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```speeds. For this part,
assume a constant rotational loss of 300 W over the speed range.
4.25 A permanent magnet de motor drives a mechanical load requiring a constant
torque of 25 N · m. The motor produces 10 N · m with an armature current
of 10 A. The resistance of the armature circuit is 0.2 D. A 200 V de supply is
applied to the armature terminals. Determine the speed of the motor.
4.26 A de shunt motor drives an elevator load which requires a constant torque
of 300 N · m. The motor is connected to a 600 V de supply and the motor
rotates at 1500 rpm. The armature resistance is 0.5 D.
(a) Determine the armature current.
(b) If the shunt field flux is reduced by 10%, determine the armature current
and the speed of the motor.
4.27 A de shunt motor (50 hp, 250 V) is connected to a 230 V supply and delivers
power to a load drawing an armature current of 200 amperes and running
at a speed of 1200 rpm. Ra = 0.2 D.
(a) Determine the value of the generated voltage at this load condition.
(b) Determine the value of the load torque. The rotational losses are 500
watts.
(c) Determine the efficiency of the motor if the field circuit resistance is
11s n.
4.28 A de shunt machine (23 kW, 230 V, 1500 rpm) has Ra = 0.1 D.
1. The de machine is connected to a 230 V supply. It runs at 1500 rpm at
no-load and 1480 rpm at full-load armature current.
(a) Determine the generated voltage at full load.
(b) Determine the percentage reduction of flux in the machine due to
armature reaction at full-load condition.
2. The de machine now operates as a separately excited generator and the
field current is kept the same as in part 1. It delivers full load at rated
voltage.
(a) Determine the generated voltage at full load.
(b) Determine the speed at which the machine is driven.
(c) Determine the terminal voltage if the load is thrown off.
4.29 A de shunt machine (10 kW, 250 V, 1200 rpm) has Ra = 0.25 D. The machine
is connected to a 250 V de supply, draws rated armature current, and rotates
at 1200 rpm.
(a) Determine the generated voltage, the electromagnetic power developed,
and the torque developed.
(b) The mechanical load on the motor shaft is thrown off, and the motor
draws 4 A armature current.
(i) Determine the rotational loss.
Problems 205
(ii) Determine speed, assuming no armature reaction.
(iii) Determine speed, assuming 10% change in flux due to armature
reaction, for a change of armature current from rated value to 4 A.
4.30 A 240 V, 2 hp, 1200 rpm de shunt motor drives a load whose torque varies
directly as the speed. The armature resistance of the motor is 0.75 !1. With
Ir = 1 A, the motor draws a line current of 7 A and rotates at 1200 rpm.
Assume magnetic linearity and neglect armature reaction effect.
(a) The field current is now reduced to 0.7 A. Determine the operating speed
of the motor.
(h) Determine the line current, mechanical power developed, and efficiency
for the operating condition of part (a). Neglect rotational losses.
4.31 Repeat Problem 4.30 if the load torque is constant. Determine the torque.
4.32 A 125 V, 5 kW, 1800 rpm de shunt motor requires only 5 volts to send full-
load current through the armature when the armature is held stationary.
(a) Determine the armature current if full-line voltage is impressed across
the armature at starting.
(h) Determine the value of the external resistance needed in series with the
armature to limit the starting current to 1.5 times the full-load current.
(c) The motor is coupled to a mechanical load by a belt. Determine the
generated voltage at full-load condition (V, = 125 V, n = 1800 rpm,
I a = /a(mtcdl). If the belt breaks, determine the speed of the motor. Neglect
rotational losses and assume 10% reduction of flux due to armature
reaction at full load.
4.33 A de motor is mechanically connected to a constant-torque load. When the
armature is connected to a 120 V de supply, it draws an armature current of
value 8 A and runs at 1800 rpm. The armature resistance is Ra = 0.08 !1.
Accidentally, the field circuit breaks and the flux drops to the residual flux,
which is only 5% of the original flux.
(a) Determine the value of the armature current immediately after the field
circuit breaks (i.e., before the speed has had time to change from
1800 rpm).
(h) Determine the theoretical final speed of the motor after the field cir-
cuit breaks.
4.34 At standstill, a de series motor draws 5 amperes and develops 5 N · m torque
when connected to a 5 V de supply. The series motor is mechanically coupled
to a load. It draws 10 amperes when connected to a 120 V de supply and
drives the load at 300 rpm. Assume magnetic linearity.
(a) Determine the torque developed by the motor.
(h) Determine the value of the external resistance required to be connected
in series with the motor.
4.35 A de series motor (230 V, 12 hp, 1200 rpm) is connected to a 230 V supply,
draws a current of 40 amperes, and rotates at 1200 rpm. Ra = 0.25 !1 and
Rs, = 0.1 n. Assume magnetic linearity.
(a) Determine the power and torque developed by the motor.
(h) Determine the speed, torque, and power if the motor draws 20 amperes.
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206 chapter 4 DC Machines
4.36 A 50 hp, 200 V, 1800 rpm shunt motor requires a starter box. During the
start, the armature current is constrained within the range 200 to 400 A. The
armature circuit resistance is 0.15 !1. Determine the required number of
resistors and the value of each resistor in the starter box.
4.37 The Ward-Leonard speed control system shown in Fig. 4.58a uses two identi-
cal de machines of rating 250 V, 5 kW, 1200 rpm. The armature resistance
of each machine is 0.5 ohms. The generator is driven at a constant speed of
1200 rpm. The magnetization characteristic of each machine at 1200 rpm is
as follows:
(A) 0.0 I 0.1 I 0.21 0.31 0.41 0.51 0.61 0.71 0.811.0 11.211.4
Ea (V) 5 60 120 160 190 212 230 242 250 262 270 273
Neglect the effect of armature reaction.
(a) If the motor field current 11m is kept constant at 0.8 A, determine the
maximum and minimum values of the generator field current, l 1g, re-
quired for the motor to operate in a speed range of 200 to 1200 rpm at
full-load armature current.
(b) The generator field current is kept at 1.0 amps and the motor field current
is reduced to 0.2 amp. Determine the speed of the motor at full-load
armature current.
4.38 Repeat Example 4.11 if a single-phase semiconverter (Fig. 4.60 or Fig. 10.24a)
is used to control the speed of the de motor.
4.39 Repeat Example 4.12 if a three-phase semiconverter is used to control the
speed of the de motor.
4.40 A de series motor drives an elevator load that requires a constant torque of
200 N · m. The de supply voltage is 400 V and the combined resistance of the
armature and series field winding is 0.75 !1. Neglect rotational losses and
armature reaction effect.
(a) The speed of the elevator is controlled by a solid-state chopper. At 50%
duty cycle (i.e., a = 0.5) of the chopper, the motor current is 40 amps.
Determine the speed and the horsepower output of the motor and the
efficiency of the system.
(b) The elevator is controlled by inserting resistance in series with the arma-
ture of the series motor. For the speed of part (a), determine the values
of the series resistance, horsepower output of the motor, and efficiency
of the system.
chapter five
INDUCTION
{ASYNCHRONOUS)
MACHINES
The induction machine is the most rugged and the most widely used machine
in industry. Like the de machine discussed in the preceding chapter, the
induction machine has a stator and a rotor mounted on bearings and sepa-
rated from the stator by an air gap. However, in the induction machine both
stator winding and rotor winding carry alternating currents. The alternating
current (ac) is supplied to the stator winding directly and to the rotor winding
by induction-hence the name induction machine.
The induction machine```