Inductors

Inductors in Series and Parallel

Series Inductors Without Magnetic Coupling

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; L₁, 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

where
L_t is the total inductance
L₁, L₂ are the inductances of L₁, L₂
M is the mutual inductance between the two inductors

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

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?

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