Environmental Engineering Reference
In-Depth Information
z
B
B
B
E
n
x
E
n
y
FIGURE 7.3
Rectangular loop rotated by outside force with angular velocity,
q
, in a uniform external mag-
netic field, a generator.
7.1.1 F
ARADAY
'
S
L
AW OF
E
LECTROMAGNETIC
I
NDUCTION
Another way of looking at electromotive forces is by Faraday's law of electromagnetic induction.
The amount of magnetic flux, &
M
, is equal to the strength of the magnetic field times the area:
(7.10)
&
M
BA
u
BA
cos(Q)
where
k
is the angle between
B
and
A
. The electromotive force is then equal to the negative change
in magnetic flux with time:
E
$&
$
t
(7.11)
In generators and motors, the magnetic field and area can be kept constant, and the angle between
the two changed by rotating a loop of wire. This gives an alternating voltage and current, which vary
like a sine wave.
Induction is where you have two coils, where the changing magnetic flux in one coil causes a
changing current in the next coil. A transformer works by induction. If the load is pure resistance,
then the voltage is in phase (0 phase angle) with the current. For a capacitor the voltage lags the cur-
rent by 90°, and for an inductor the voltage leads the current by 90° (
Figure 7.4
). In the figure, all the
voltages are set with an angle of zero and the current is then shown in relation to the voltage (starting
at a different angle for the sine curve). Check the links for the relation between voltage and current.
7.1. 2 P
HASE
A
NGLE AND
P
OWER
F
ACTOR
The instantaneous voltage and current are given by
v
V
p
sin (
qt
),
i
I
p
sin (
qt
b
)
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