There are two solenoid of same length and inductance L but their diameters differ to the extent that one can just fit into the other. They are connected in three different ways in series.
(1) They are connected in series but separated by large distance.
(2) They are connected in series with one inside the other and senses of the turns coinciding.
(3) Both are connected in series with one inside the other with senses of the turns opposites,
as depicted in figures 1, 2 and 3 respectively. The total inductance of the solenoids in each of the case 1, 2 and 3 are respectively.