Electrical Engineering ⇒ Topic : Reluctance (S)

Reluctance (S). Reluctance is a measure of opposition offered by a magnetic circuit to the setting up of flux.

The reluctance (S) of a magnetic circuit is given by

                                                                        ...........  (1)

where l = length of the magnetic circuit,

          A = toss-sectional area of the magnetic circuit,

          μ₀= absolute permeability, and

          μ_r= relative permeability.

Reluctance of a magnetic circuit is the ratio of rn.rn.f. and flux

                                                                    ...........  (2)

The unit of reluctance is AT/Wb. Since 1 AT/Wb = 1/henry, the unit of reluctance is "reciprocal henry"

RELUCTANCE OF A MAGNETIC CIRCUIT

In the previous section, it has been shown that the magnetic field intensity in the ring specimen = I N/l. Let (to be the magnetic flux in the ring specimen.and let A be the cross-sectional area of the specimen. If B is the magnetic flux density in the specimen, then

and let A be the cross-sectional area of the specimen. If B is the magnetic flux density in the specimen, then

                                       H = I N I L                                ............... (1)                   

                                       Φ =B x A                                  ............... (2)

But we also know that

                                     B = μH                                      ................ (3)

where, μ is the permeability of the material of the specimen.

From Eqs (1) and (2), we get

                                   Φ = μ  H A                                    .............(4)

We know that for an electric circuit, current = emf resistance.

In a similar manner, in a magnetic circuit, the magnetic flux can be defined as magnetic flux = mmf/reluctance

Therefore, reluctance of a magnetic circuit

                           (S) = mmf / flux

                        i.e. S = H  .l/ μHA [from Eqs (1) and (2)]

                         i.e. S = l /μ                                              .............. (5)

Reluctance has the units of l l henry, as seen from Eq. (5) and has the same dimensions as ampere/weber. The reluctance is expressed in units of ampere/weber and it is directly proportional to the length of the magnetic path and is inversely proportional to the cross-sectional area of the specimen. From the above expression, it can be seen that for a given set of dimensions,the reluctance of the air path is many times more than the reluctance of a magnetic material. The following table gives a comparison between resistance and reluctance.