COVERED
SOLUTION MANUAL
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PROBLEM SOLUTIONS: Chapter 1
Problem 1.1
Part (a):
Rc = lc = lc
µA µ µ A = 0 A/Wb
c r 0 c
g
Rg = = 1.017 × 106 A/Wb
µ 0A c
part (b):
NI
Φ= = 1.224 × −4
Wb
Rc + g 10
R
part (c):
λ = N Φ = 1.016 × 10−2 Wb
part (d):
λ
L = = 6.775 mH
I
Problem 1.2
part (a):
lc lc 5
Rc = = µ µ A = 1.591 × 10 A/Wb
µAc r 0 c
g
Rg = = 1.017 × 106 A/Wb
µ 0A c
part (b):
NI
Φ= = 1.059 × −4
Wb
Rc + g 10
R
part (c):
λ = N Φ = 8.787 × 10−3 Wb
part (d):
λ
L= = 5.858 mH
I
,2
Problem 1.3
part (a):
Lg
N= = 110 turns
µ0Ac
part (b):
Bcore
I = = 16.6 A
µ0N/g
Problem 1.4
part (a):
L(g + lcµ0/µ) L(g + lcµ0/(µrµ0))
N = = = 121 turns
µ0Ac µ0Ac
part (b):
Bcore
I = = 18.2 A
µ0N/(g + lcµ0/µ)
Problem 1.5
part (a):
part (b):
3499
µr = 1 + √ = 730
1+ 0.047(2.2)7.8
g + µ0lc/µ
I =B = 65.8 A
µ0N
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part (c):
Problem 1.6
part (a):
NI Ag x
Hg = ; B = = Bg 1−
2g X0
c B g
Ac
part (b): Equations
2gHg + Hclc = NI; BgAg = BcAc
and
Bg = µ0Hg; Bc = µHc
can be combined to give
NI NI
Bg = µ A = µ x
2g + 0
µ Ac
g
(lc + lp) 2g + µ
0
1− X0 (lc + lp)
Problem 1.7
part (a):
µ0
g+ (lc + lp)
µ
I =B = 2.15 A
µ0N
part
(b): 1199
µ= 0 1+ √ = 1012 µ0
µ 1 + 0.05B8
µ0
g+ (lc + lp)
µ
I =B = 3.02 A
µ0N