Determine Total magnetic flux:
A ring is composed of three sections. The cross-sectional area is 0.001 m2 for each section. The mean lengths of each section are la = 0.3 m, lb = 0.2m, lc = 0.1 m. An air-gap length of 0.1 mm is cut in the ring. Relative permeabilities for sections a, b, c are 5000, 1000 and 10000 respectively. Flux in the air gap is 7.5 × 10- 4 Wb and the coil has 100 turns. Determine (a) Total m.m.f, and (b) exciting current.
Solution
Reluctance of section a of ring
Sa =( la/ μ0 μra A )= 0.3 / (4π× 10- 7 × 5000 × 0.001)
= 47746.37 AT/Wb
Reluctance of section b of ring
Sb = lb/ μ0 μrb A =0.2 / (4π× 10- 7 × 1000 × 0.001)
= 159154.57 AT/Wb
Reluctance of section c of ring
Sc = lc/ μ0 μrc A =0.1 / 4π× 10- 7 × 10000 × 0.001 = 7957.73 AT/Wb
Reluctance of air-gap
S g = lg / μ0 Ag = 0.1 × 10- 3/4π× 10- 7 × 0.001
= 79577.73 AT/Wb
Total Reluctance
S = Sa + Sb + Sc + Sg = 294436.4 AT/Wb
(a) Total m.m.f = Flux × Reluctance = 7.5 × 10- 4 Wb × 294436.4 AT/Wb = 220.83 AT.
(b) Exciting Current = m.m.f/ No. of turns = 220.83/100 = 2.21 Amp