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Chapter 1
1-4. A motor is supplying 60 N m of torque to its load. If the motor’s shaft is turning at 1800 r/min, what is the mechanical
power supplied to the load in watts? In horsepower ? (11,310 W, 15.2 hp )
1-5. A ferromagnetic core is shown in Figure P1-2. The depth of the core is 5 cm. The other dimensions of the core are as
shown in the figure. Find the value of the current that will produce a flux of 0.005 Wb. With this current, what is the flux
density at the top of the core? What is the flux density at the right side of the core? Assume that the relative permeability
of the core is 1000. (i =2.52 A, The flux density on the top of the core is B =0.67 T, The flux density on the right side of
the core is B =2.0 T)
1-6. A ferromagnetic core with a relative permeability of 1500 is shown in Figure P1-3. The dimensions are as shown in the
diagram, and the depth of the core is 7 cm. The air gaps on the left and right sides of the core are 0.070 and 0.020 cm,
respectively. Because of fringing effects, the effective area of the air gaps is 5 percent larger than their physical size. If
there are 400 turns in the coil wrapped around the center leg of the core and if the current in the coil is 1.0 A, what is the
flux in each of the left, center, and right legs of the core? What is the flux density in each air gap? ( center =0.0033 Wb,
left =0.00193 Wb, right =0.00229 Wb, Bleft (0.07cm) =0.375 T, Bright (0.05cm) = 0.445 T )
1-8. A core with three legs is shown in Figure P1-5. Its depth is 5 cm, and there are 200 turns on the leftmost leg. The relative
permeability of the core can be assumed to be 1500 and constant. What flux exists in each of the three legs of the core?
What is the flux density in each of the legs? Assume a 4% increase in the effective area of the air gap due to fringing
effects. ( center =0.00156 Wb, left =0.00235 Wb, right = 0.00079 Wb, Bcenter =0.208 T, Bleft =0.522 T, Bright  0.176 T )
1-9. A wire is shown in Figure P1-6 which is carrying 5.0 A in the presence of a magnetic field. Calculate the magnitude and
direction of the force induced on the wire. ( F = 1.25 N, direct into the page)
1-10. The wire is shown in Figure P1-7 is moving in the presence of a magnetic field. With the information given in the figure,
determine the magnitude and direction of the induced voltage in the wire. ( eind = 0.442 V, positive down)
1-11. Repeat Problem 1-10 for the wire in Figure P1-8.( eind =0 V )
1-13. A core with three legs is shown in Figure P1-10. Its depth is 8 cm, and there are 400 turns on the center leg. The
remaining dimensions are shown in the figure. The core is composed of a steel having the magnetization curve shown in
Figure 1-10c. Answer the following questions about this core:
(a) What current is required to produce a flux density of 0.5 T in the central leg of the core?
(b) What current is required to produce a flux density of 1.0 T in the central leg of the core? Is it twice the current in part
(a)?
(c) What are the reluctances of the central and right legs of the core under the conditions in part (a)?
(d) What are the reluctances of the central and right legs of the core under the conditions in part (b)?
(e) What conclusion can you make about reluctances in real magnetic cores?
((a) i =0.13 A, (b) ) i =0.22 A This current is less not twice the current in part (a), (c) Rcenter =5.25 kA t/Wb, Rright = 22.5
kA t/Wb, (d) Rcenter =5.25 6.0 kA t/Wb, Rright = 15.75 kA t/Wb)
1-14. A two-legged magnetic core with an air gap is shown in Figure P1-11. The depth of the core is 5 cm, the length of the air
gap in the core is 0.06 cm, and the number of turns on the coil is 1000. The magnetization curve of the core material is
shown in Figure P1-9. Assume a 5 percent increase in effective air-gap area to account for fringing. How much current is
required to produce an air-gap flux density of 0.5 T? What are the flux densities of the four sides of the core at that
current? What is the total flux present in the air gap? (i=0.691 A, Btop  Bleft  Bbottom =0.262 T, Bright =0.524 T,
 =0.00131 Wb)
1-15. A transformer core with an effective mean path length of 10 in has a 300-turn coil wrapped around one leg. Its crosssectional area is 0.25 in2, and its magnetization curve is shown in Figure 1-10c. If current of 0.25 A is flowing in the coil,
what is the total flux in the core? What is the flux density? (  =0.000205 Wb, B =1.27 T)
1-16. The core shown in Figure P1-2 has the flux  shown in Figure P1-12. Sketch the voltage present at the terminals of the
coil.
1-17. Figure P1-13 shows the core of a simple dc motor. The magnetization curve for the metal in this core is given by Figure
1-10c and d. Assume that the cross-sectional area of each air gap is 18 cm2 and that the width of each air gap is 0.05 cm.
The effective diameter of the rotor core is 4 cm.
