COMBINING PHASORS
Cuthbert Nyack
The result of combining 2 phasors aÐa
(green line) and bÐb (red line) is
shown by the applet above. The magnitudes and phases of both
phasors can be varied by the scrollbars. The notation
aÐa means that the magnitude
of the phasor is a and the angle it makes with the horizontal
axis is a. In the above applet try
to determine which line corresponds to addition, subtraction,
multiplication and division.
Addition:-
The result of adding 2 phasors can be summarised below.
aÐa +
bÐb =
cÐg
c = Ö{ [a cos(a)
+ b cos(b) ]2 +
[a sin(a) +
b sin(b) ]2}
g = atan{
[a sin(a) +
b sin(b) ]/
[a cos(a)
+ b cos(b)] }
Subtraction:-
The result of subtracting 2 phasors can be summarised below.
aÐa -
bÐb =
cÐg
c = Ö{ [a cos(a)
- b cos(b) ]2 +
[a sin(a) -
b sin(b) ]2}
g = atan{
[a sin(a) -
b sin(b) ]/
[a cos(a)
- b cos(b)] }
Multiplication:-
The result of multiplying 2 phasors can be summarised below.
aÐa ´
bÐb =
cÐg
c = a ´ b
g = a +
b
Division:-
The result of Dividing 2 phasors can be summarised below.
aÐa ÷
bÐb =
cÐg
c = a ÷ b
g = a -
b
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COPYRIGHT © 1996 Cuthbert A. Nyack.