Machine_HW1

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Electrical Machines (I) 
Homework 1 
(Deadline on Thursday 6 Nov.) 
 
Q1) For the toroid shown in the figure if: 
Ri = 3.4 cm, Ro = 4.0 cm g = 0.2 cm, N=65 turns and μ=750 μo 
Calculate: 
a) The mean core length lc and the core cross-sectional area Ac. 
b) The reluctance of the core Rc and that of the gap RAG. 
c) The inductance L 
d) The current (i) if B=1.35T 
e) The flux linkage of the (λ) coil 
 
Q2) 
Area: AA and AB = 7 cm2, AC = 14 cm2 
Length: lA and lB = 17 cm, lC = 5.5 cm, lAG = 0.4 cm 
The material is M-5, N1= N2=100, Assume I1= I2 
a) How many amperes are required to produce a 
flux density of 1.2 T in the air gap? 
(Note: from B/H curve H = 14 A/m.) 
b) Under the condition of part (a), how many joules 
of energy are stored in the magnetic field in the 
air gap? 
c) Calculate the inductance. 
 
 
Q3) Based on the magnetic structure shown in Figure 3 Find: 
a) The inductance of the winding 
b) The flux density Bl in gap 1 when the winding is carrying a 
current (i). 
Neglect fringing effects at the air gap and the core reluctance. 
Figure 1: Q1 
Figure 2: Q2 
Figure 3: Q3