181021-1352 EDT
mbrooke:
I have no idea where over time, what classes, or self learning I came to some of my knowledge about power factor. One part of the process is clear. I grew up with Weston and Simpson meters. Before I new about electrodynamometer meters (Weston) I worked with Weston and Simpson DC meters with a rectifier for AC voltage. These rectifier meters were calibrated to read the RMS value of an AC sine wave. Whereas an electrodynamometer meter reads true RMS directly within its frequency capability, and works on both AC and DC with some trouble in the near zero frequency to possibly 20 Hz because of the mechanical averaging time constant. A hot wire meter also reads RMS directly and up into the MHz range.
Before about 1950 there were no electronic true RMS meters. True RMS requires multiplication.
RMS measurements relate to power in a resistive load. In the early 1950s we were doing signal detectability work, and this meant measuring power of a random gaussian signal (noise). Using an average reading meter (one using a simple full wave bridge, Simpson 260, or HP wider bandwidth) required a correction factor.
In the study of what RMS was and how to calculate its value from a waveform was another step. One does not need calculus to do an approximation, but it does require an understanding of what calculus is all about.
RMS is not mentioned much in DC circuit analysis, but it does apply. RMS starts to appear in AC circuit theory, physics, math, and calculus courses.
The concept of power factor appeared in the late 1800s with the advent of AC machines.
On an instantaneous basis p = v*i, and average power is the result of adding many small time increments of power over time, and then taking the average value. Calculus is nothing more than a means of taking infinity small increments and adding them together when you have an equation that defines the function. In general power at one instant of time (steady state) does not affect power at some other time (a scalar quantity), and therefore each separate increment of power can be added to others with simple addition.
When your load is not a pure resistance, then v = i*R may not hold true, and then v and i might not be well correlated. When this happens Vrms times Irms many not equal average power.
I believe power factor was originally defined in the 1800s as I defined it in an earlier post. In some ways power factor is a strange animal in the it may relate two uncorrelated values to some other value. In some circuits knowing the waveform of voltage does not allow you to know the waveform of current without detailed knowledge of the circuit. And detailed knowledge of the circuit may allow you to easily know the current and voltage relationship. A simple RL load is easy, but a bridge rectifier with capacitor input filter and a non-linear load can be difficult.
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