Environmental Engineering Reference
In-Depth Information
v
i
i
Time
v
C
Figure A.8
Capacitor excited by AC voltage
v
i
p
Time
Figure A.9
Power in a capacitive component
π
2
⎛
⎝
⎞
⎠
i
=
(
ω
CV t
)
cos
ω
=
I
sin
ω
t
+
(A.15)
where
=
(
)
I
ω
CV
(A.16)
The current is now said to
lead
the voltage by 90 ° or the voltage to
lag
the current by the
same amount.
The simple capacitor circuit is characterized by a power curve (Figure A.9), which is
similar to that of the pure inductor.
A capacitor, also a storage element, does not dissipate power as it reacts against changes in
voltage; it merely absorbs and releases power, alternately.
There is one fi nal observation that must be stressed. A comparison between the sinusoidal
power waveforms in Figures A.7 and A.9 reveals that they are always in opposition when
viewed with respect to the voltage waveform. That is to say, during periods when the power
in the inductance is positive, the power in the capacitance is negative and vice versa. This is
an important fact that will be returned to later.
A.6 Phasors
In the above analysis the AC variations of voltage, current and power were depicted as sinu-
soidally varying functions of time. This is acceptable for an introductory exposition of the
relationships of these quantities for single-circuit elements. In real life, power circuits consist
