Environmental Engineering Reference
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A B
(a).
A
B
A
90 degrees
(b).
AB
B
B
-90 degrees
(c).
AB
A
180 degrees
B
A
B
(d).
A
Waveforms
Phasors
Figure A.11
Phasor representation of AC quantities
C = 10
36.86°
B = 6 90°
q = 36.86°
A = 8
Figure A.12
Addition of phasors
In fact, phasors add up in exactly the same way as vectors that represent velocities or forces
in mechanical systems. As explained in Section A.4 the 'effective' value of an AC waveform
is its RMS value; hence AC quantities, unless stated otherwise, are always labelled in terms
of their RMS value and are expressed by a capital letter. For example, V and I represent the
RMS values of the general sinusoids
(
) =
(
)
(
) =
(
)
v
=
2
V t
sin
ωφ
+
V t
sin
ωφ
+
and
i
=
2
I
sin
ωθ
t
+
I
sin
ωθ
t
+
respectively, where V and I are the peak values and
φ
and
θ
are phase angles with respect
to a reference sinusoid.
 
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