BASIC PRINCIPLES OF MAGNETIC CIRCUITS:

The path of the magnetic flux is called magnetic circuit. Notations used are,φ=flux in Wb;
A=area of magnetic path in m2;l=length of magnetic path in m;H=magnetic field intensity in AT/m;
AT=mmf in ampere turn;μ=μoμr;μ=absolute permeability of magnetic material inH/m;μo=permeability of free space=4πx10-7H/m;μr=relative permeability=1 for air;S=reluctance in Amp/Wb;Δ=permeance.Wb/A.
In Electric circuit,Ohms law gives relation between current,emf and resistance,while in magnetic circuit, a similar relation exists relating flux,mmf and reluctance.This is known as Ohms law of Magnetic circuit and is expressed as
Flux(φ)=mmf(AT)/Reluctance(S).---(1).Also,Reluctance(S)=length/area x permeability →S=l/Axμ—(2)
From,(1),AT= φ x S=φx l/Axμ= φ/Ax l/μ=Bx l/μ;AT/l= B/μ;∴H= B/μ;→ B=μH---(3).,
For the core material of length’l’ and carrying uniform flux,the total mmf is,AT=H x l—(4).
In series magnetic circuit the total reluctance is the sum of reluctance of individual paths.
S=S1+S2+S3+-----+Sn.where,S=Total reluctance;S1,S2—reluctance of individual paths.The total mmf acting around a complete magnetic circuit is mmf=φ x S=φx(S1+S2+S--)=AT1+ AT2+ AT3 – ATn=H1l1+ H2l2-(5).
In parallel magnetic Circuit, the same mmf is applied to each of the parallel paths and the total flux divides between the paths inversely proportional to the reluctance.
Ie φ= φ1+ φ2+ φ3;Dividing by AT, we get,φ/AT= φ1 /AT+ φ2 /AT+ φ3/AT→1/S=1/S1+1/S2→Δ=Δ1 +Δ2—(6).
Note:For Series magnetic circuit;S=S1+S2+S3 →mmf/Reluctance=l1/μoμrA1 + l2/μoμrA2 +---
For parallel magnetic circuit; 1/S=1/S1+1/S2→Δ=Δ1 +Δ2; S=Reluctance;Δ=Permeance(=1/S).