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Proof
"Capacitive Reactive Power is Always Negative."
Actually, the above title does not make sense.
The real meaning is:
Capacitively generated reactive power is always negative.
(The word "capacitive" should not modify the phrase, "reactive power."
Instead, say the reactive power is "negative."
or use an algebraic sign of "–" on the numeric amount.)
The reactance of a capacitor is
XC = –1/ωC.
Assuming that frequency, ω, and capacity, C, are
always positive, which is conventionally the case,
then capacitively generated reactance is always negative.
Now the resulting reactive power is
Q = |VRMS|2/XC.
Thus since XC is always negative, capacitively
generated reactive power is also always negative.
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