When inductors are well shielded or are located far enough apart from one another, the effect of mutual inductance is negligible. If there is no mutual inductance (magnetic coupling) and the inductors are connected in series, the total inductance is equal to the sum of the individual inductances. As a formula:

where L_T is the total inductance; L ₁, L₂, L₃ are the inductances of L₁, L₂, L₃; and L_n means that any number (n) of inductors may be used. The inductances of inductors in series are added together like the resistances of resistors in series.

SERIES INDUCTORS WITH MAGNETIC COUPLING

When two inductors in series are so arranged that the field of one links the other, the combined inductance is determined as follows:

The plus sign is used with M when the magnetic fields of the two inductors are aiding each other, as shown in figure 2-14.The minus sign is used with M when the magnetic field of the two inductors oppose each other, as shown in figure 2-15. The factor 2M accounts for the influence of L₁ on L₂ and L₂ on L₁.

Figure 2-14. - Series inductors with aiding fields.

Figure 2-15. - Series inductors with opposing fields.

Example problem:

A 10-H coil is connected in series with a 5-H coil so the fields aid each other. Their mutual inductance is 7 H. What is the combined inductance of the coils?

Q.15 Two series-connected 7-H inductors are adjacent to each other; their coefficient of coupling is 0.64. What is the value of M?
Q.16 A circuit contains two series inductors aligned in such a way that their magnetic fields oppose each other. What formula should you use to compute total inductance in this circuit?
Q.17 The magnetic fields of two coils are aiding each other. The inductance of the coils are 3 H and 5 H, respectively. The coils' mutual inductance is 5 H. What is their combined inductance?

PARALLEL INDUCTORS WITHOUT COUPLING

The total inductance (L_T) of inductors in parallel is calculated in the same manner that the total resistance of resistors in parallel is calculated, provided the coefficient of coupling between the coils is zero. Expressed mathematically: