Page 79 - Solutions Manual to accompany Electric Machinery Fundamentals

Chapter 3: AC Machinery Fundamentals

3-1. The simple loop is rotating in a uniform magnetic field shown in Figure 3-1 has the following
characteristics:

B  1.0 T to the right r  01.m
l  0.3 m  = 377 rad/s
m
t
(a) Calculate the voltage e () induced in this rotating loop.
tot
(b) What is the frequency of the voltage produced in this loop?
(c) Suppose that a 10  resistor is connected as a load across the terminals of the loop. Calculate the
current that would flow through the resistor.
(d) Calculate the magnitude and direction of the induced torque on the loop for the conditions in (c).

(e) Calculate the instantaneous and average electric power being generated by the loop for the
conditions in (c).
(f) Calculate the mechanical power being consumed by the loop for the conditions in (c). How does
this number compare to the amount of electric power being generated by the loop?
 m

c r
d
N v S
v cd ab
b
a

B

B is a uniform magnetic
field, aligned as shown.
SOLUTION
(a) The induced voltage on a simple rotating loop is given by

e  2t  r Bl sin t (3-8)
ind


e  2 0.1 mt   377 rad/s 1.0 T 0.3 m sin377t
ind
e  22.6 sin377 Vt  t
ind
(b) The angular velocity of the voltage produced in the loop is 377 rad/s. Frequency is related to
angular velocity by the equation   2 f , so
 377
f    60 Hz
2  2 

(c) If a 10  resistor is connected as a load across the terminals of the loop, the current flow would be:
e 22.6 sin377 V
t
 
t
it ind   2.26 sin 377 A
R 10 
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