctance as compared to the other pair. Since in both cases, flux passes through both pair of arms so effective reluctance should remain same in both cases and hence the mutual Inductance. Whats wrong with this explanation?

• I think that the "official" answer is incorrect. The mutual inductance remains the same. – Roger C. Oct 30 '15 at 19:12
• Does it say, elsewhere, that the core is operating in saturation? – Brian Drummond Oct 30 '15 at 23:56
• all the information needed is given, core is assumed not to be in saturation – Kush Kulshrestha Oct 31 '15 at 12:10

The mutual inductance can be found as $$L=\frac { N_1 N_2 } \Re$$ where $N_1$ and $N_2$ is the number of turns of each winding and $\Re$ is the reluctance of the magnetic closed circuit.
$\dfrac{\text{effective length of core}}{\mu\times \text{effective area of core}}$