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.
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. µr 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
= NµoµrHA, B = µoµrH
= µoµr NHA/I = µoµrN. Ni/1 A/i
Let H = Ni/L
L = µoµr N2A/I