PROBLEMS 613supply. The frequency of the supply connected
to the stator is 60 Hz.
(a) Let the rotor be driven at 3600 r/min in either
direction by an auxiliary synchronous motor.
If the slip-ring voltage is 20 V, what frequen-
cies and voltages can be available at the slip
rings when the rotor is at standstill?
(b) If the slip-ring voltage is 400 V, when the
rotor frequency is 120 Hz, at what speed must
the rotor be driven in order to give 150 Hz
at the slip-ring terminals? What will the slip-
ring voltage be in this case?*13.1.7A three-phase, wound-rotor induction machine,
with its shaft rigidly coupled to the shaft of a
three-phase synchronous motor, is used to change
balanced 60-Hz voltages to other frequencies at
the wound-rotor terminals brought out through
slip rings. Both machines are electrically con-
nected to the same balanced three-phase, 60-Hz
source. Let the synchronous motor, which has
four poles, drive the interconnecting shaft in the
clockwise direction, and let the eight-pole bal-
anced three-phase stator winding of the induc-
tion machine produce a counterclockwise rotat-
ing field, i.e., opposite that of the synchronous
motor. Determine the frequency of the rotor volt-
ages of the induction machine.
13.1.8A synchronous generator has a rotor with six
poles and operates at 60 Hz.
(a) Determine the speed of prime mover of the
generator.
(b) Repeat part (a) if the generator has 12 poles.
(c) Repeat part (a) if the generator has 2 poles.
13.1.9Repeat Problem 13.1.8 if the generator operates
at 50 Hz.
13.1.10A three-phase ac motor, used to drive a draft fan,
is connected to a 60-Hz voltage supply. At no-
load, the speed is 1188 r/min; at full load, the
speed drops to 1128 r/min.
(a) Determine the number of poles of this ac
motor.
(b) Comment on whether this motor is an induc-
tion motor or a synchronous motor.
13.1.11A dc shunt machine has an armature winding
resistance of 0.12and a shunt-field winding
resistance of 50. The machine may be run on
250-V mains as either a generator or a motor.
Find the ratio of the speed of the generator to the
speed of the motor when the total line current is
80 A in both cases.
13.1.12A 100-kW, dc shunt generator, connected to a
220-V main, is belt-driven at 300 r/min, when
the belt suddenly breaks and the machine con-
tinues to run as a motor, taking 10 kW from the
mains. The armature winding resistance is 0.025
, and the shunt field winding resistance is 60.
Determine the speed at which the machine runs
as a motor.
*13.1.13A dc shunt motor runs off a constant 200-V
supply. The armature winding resistance is 0.4,
and the field winding resistance is 100. When
the motor develops rated torque, it draws a total
line current of 17.0 A.
(a) Determine the electromagnetic power devel-
oped by the armature under these conditions,
in watts and in horsepower.
(b) Find the total line current drawn by the motor
when the developed torque is one-half the
rated value.
13.1.14A dc machine, operating as a generator, develops
400 V at its armature terminals, corresponding to
a field current of 4 A, when the rotor is driven at
1200 r/min and the armature current is zero.
(a) If the machine produces 20 kW of electro-
magnetic power, find the corresponding ar-
mature current and the electromagnetic
torque produced.
(b) If the same machine is operated as a motor
supplied from a 400-V dc supply, and if the
motor is delivering 30 hp to the mechanical
load, determine: (i) the current taken from
the supply, (ii) the speed of the motor, and
(iii) the electromagnetic torque, if the field
current is maintained at 4 A. Assume that
the armature circuit resistance and the me-
chanical losses are negligible.
(c) If this machine is operated from a 440-V dc
supply, determine the speed at which this
motor will run and the current taken from
the supply, assuming no mechanical load, no
friction and windage losses, and that the field
current is maintained at 4 A.
13.1.15Consider the operation of a dc shunt motor that is
affected by the following changes in its operating
conditions. Explain the corresponding approxi-
mate changes in the armature current and speed
of the machine for each change in operating con-
ditions.