Q. Give the expression for inductance of a ?N?   turn coil wound on a core having length I cross - sectional area A and magnetic permeability µ. Explain the significance of different terms involved.

Ans. 

Let an inductor L with turns N is wound over a core. In an ideal inductor, as we all know, no power loss take place therefore, we must use a very good magnetic material having B-H loop areas, also the operating point lies in the liner zone of B-H character, in order to get a constant value of inductance i.e. µ_r may be constant.

                        Let the lamination thickness is extremely small & core material has a very high resistivity ρ.

                       Let φ be the flux when current I flows through the coil

                       Then  total flux linkage = Nφ

                       Inductance               L = Nφ/i

                                                          = NBA/I, φ = B × A

                                                          = Nµ_oµ_rHA, B = µ_oµ_rH

                                                          =  µ_oµ_r NHA/I = µ_oµ_rN. Ni/1 A/i

                           Let                  H = N_i/L

                                                  L = µ_oµ_r N²A/I