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:
“It is not an exaggeration to say that play is as basic to your child’s total development as good food, cleanliness, and rest.”
—Joanne E. Oppenheim (20th century)
“Nowhere are our calculations more frequently upset than in war.”
—Titus Livius (Livy)
“The real grounds of difference upon important political questions no longer correspond with party lines.... Politics is no longer the topic of this country. Its important questions are settled... Great minds hereafter are to be employed on other matters.... Government no longer has its ancient importance.... The people’s progress, progress of every sort, no longer depends on government. But enough of politics. Henceforth I am out more than ever.”
—Rutherford Birchard Hayes (1822–1893)
“Think of the earth as a living organism that is being attacked by billions of bacteria whose numbers double every forty years. Either the host dies, or the virus dies, or both die.”
—Gore Vidal (b. 1925)