(a) It is desired to build a machine with as great a flux density as possible while avoiding excessive saturation in the core.
What would be a reasonable maximum flux density for this core?
(b) What would be the total flux in the core at the flux density of part (a)?
(c) The maximum possible field current for this machine is 1 A. Select a reasonable number of turns of wire to provide
the desired flux density while not exceeding the maximum available current.
((a) From Figure 1-10c, a reasonable maximum flux density would be about 1.2 T. Notice that the saturation effects
become significant for higher flux densities.,(b)  = 0.00192 Wb, (c) one possible choice for the number of turns is N
= 1000.)
Chapter 9
9-1. If the resistor Radj is adjusted to 175  what is the rotational speed of the motor at no-load conditions? (n= 1063 r/min)
9-2. Assuming no armature reaction, what is the speed of the motor at full load? What is the speed regulation of the motor?
(n= 967 r/min, SR= 9.9%)
9-3. If the motor is operating at full load and if its variable resistance Radj is increased to 250  , what is the new speed of the
motor? Compare the full-load speed of the motor with Radj = 175  to the full-load speed with Radj = 250  . (Assume no
armature reaction, as in the previous problem.) (n= 1061 r/min, Note that Radj has increased, and as a result the speed of
the motor n increased.)
9-4. Assume that the motor is operating at full load and that the variable resistor Radj is again 175  . If the armature reaction is
1200 A turns at full load, what is the speed of the motor? How does it compare to the result for Problem 9-2? (n= 1447
r/min, The motor with armature reaction runs at a higher speed than the motor without armature reaction.)
9-5. If Radj can be adjusted from 100 to 400  , what are the maximum and minimum no-load speeds possible with this motor?
(nmin= 1004 r/min, nmax= 1447 r/min)
9-6. What is the starting current of this machine if it is started by connecting it directly to the power supply VT ? How does this
starting current compare to the full-load current of the motor? (IL,start=600 A, The rated current is 55 A, so the starting
current is 10.9 times greater than the full-load current. This much current is extremely likely to damage the motor.)
9-8. What is the no-load speed of this separately excited motor when Radj = 175  and (a) VA = 120 V, (b) VA = 180 V, (c) VA =
240 V? ((a) n= 531 r/min, (b) n= 797 r/min, (c) n= 1063 r/min)
9-9. For the separately excited motor of Problem 9-8:
(a) What is the maximum no-load speed attainable by varying both VA and Radj ?
(b) What is the minimum no-load speed attainable by varying both VA and Radj ?
((a) nmax= 1447 r/min, (b) nmin= 502 r/min)
9-13. A 7.5-hp 120-V series dc motor has an armature resistance of 0.2  and a series field resistance of 0.16  . At full load,
the current input is 58 A, and the rated speed is 1050 r/min. Its magnetization curve is shown in Figure P9-5. The core
losses are 200 W, and the mechanical losses are 240 W at full load. Assume that the mechanical losses vary as the cube of
the speed of the motor and that the core losses are constant.
(a) What is the efficiency of the motor at full load?
(b) What are the speed and efficiency of the motor if it is operating at an armature current of 35 A?
(c) Plot the torque-speed characteristic for this motor.
((a)  =80.4%, (b) n= 1326 r/min, ),  =73.2%, (c) The resulting torque-speed characteristic is shown below:)
9-14. A 20-hp 240-V 76-A 900 r/min series motor has a field winding of 33 turns per pole. Its armature resistance is 0.09  ,
and its field resistance is 0.06  . The magnetization curve expressed in terms of magnetomotive force versus EA at 900
r/min is given by the following table:
EA, V
A turns
95
150
188
212
229
243
500
1000
1500
2000
2500
3000
Armature reaction is negligible in this machine.
(a) Compute the motor’s torque, speed, and output power at 33, 67, 100, and 133 percent of full-load armature current.
(Neglect rotational losses.)
(b) Plot the terminal characteristic of this machine.
((a) at 33%  ind  36 N m , n = 1586 r/min, Pconv  5976 W
at 67%  ind  106 N m , n = 1062 r/min, Pconv  11,780 W
at 100%  ind  185 N m , n = 899 r/min, Pconv  17,370 W
at 133%  ind  271 N m , n = 803 r/min, Pconv  22,770 W
(b) The resulting torque-speed characteristic is shown below:)
9-15. A 300-hp 440-V 560-A, 863 r/min shunt dc motor has been tested, and the following data were taken:
Blocked-rotor test:
VA = 16.3 V exclusive of brushes
VF = 440 V
IA = 500 A
IF = 8.86 A
No-load operation:
VA = 16.3 V including brushes
IF = 8.76 A
IA = 2.31 A
n = 863 r/min
What is this motor’s efficiency at the rated conditions? [Note: Assume that (1) the brush voltage drop is 2 V; (2) the core
loss is to be determined at an armature voltage equal to the armature voltage under full load; and (3) stray load losses are
1 percent of full load.] (  =88.7%)
9-16. The motor described above is connected in shunt.
