When two coupled coils of equal self-inductance are connected

When two coupled coils of equal self-inductance are connected in series in one way the net inductance is 12 mH, and when they are connected in the other way, the net inductance is 4 mH. The maxiumum value of net inductance when they are connected in parallel in a suitable way is _________ mH

As, 2L + 2M = 12
2L – 2M = 4
Then, L = 4
⇒ M = 2
To get maximum value in parallel connection,

L_max =	(L + M)(L + M)	= 3 mH.
	2L + 2M