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Phasor Math and AC Circuits
Mathematically, phasors behave a lot like exponential numbers. This is not a coincidence;
treated as complex numbers, a phasor like
23
∠
40°
is really
23
40°i
, where
i
is the
imaginary square root of negative one. What you need to know is that when you multiply
two phasors, the amplitudes multiply, but the angles add. For instance, (5
∠
30°)·(7
∠
45°)
= 35
∠
15° because 5·7=35, and 30+45=15. When you divide phasors, the amplitudes
divide, but the angles subtract (top minus bottom). (8
∠
50°)/(2
∠
60°) = 4
∠
10° because
8/2=4 and 5060=10.
Unfortunately, the only time you can directly add or subtract two phasors is if they have
the same angle. You can add two reactances like this:
4
90°+11
90° = 15
90°
, but
you
cannot
simply add a resistance such as
3
0°
directly to a reactance such as
2
90°
.
Instead, you must combine them to create an impedance:
!
Z
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 Spring '11
 Tibbets

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