Like a vampire, you kill it and kill it, and it just keeps coming out of it's grave at the next full moon!
OK, here's the story, in very simple terms, that explains both the science and the silliness behind these magic widgets:
Let's start with AC theory. How is AC different from DC? Well, AC varies in voltage over time. Since the voltage varies, so does the current drawn by any load. That's the first brick in our wall of theory.
Remember, where you have electricity, you also have a magnetic field. And vice-versa. We make current flow, in fact, by moving a magnet past a wire. Hoe many magnets, how often, is what give AC it's particular 'frequency.' As a corillary to this, a second magnetic field near a circuit can be used to either impede ot assist the flow of current. That's brick #2.
So ... when you have a wire coiled tightly together, the magnetic field of one section of the wire affects the magnetic field of the section of wire next to it. When you have this wire in a nice tight coil, this interaction gives the overall magnetic field a 'spin,' since - remember, this is AC - the macnetic field changes over time, and it takes time for that change to move from one end of the wire to the other. Brick #3
A motor, transformer, ballast, relay, solenoid - in short, anything with a coil of wire in it - has this interacting magnetic field. This magnetic field, as well as the induced magnetic fields of any stators or secondary windings, act to impede the flow of current. Brick #4
Now ... how is this impedence different from simple resistance? Again, we're talking about AC. The equation for resistance (volts divided by amps) only works (using simple math) when you can measure the volts and the amps AT THE SAME TIME. The magnetic field interference has the effect -you can see this on an oscilliscope - of introducing a delay in the amp curve as compared to the volt curve. So, when you measure the volts and amps together, you are measuring the current drawn at a different time, different voltage than the voltage you're measuring at that instant.
The effect of this delay is that you are measuring more watts than you are actually using. The electric meter runs 'fast.' This is the mortar that holds the sales pitch together. This artificially high use is described by the term 'power factor.'
Now ... for the magic widget: Remember I told you you could either impede ot assist the magnetic field? Well, there's a component that does just that: the capacitor. A very, very eccentric man named Steinmetz figured this out - and also was able to use capacitors to counter the impedence of the coils. The 'power factor correcting capacitor' was born. (It's worth reading a bit about this guy).
OK, so the thing works. Why do I denounce it as a fraud? Two reasons.
First, they can only correct something that is created by coils of wires. Motors, fluorescent ballasts, transformers, etc. Very little of our household loads are able to introduce a power factor into our useage. They're correcting a problem that is negligible.
Second, most motors, ballasts, etc., already have power factor correcting capacitors built into them! You're paying for something you already have.
But, you say, isn't 'more' of a good thing 'better?' Remember the time relationship I mentioned? Too much correction, and you're again making the amp curve out of time with the volt curve - and thus, you're now getting high meter readings again.
Lastly .... there's a type of math that accounts for things that change over time. It's called 'calculus.' If you look at more involved forms of Ohm's law, you will find a calculus expression in there. If you use calculus, you calculations work again - even for AC