Question

A ring composed of three sections. The cross-sectional area is 0.001 m² for each section. The mean arc length are l_a = 0.3 m, l_b = 0.2 m, l_c = 0.1 m. An air-gap length of 0.1 mm is cut in the ring. Mr for sections a, b, c are 5000, 1000, and 10,000 respectively. Flux in the air gap is 7.5 × 10⁻⁴ W_b. Find (i) mmf (ii) exciting current if the coil has 100 turns, (iii) reluctances of the sections

Answer 1

Area = 0.001 sq.m

l_a = 0.3 m, l_b = 0.2 m, l_c = 0.1 m, l_g = 0.1 × 10⁻³m 

μ_ra = 5000, μ_rb = 1000, μ_rc = 10,000 μ_o = 4π × 10⁻⁷ 

φ = 7.5 × 10⁻⁴ Wb 

(iii) Calculations of Reluctances of four parts of the magnetic circuit :

(a) Reluctance of air gap, Reg = 1/μ₀ x (0.1 x 10^-3)/0.001) = 1000/(4π x 0.001) = 79618

(b) Reluctance of section ‘a’ of ring

= R_ea = 1/μ₀μ_a x 0.3/0.001 = (10⁷ x 0.3)/(4π x 47770 x 5000 x 0.001) = 47770

(c) Reluctance of section ‘b’ of the ring

= R_eb = 1/μ₀μ_r x 0.20/0.001 = 10⁷/(4π x 1000) x 0.10/0.001 = 15923.6

(d) Reluctance of section ‘c’ of the ring

= R_ec = 1/μ₀μ_rb x 0.20/0.001 = 10⁷/(4π x 1000) x 0.10/0.001 = 7961

Total Reluctance = R_eg + R_ea + R_eb + R_ec = 294585 

(i) Total mmf required = Flux × Reluctance 

= 7.5 × 10⁻⁴ × 294585 = 221 amp-turns 

(ii) Current required = 221/100 = 2.21 amp