Inductors in dc circuits:

If it is required to increases the value of inductance in a circuit, then two or more inductors may be connected in series.  The total inductance then depends on the sum of individual inductances and the mutual coupling between them.

With no mutual coupling:

          L_T  =  L₁  +  L₂  etc

If the coils are positioned so that the mutual induced emf's in each coil aid the self induced emf's then the coils are said to be series aiding, and 

          L_T  =  L₁  +  L₂   +  2M

If the coils are positioned so that mutually induced emf's in each coil oppose the self induced emf's, the coils are said to be in series opposing, and

          L_T  =  L₁  +  L₂   -  2M

Thus if the position of L₂ reference to L₁ can be reversed, then the total inductance will vary between:

          L_T  =  L₁  +  L₂   +  2M

and   L_T  =  L₁  +  L₂    -  2M

giving a total variation of 4M.

A device which will achieve this is called variometer.  It consists of two coils located one inside the other.  The outer coil (stator) is stationary whilst the inner coil (rotor) is capable of rotation through 180 degrees.  The coils are mutually coupled and connected in series, in one position the rotor field aids the stator field, when the rotor is turned 180º the rotor field opposes the stator field.  Then the coils are at 90 degrees to each other, mutual coupling is negligible.