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169 The wire of Problem 168 induces a time-varying
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emf of e1 (t) = 002 cos 10t A second wire is placed in the same magnetic eld but has a length of 01 m, as shown in Figure P169 The position of this wire is given by x(t) = 1 01 sin 10t Find the induced emf e(t) de ned by the difference in emf s e1 (t) and e2 (t)
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i N l1 A1 l2 A2 l3 A3
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b Compare the mmf drop across the air gap to that across the rest of the magnetic circuit Discuss your results using the value of for each material
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a I c 0003 m d N = 100 t f e
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N = 100 turns l1 = 30 cm A1 = 100 cm2 l2 = 10 cm
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A2 = 25 cm2 l3 = 30 cm A3 = 100 cm2
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Figure P1616 Figure P1613
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1617 Find the magnetic ux, , established in the
series magnetic circuit of Figure P1617
1614 The magnetic circuit shown in Figure P1614 has
two parallel paths Find the ux and ux density in each of the legs of the magnetic circuit Neglect fringing at the air gaps and any leakage elds N = 1,000 turns, i = 02 A, lg1 = 002 cm, and lg2 = 004 cm Assume the reluctance of the magnetic core to be negligible
I=2A
N = 100 turns i 4 cm lg1 1 cm 2 cm Cross-section 1 cm 1 cm N lg2 1 cm 1 cm
8m 00
Figure P1614
1615 Find the current necessary to establish a ux of
= 3 10 4 Wb in the series magnetic circuit of Figure P1615 Here, liron = lsteel = 03 m, Area (throughout) = 5 10 4 m2 , and N = 100 turns
Cast iron
Cast steel
N turns
Figure P1615
a Find the current, I , required to establish a ux = 24 10 4 Wb in the magnetic circuit of Figure P1616 Here, Area(throughout) = 2 10 4 m2 , lab = lef = 005 m, laf = lbe = 002 m, lbc = ldc , and the material is sheet steel
;; ; ; ; ;
Area = 0009 m2 Cast steel
;; ;;
Figure P1617
1618 For the series-parallel magnetic circuit of
Figure P1618, nd the value of I required to establish a ux in the gap of = 2 10 4 Wb Here, lab = lbg = lgh = lha = 02 m, lbc = lfg = 01 m, lcd = lef = 0099 m, and the material is sheet steel
N = 200 turns
Area = 2 10-4 m2
Figure P1618
b 1
Area for sections other than bg = 5 10-4 m2
16
Principles of Electromechanics
1619 Refer to the actuator of Figure P1619 The entire
device is made of sheet steel The coil has 2,000 turns The armature is stationary so that the length of the air gaps, g = 10 mm, is xed A direct current passing through the coil produces a ux density of 12 T in the gaps Determine: a The coil current b The energy stored in the air gaps c The energy stored in the steel
Section 3: Transformers 1621 For the transformer shown in Figure P1621,
N = 1,000 turns, l1 = 16 cm, A1 = 4 cm2 , l2 = 22 cm, A2 = 4 cm2 , l3 = 5 cm, and A3 = 2 cm2 The relative permeability of the material is r = 1,500 a Construct the equivalent magnetic circuit, and nd the reluctance associated with each part of the circuit b Determine the self-inductance and mutual inductance for the pair of coils (ie, L11 , L22 , and M = L12 = L21 )
140 175
i 80 /2 /2 N turns
l1, A1
l2 , A2 l3, A3 N turns
Figure P1621
175 All dimensions are in mm
1622 A transformer is delivering power to a 300resistive load To achieve the desired power transfer, the turns ratio is chosen so that the resistive load referred to the primary is 7,500 The parameter values, referred to the secondary winding, are: r1 = 20 L1 = 10 mH L2 = 10 mH Lm = 25 mH r2 = 20
Figure P1619
1620 A core is shown in Figure P1620, with
r = 2,000 and N = 100 Find: a The current needed to produce a ux density of 04 Wb/m2 in the center leg b The current needed to produce a ux density of 08 Wb/m2 in the center leg
Core losses are negligible a Determine the turns ratio b Determine the input voltage, current, and power and the ef ciency when this transformer is delivering 12 W to the 300- load at a frequency f = 10,000/2 Hz
1623 A 220/20-V transformer has 50 turns on its
8 cm i 26 8 cm cm 8 cm 20 cm N 8 cm
low-voltage side Calculate a The number of turns on its high side b The turns ratio when it is used as a step-down transformer c The turns ratio when it is used as a step-up transformer
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