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 basic idea which runs right through modern history and modern liberalism is that the public has got to be marginalized. The general public are viewed as no more than ignorant and meddlesome outsiders, a bewildered herd.”
—Noam Chomsky (b. 1928)
“Nowhere are our calculations more frequently upset than in war.”
—Titus Livius (Livy)
“Constant revolutionizing of production ... distinguish the bourgeois epoch from all earlier ones. All fixed, fast-frozen relations, with their train of ancient and venerable prejudices are swept away, all new-formed ones become antiquated before they can ossify. All that is solid melts into air, all that is holy is profaned, and man is at last compelled to face with sober senses, his real conditions of life, and his relations with his kind.”
—Karl Marx (1818–1883)
“The principle of majority rule is the mildest form in which the force of numbers can be exercised. It is a pacific substitute for civil war in which the opposing armies are counted and the victory is awarded to the larger before any blood is shed. Except in the sacred tests of democracy and in the incantations of the orators, we hardly take the trouble to pretend that the rule of the majority is not at bottom a rule of force.”
—Walter Lippmann (1889–1974)