Comparison of the Magnetic Circuit with the Electric Circuit

The steady electric current in a simple electric circuit comprised of a conductor of length l and uniform cross-sectional area A is expressed by

[3-44]

where V = the voltage drop over the length l and ρ = the resistivity of the conductor.

Equation 3-44 can be expressed in accordance with Ohm's law as

[3-45]

where R = ρl/A, the electrical resistance expressed in ohms. Similarly Eq. 3-43 can be reduced to

[3-46]

where F = mmf in ampere turns NI and R = l/μA, the magnetic reluctance.

A comparison of Eq. 3-45 with Eq. 3-46 shows that the flux φ in the magnetic circuit corresponds to the current I in the electric circuit and that the mmf F or NI the magnetic circuit corresponds to the emf V in the electric circuit. A similar comparison holds for the magnetic reluctance and the electrical resistance R.

There is a marked difference between the magnetic circuit and the electric circuit in an important respect. The current in an electric circuit can be confined very effectively to the desired path by insulating the conducting parts from each other. The conductivity of a good insulating material is of the order of 10^-20, that of a good electrical conducting material. This means that an electric current can be confined to the desired path with very little leakage. The magnetic circuit cannot be isolated nearly as effectively because the most practical magnetic insulator is air. There are no materials that have a substantially greater reluctivity than air. The permeability of air is generally greater than 10^-4 and frequently only about 10^-2 times that of the ferromagnetic material to which the flux is to be confined. Magnetic circuits generally have appreciable leakage that may become very pronounced if the magnetic material is interrupted by an air gap such that the major component of the flux crosses the gap. An air gap has relatively high reluctance and may have several times the reluctance of the remainder of the magnetic circuit although the length of the air gap may be quite short compared with the total circuit. An air gap is usually paralleled by surrounding air spaces. The flux divides between the air gap and the parallel air spaces, giving rise to relative high leakage, depending upon the length of the air gap.