Fundamental Electrical and Electronic Principles, Third Edition

Electromagnetism 1795.19 Factors Affecting InductanceConsider a coil of N turns wound on to a non-magnetic core, of2uniform csa A metre and mean length metre. The coil carries acurrent of I amp, which produces a flux of Φ weber. From equation(5.11), we know that the inductance will beNΦL henry, but Φ BA weberINBAtherefore, L henry……………[ 1]IAlso, magnetic field strength, HNI l; so IH lNand substituting this expression for I into equation [1]NBA BANL Hl/N Hl2……………[ 2]Now, equation [2] contains the term B H , which equals μ oμ r0 rN Atherefore, L μμ 2henryl(5.12)We also know thatlreluctanceμμ 0 r A , SNhence L 2 henry(5.13)SNotes:εεAN1 Equation (5.12) compares with C o r ( 1)farad for acapacitor.d2 If the number of turns is doubled, then the inductance isquadrupled, i.e. L N 2 .3 The terms A and in equation (5.12) refer to the dimensions ofthe core, and NOT the coil.Worked Example 5.232Q A 600 turn coil is wound on to a non-magnetic core of effective length 45 mm and csa 4 cm .(a) Calculate the inductance, (b) The number of turns is increased to 900. Calculate the inductancevalue now produced. (c) The core of the 900 turn coil is now replaced by an iron core having a relativepermeability of 75, and of the same dimensions as the original. Calculate the inductancein this case.