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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; *L*_{1}, *L*_{2},
*L*_{3} are the inductances of *L*_{1}, *L*_{2}, *L*_{3};
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

*L*_{1}, *L*_{2} are the inductances of *L*_{1}, *L*_{2}

*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 figure above. The minus sign is used with *M* when the magnetic field of the two inductors oppose
each other, as shown in figure below. The factor 2*M* accounts for the influence of *L*_{1}
on *L*_{2} and *L*_{2} on *L*_{1}.

**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