Basic Calculations Using Real Numbers
A perfect resistor stores no energy, so current and voltage are in phase. Therefore there is no reactive power and . Therefore for a perfect resistor
For a perfect capacitor or inductor there is no net power transfer, so all power is reactive. Therefore for a perfect capacitor or inductor:
Where X is the reactance of the capacitor or inductor.
If X is defined as being positive for an inductor and negative for a capacitor then we can remove the modulus signs from Q and X and get
Instantaneous power is defined as:
where v(t) and i(t) are the time varying voltage and current waveforms.
This definition is useful because it applies to all waveforms, whether they are sinusoidal or not. This is particularly useful in power electronics, where nonsinusoidal waveforms are common.
In general, we are interested in the real power averaged over a period of time, whether it is a low frequency line cycle or a high frequency power converter switching period. The simplest way to get that result is to take the integral of the instantaneous calculation over the desired period.
This method of calculating the average power gives the real power regardless of harmonic content of the waveform. In practical applications, this would be done in the digital domain, where the calculation becomes trivial when compared to the use of rms and phase to determine real power.
Read more about this topic: AC Power
Famous quotes containing the words basic, calculations, real and/or numbers:
“The research on gender and morality shows that women and men looked at the world through very different moral frameworks. Men tend to think in terms of “justice” or absolute “right and wrong,” while women define morality through the filter of how relationships will be affected. Given these basic differences, why would men and women suddenly agree about disciplining children?”
—Ron Taffel (20th century)
“Nowhere are our calculations more frequently upset than in war.”
—Titus Livius (Livy)
“Unbreachable the fort
Of the long-batter’d world uplifts its wall;
And strange and vain the earthly turmoil grows,
And near and real the charm of thy repose,
And night as welcome as a friend would fall.”
—Matthew Arnold (1822–1888)
“... there are persons who seem to have overcome obstacles and by character and perseverance to have risen to the top. But we have no record of the numbers of able persons who fall by the wayside, persons who, with enough encouragement and opportunity, might make great contributions.”
—Mary Barnett Gilson (1877–?)