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Sahithyan's S2
Sahithyan's S2 — Theory of Electricity

Coupled Circuits

Self inductance

When the magnetic field produced by a coil causes an emf on itself.

Mutual coupling

Mutual coupling between coils exist when one (secondary coil) is in the magnetic field created by the other coil (primary coil).

When a time-varying current flows in the primary coil, a time-varying flux is produced, which produces a back emf .

Magnetic field

Magnetic field strength

Denoted by . Measured in ampere per meter ().

Magnetic permeability

Measure of magnetization on a material when a magnetic field is applied. Depends on the material. Denoted by . Meausred in or .

Magnetic flux density

Measure of strength and direction of the magnetic field. Denoted by . Measured in tesla () or or .

Laws

Faraday’s Law

The magnetic flux passing through a surface A is given by the surface integral:

Ampere’s Law

Line integral of magnetic field intensity around a closed path is equal to the sum of the currents owing through the surface bounded by the path.

When is constant (magnitude and direction) along the path, the above equation reduces to .

Definitions

Magnetomotive force

A force acted on a coil carrying current. Denoted by .

Here:

  • - number of turns
  • - current in the coil

Reluctance

Reluctance of a path for magnetic flux:

Here:

  • - Length of the path
  • - Permeability
  • - Cross-sectional area

Mutual Inductance

When 2 coils are coupled, part of the magnetic flux produced in the primary coil links with secondary coil.

Coefficient of coupling

Ratio between the produced magnetic flux and linked magnetic flux. Denoted by . Less than or equal to 1.

Induced emf

Since the produced flux is time-varying, an emf is induced in the second coil.

In the linear region of magnetization characteristic:

Here is the mutual inductance.

Practically, coupling between the primary and secondary coils is identical to the coupling between secondary and primary coils.

Energy stored

The last component is the effective energy stored in the mutual inductance. It is added to the energy when the produced fluxes on each coil aid each other; subtracted when they oppose each other.

Dot notation

One terminal of the coils is marked with a dot. If both currents enter or exit from the dotted terminals, the fields aid; mutual inductance is positive. Otherwise the fields oppose; mutual inductance is negative.