Effects of mutual inductance:

Mutual inductance can operate to increase the inductance of a pair of series connected inductors, or to decrease it. This is because magnetic fields might reinforce each other, or they might react against each other.

When 2 inductors are connected in series, and there is reinforcing mutual inductance among them, the total inductance L can be given in formula:

L = L₁ + L₂ + 2M

here L₁ and L₂ are the values of individual inductors, and M is mutual inductance. All the inductances should be expressed in the same size units.

Problem:

Assume that two coils, having values of 30 µH and 50 µH, are connected in series such that their fields reinforce, as shown in the Figure given below, and that the coefficient of coupling is 0.5. What is total inductance of combination? 

First, calculate M from k. According to the formula for this, given above, M= 5(50 × 30)^1/ 2=19.4 µH. Then total inductance is equal to L= L₁ + L₂ =2M = 30 + 50 + 38.8 +118.8 µH, rounded to 120 µH as only 2 significant digits can be justified.

When the 2 inductors are connected in series and mutual inductance is in opposition, the total inductance L can be given by the formula

L = L₁ + L₂ - 2M

where, again, L₁ and L₂ are values of the individual inductors.

 
Figure--             Illustration for Problem