1-1/4 The maganetic circuit of na inductance coil has a reluctance of 1500 A-

t/Wb. The coil is wound with 200 turns of aluminum wire, and draws 3 A
when connected to a 24 V battery. Determine (a) the core flux (b) the
resistance of the coil.
ꭆ = 1500 A-t/Wb
N= 200 turns
I=3A
V = 24 V

a)
Ꞙ=N × I ; Ꞙ=200 ×3 A
Ꞙ=600 mmf
Ꞙ 600 mmf
Φ= = =0.4 Wb
Ꞙ A−t
1500
Wb
Φ=0.4 Wb

b)
V V 24 V
I= ; R= ; R= =8Ω
R I 3A

1-2/4 A magnetic circuit constructed of sheet steel has an average length of

1.3 m and a cross sectional area of 0.024 m2 . A 50 turn coil wound on the
ring has resistance of 0.82 Ω , and draws a 2A from a DC supply. The
reluctance of the for this condition is 7425 A-t/Wb. Determine (a) flux
density; (b) voltage applied.
a)
l=1.3 R=0.82Ω
2
A=0.024 m I =2 A
A−t
N=50 turns Ꞙ=7425
Wb

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 Ꞙ N ×I 50 ×2 A
Φ= = = =0.0135Wb
Ꞙ Ꞙ A−t
7425
Wb
Φ 0.0135 Wb
B= = =0.563 T
A 0.024 m 2

b)
V
I= ; V =I × R ;V =2 A × 0.82 Ω=1.64 V
R

1-3/4 A magnetic circuit has an average length of 1.4 m and a cross sectional
area of 0.25 m2 . Excitation is provided by 140-turn, 30 Ω coil. Determine
the voltage required to establish a flux density of 1.56 T. The reluctance of the
magnetic circuit, when operating at this flux density is 768 A-t/Wb.
l=1.4 m R=30 Ω

A=0.25 m2 I =1.56 T
A−t
N=140 turns Ꞙ=768
Wb

Φ=B × A=1.56 T × 0.25 m2=0.39 Wb

A−t
0.39Wb ×768
Ꞙ N ×I Φ ×Ꞙ wb
Φ= = ; I= = =2.14 A
Ꞙ Ꞙ N 140
V
I= ; V =I × R ;V =2.14 A ×30 Ω=64.2V
R

1-4/5 A ferromagnetic core in the shape of a doughnut has cross sectional

section area of 0.11 m2 and an average length of 1.4 m. The permeability of
the core is 1.206 ×10−3 Wb/A-t. Determine the reluctance of the magnetic
circuit.
l=1.4 m
2
A=0.11 m
Wb
μ=1.206 ×10−3
A−t

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 1 l 1 1.4 m A−t
Ꞙ= × = × =10.55
μ A −3 Wb 0.11 m 2
Wb
1.206 ×10
A−t

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 1-5/5 A magnetic circuit has a mean length of 0.80m, a cross-sectional area
0.06 m2 , and relative permeability of 2167. Connecting its 340-turn 64 Ω
magnetizing coil to a DC circuit causes a 56 V drop across the coil. Determine
the flux density in the core
l=0.80 m R=64 Ω
2
A=0.06 m N ¿ 340
Wb
μr =2167 V =56 V
A−t
V 56 V
I= = =0.875 A
R 64 Ω
l 0.80 m
Ꞙ= =
μr × μ0 × A Wb Wb
2167 × 4 π ×10−7 × 0.06 m2
A−t A−t−m
A−t
Ꞙ=4.896 ×103
Wb
Ꞙ N × I 0340 ×0.875 A
Φ= = = =0.06076 Wb
Ꞙ Ꞙ 3 A−t
4.896 ×10
wb
Φ 0.06076 Wb
B= = =1.013 T
A 0.06 m
2

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