Re: [Phys-L] AC power calculations

[David Bowman <David_Bowman@georgetowncollege.edu>]

Regarding BC's questions:

> I don’t think they are across the 120 or 240, no?

Suppose a mains branch line is supplying power to multiple parallel impedance loads such that R_i is the resistance of the i-th load and X_i is the reactance of the i-th load.  (Here we take X_i to be positive if it is inductive.)  It is a straightforward exercise to show that the power factor on the upstream part of the line will have its power factor corrected to a purely resistive load if a capacitor is place directly across the main line whose capacitance is

C = (1/omega)*SUM_i {X_i/(R_i^2 + X_i^2)}, 

assuming that sum is actually positive, so the whole uncorrected load on the line is actually inductive to start with.

Personally I don't see any problem with placing a nonpolar (with appropriately rated breakdown voltage allowing for maximum spikes, and appropriately rated for high currents) capacitor across the line.  The whole point of the capacitor is for it to have large current flows so it can correct the phase of the current upstream on the line.

> Question:  will two electrolytics back to back work as a non-polarized cap?

No. That guarantees that both charging polarities will have one of the capacitors in backwards.

David Bowman