Page 80 - Solutions Manual to accompany Electric Machinery Fundamentals

(d) The induced torque would be:
 ind   2rilΒ sin  (3-17)
t
 ind   2t  0.1 m 2.26 sin t  A 0.3 m 1.0 T sin t 
2
 ind  t  0.136 sin 377 N m, counterclockwise

t
(e) The instantaneous power generated by the loop is:
 e i
Pt ind  22.6 sin377 V 2.26 sin 377 At  t  51.1 sin 377 Wt 2
The average power generated by the loop is

P  1 T  51.1 sin  t dt  25.55 W
2
ave
T
(f) The mechanical power being consumed by the loop is:
P   ind 0.136 sin 377 N mt  377 rad/s  51.3 sin  2 t W

2
Note that the amount of mechanical power consumed by the loop is equal to the amount of electrical
power created by the loop (within roundoff error). This machine is acting as a generator, converting
mechanical power into electrical power.
3-2. Develop a table showing the speed of magnetic field rotation in ac machines of 2, 4, 6, 8, 10, 12, and 14
poles operating at frequencies of 50, 60, and 400 Hz.
SOLUTION The equation relating the speed of magnetic field rotation to the number of poles and electrical
frequency is
120 f
n  se
sm
P
The resulting table is
Number of Poles f = 50 Hz f = 60 Hz f = 400 Hz
e
e
e
2 3000 r/min 3600 r/min 24000 r/min
4 1500 r/min 1800 r/min 12000 r/min
6 1000 r/min 1200 r/min 8000 r/min
8 750 r/min 900 r/min 6000 r/min
10 600 r/min 720 r/min 4800 r/min
12 500 r/min 600 r/min 4000 r/min
14 428.6 r/min 514.3 r/min 3429 r/min

3-3. The first ac power system in the USA ran at a frequency of 133 Hz. If the ac power for this system were
produced by a 4-pole generator, how fast would the shaft of the generator have to rotate?

SOLUTION The equation for the speed of the shaft is
120 f 120  133 Hz
n  se   3990 r/min
sm
P 4
3-4. A three-phase Y-connected four-pole winding is installed in 24 slots on a stator. There are 40 turns of
wire in each slot of the windings. All coils in each phase are connected in series. The flux per pole in the
machine is 0.060 Wb, and the speed of rotation of the magnetic field is 1800 r/min.
(a) What is the frequency of the voltage produced in this winding?
(b) What are the resulting phase and terminal voltages of this stator?

SOLUTION
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