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)
“Now, since our condition accommodates things to itself, and transforms them according to itself, we no longer know things in their reality; for nothing comes to us that is not altered and falsified by our Senses. When the compass, the square, and the rule are untrue, all the calculations drawn from them, all the buildings erected by their measure, are of necessity also defective and out of plumb. The uncertainty of our senses renders uncertain everything that they produce.”
—Michel de Montaigne (1533–1592)
“A man’s real life is that accorded to him in the thoughts of other men by reason of respect or natural love.”
—Joseph Conrad (1857–1924)
“What culture lacks is the taste for anonymous, innumerable germination. Culture is smitten with counting and measuring; it feels out of place and uncomfortable with the innumerable; its efforts tend, on the contrary, to limit the numbers in all domains; it tries to count on its fingers.”
—Jean Dubuffet (1901–1985)