# 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.

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