(a) What is the no-load speed of this motor when Radj = 120  ?
(b) What is its full-load speed?
(c) Under no-load conditions, what range of possible speeds can be achieved by adjusting Radj?
((a) n=1125 r/min, (b) n=1060 r/min, (c) nmax=1440 r/min, nmin=1004 r/min)
9-21. A 15-hp 120-V 1800 r/min shunt dc motor has a full-load armature current of 60 A when operating at rated conditions.
The armature resistance of the motor is RA = 0.15  , and the field resistance RF is 80  . The adjustable resistance in the
field circuit Radj may be varied over the range from 0 to 200  and is currently set to 90  . Armature reaction may be
ignored in this machine. The magnetization curve for this motor, taken at a speed of 1800 r/min, is given in tabular form
below:
E A, V 5
78
95
112
118
126
IF , A
0.00
0.80
1.00
1.28
1.44
2.88
(a) What is the speed of this motor when it is running at the rated conditions specified above?
(b) The output power from the motor is 7.5 hp at rated conditions. What is the output torque of the motor?
(c) What are the copper losses and rotational losses in the motor at full load (ignore stray losses)?
(d) What is the efficiency of the motor at full load?
(e) If the motor is now unloaded with no changes in terminal voltage or Radj , what is the no-load speed of the motor?
(f) Suppose that the motor is running at the no-load conditions described in part (e). What would happen to the motor if
its field circuit were to open? Ignoring armature reaction, what would the final steady state speed of the motor be
under those conditions?
(g) What range of no-load speeds is possible in this motor, given the range of field resistance adjustments available with
Radj?
((a) n=1800 r/min, (b)  out  59.4 N m , (c) PCU = 851W,Prot=2070 W, (d)  =79.4%, (e) n=1873 r/min, (f) If the field
circuit opens, the field current would go to zero and speed increase to a very high speed, n = 48,700 r/min, (g)
nmax=2706 r/min, nmin =1711 r/min)
9-22. The magnetization curve for a separately excited dc generator is shown in Figure P9-7. The generator is rated at 6 kW,
120 V, 50 A, and 1800 r/min and is shown in Figure P9-8. Its field circuit is rated at 5A. The following data are known
about the machine:
RA = 0.18 
VF =120 V
Radj = 0 to 30 
RF = 24 
NF =1000 turns per pole
Answer the following questions about this generator, assuming no armature reaction.
(a) If this generator is operating at no load, what is the range of voltage adjustments that can be achieved by changing Radj
(b) If the field rheostat is allowed to vary from 0 to 30 . and the generator’s speed is allowed to vary from 1500 to 2000
r/min, what are the maximum and minimum no-load voltages in the generator?
((a) the maximum no-load voltage is 129 V, the minimum no-load voltage is 87 V,(b) the maximum no-load voltage is
143 V, the minimum no-load voltage is 72.8 V )
9-23. If the armature current of the generator in Problem 9-22 is 50 A, the speed of the generator is 1700 r/min, and the
terminal voltage is 106 V, how much field current must be flowing in the generator? ( iF = 4.2 A)
9-24. Assuming that the generator in Problem 9-22 has an armature reaction at full load equivalent to 400 A turns of
magnetomotive force, what will the terminal voltage of the generator be when IF = 5 A, nm = 1700 r/min, and IA = 50 A?
(VT=110V)
9-25. The machine in Problem 9-22 is reconnected as a shunt generator and is shown in Figure P9-9. The shunt field resistor
Radj is adjusted to 10  , and the generator’s speed is 1800 r/min.
(a) What is the no-load terminal voltage of the generator?
(b) Assuming no armature reaction, what is the terminal voltage of the generator with an armature current of 20 A? 40 A?
(c) Assuming an armature reaction equal to 200 A turns at full load, what is the terminal voltage of the generator with an
armature current of 20 A? 40 A?
(d) Calculate and plot the terminal characteristics of this generator with and without armature reaction .
((a) 112 V, (b) If armature current = 20 A; VT =106 V, If armature current = 40; VT =98 V, (c) If armature current =
20 A; VT =103 V, If armature current = 40; this is not a stable operating condition, (d) with and without armature
reaction is shown below:)
With out armature
reaction
With out armature
reaction
9-26. If the machine in Problem 9-25 is running at 1800 r/min with a field resistance Radj = 10  and an armature current of 25
A, what will the resulting terminal voltage be? If the field resistor decreases to 5  while the armature current remains 25
A, what will the new terminal voltage be? (Assume no armature reaction.) (terminal voltage of 104 V, new terminal
voltage of 115 V )