Consider a circular ring made from different materials of lengths l_1, l₂ and l₃  cross-sectional areas a_1, a₂ and a₃ and relative permeability μ_r1, μ_r2 and  μ_r3 with a cut of length  I_g known as air gap. The total is the arithmetic sum of individual reluctances as they are joined in series

Total reluctance,S

=  I₁       +  I₂      +   I₃      +   I_g
  μ_oμ_r1a₁  μ_oμ_r2a₂   μ_oμ_r3a₃   μ_oa_g

Total m.m.f. = θ x S

= θ [   I₁       +  I₂      +   I₃      +   I_g ]
    μ_oμ_r1a₁  μ_oμ_r2a₂   μ_oμ_r3a₃   μ_oa_g

or  Total ampere-turns required

=  H₁l₁ + H₂l₂ + H₃l₃  + H_gl_g

= Sum of ampere-turns required for individual parts of the magnetic circuit.

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